# Electrical Energy Systems (Power Applications of

```Electrical Energy Systems
(Power Applications of Electricity)
Summary of selected topics from University of Washington course EE 351: Energy Systems
taught Fall 2015 by Prof. Baosen Zhang (BXZ)
compiled by Michael C. McGoodwin (MCM). Content last updated 5/17/2016
Introduction ................................................................................................................................................. 2
Book chapters included in the course {and/or discussed in this summary} .................................... 3
History and Basic Science ............................................................................................................................ 4
Notable Persons in the History of Electricity ........................................................................................ 4
Voltage ............................................................................................................................................... 5
Current and Charge ............................................................................................................................ 5
Relating Voltage, Current, and Power .................................................................................................. 6
Resistance and Conductance, Resistance of a Wire (Pouillet's law) ....................................................... 6
Ohm’s Law (relating V, I, and R) and Power P ...................................................................................... 7
Voltage Divider Circuit Showing Voltage Drop from Line Resistance ..................................................... 8
Alternating Current Phases and Analysis ...................................................................................................... 9
AC Nomenclature and Symbols ..................................................................................................... 9
Alternating Current Waveform Equation ...................................................................................... 10
RMS AC Voltage V ...................................................................................................................... 10
Phasors, Complex Impedance, and Phase Shifts from Inductors and Capacitors ................................. 12
Phasors ...................................................................................................................................... 12
Resistors .................................................................................................................................... 12
Inductors.................................................................................................................................... 13
Capacitors .................................................................................................................................. 14
Complex Impedance .................................................................................................................... 16
Power ......................................................................................................................................... 17
Three-Phase Systems ........................................................................................................................ 18
Advantages of 3-phase over single-phase ..................................................................................... 19
Disadvantages of 3-phase over single-phase ................................................................................ 19
3-Phase Circuit Diagrams: .......................................................................................................... 20
3-phase Current ......................................................................................................................... 22
3-phase Power ............................................................................................................................ 22
Energy Resources and Overall Energy Utilization ........................................................................................ 23
Primary Energy Sources .............................................................................................................. 23
Conversion of Primary Sources to Secondary Energy Carriers ...................................................... 24
Utilization of Energy Resources in the US in 2014 ....................................................................... 26
Overall Electrical Generation in the US and World ....................................................................... 28
Overview of AC Electrical Generation, Transmission and Distribution ......................................................... 30
Hydroelectric Power Plants ......................................................................................................................... 30
Hydroelectric Power Plant (HE PP) Capacity and Production ......................................................... 31
Largest hydroelectric plants in the world (compared to selected US plants) ................................... 31
Terminology ................................................................................................................................ 32
Types of HE PPs.......................................................................................................................... 32
Categories of turbines and how they are selected ......................................................................... 35
Impulse Turbines (mostly Pelton) ................................................................................................ 35
Reaction Turbines....................................................................................................................... 37
Fossil Fuel Power Plants ............................................................................................................................. 40
Thermal (Thermodynamic) Cycle ................................................................................................. 41
Types of Turbines (aka “Prime Movers”) used in Thermal Power Plants ......................................... 45
Efficiency of Thermal Power Plants .............................................................................................. 48
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Nuclear Power Plants ................................................................................................................................. 52
Fuel ........................................................................................................................................... 53
Nuclear Power Plant Design ........................................................................................................ 57
Renewable Energy Resources ..................................................................................................................... 59
Electrical Transmission .............................................................................................................................. 59
US Electric Transmission Grid .................................................................................................... 59
Categories of Transmission Voltage ............................................................................................. 60
Transmission and Distribution Line Conductors .......................................................................... 60
Bundled High Voltage Conductors ............................................................................................... 61
Typical Double Circuit High Voltage Power Line Configuration and Power Transmitted ................. 61
Transmission Line Inductive Reactance ....................................................................................... 62
Power Electronics ....................................................................................................................................... 64
Diodes ........................................................................................................................................ 65
Bipolar Junction Transistors BJT ................................................................................................ 66
Silicon Controlled Rectifiers SCR ................................................................................................. 69
Transformers ............................................................................................................................................. 74
Electric Machines (Motors and Generators) ................................................................................................. 84
Motors .............................................................................................................................................. 84
Synchronous Generators .................................................................................................................. 94
Electrical Safety ......................................................................................................................................... 95
Human Electrical Shock Physiology............................................................................................. 95
Ground Resistance, Ground Potential, Ground Potential Rise, Touch and Step Potentials ............. 97
Home Electrical Safety .............................................................................................................. 100
Power Receptacles (Outlets, Sockets, and Female Connectors) and Plugs (Male Connectors) ....... 103
Preventing Shock Hazards in the Home ..................................................................................... 104
Power Quality .......................................................................................................................................... 109
Power Grid and Blackouts ........................................................................................................................ 112
Future Power Systems.............................................................................................................................. 114
Glossary and Mini-Topics ......................................................................................................................... 116
Introduction
Electrical Energy Systems is a large and very important subject—these systems permeate our advanced
civilizations and we would regress to the 17th Century without them. The subject matter is complex and hard
to set down into a document (especially circuit diagrams), and vita brevis, so as usual I have been quite
selective in what I have chosen to include here. My emphasis has been on topics that are/were:
 personally relevant and practical (such as household electrical configurations)
 interesting or not personally well understood in concepts or terminology (such as 3-phase systems)
 of current societal interest (such as renewable energy resources)
I merely audited this course, and it was the first engineering course ever attended (my major was Physics
many decades earlier). I therefore claim no expertise and assume that this summary contains errors,
including errors that, if implemented, might lead to a shock hazard! I create summaries like this mostly to
assist my own learning process broadly interpreted, to provide a convenient and semi-permanent record of
what I studied for future reference, and secondarily to help students and others wanting to explore these
topics.
I have included some copyrighted material in this not-for-profit personal study aid, hopefully falling within
fair usage and fully credited. Please observe prudence in what you copy from this summary, and by all
means go to the original sources which I have referenced. If you are an author who wishes to have removed
Suggestions and corrections would be graciously accepted. Send email to this address (reformatted):
MCM at McGoodwin period NET
The course syllabus includes the following:
Instructor: Baosen Zhang, [email protected]
Assistant professor
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TAs:
Graduate PhD from Berkeley in 2013
Research in Power systems, smart grids, cyberphysical systems with people in the loop
1) John J. Sealy, [email protected];
2) Daniel Olsen, [email protected]
Textbook: Electric Energy: An Introduction, 3rd Edition, by Mohamed A. El-Sharkawi, CRC Press 2013,
hereafter called EEAI3. This is an excellent textbook which I have enjoyed reading, and noteworthy in being
the work of a UW professor just retired. It could be fruitful reading for a variety of readers. I have found
many errors of a minor degree, and may provide a suggested errata.
Class Location: Room 037, Electrical Engineering Building (EEB)
Catalog Description: “Develops understanding of modern energy systems through theory and analysis of the
system and its components. Discussions of generation, transmission, and utilization are complemented by
environmental and energy resources topics as well as electromechanical conversion, power electronics,
electric safety, renewable energy, and electricity blackouts.”
More Detailed Description: In this class we will cover the following:





History of power systems
Basics components of power systems: Generation, transmission and distribution of electricity
Renewable energy: Mainly on wind and solar, and how they are different from “conventional energy”
Electric machines and safety
After not changing much for decades, why is energy system suddenly a “hot” topic again: e.g., what is
a smart grid?
Labs:
Three Labs (First lab starting Oct 26th, Orientation Oct 19th). “There is a policy that only students
who are taking it for a grade can do the labs.” I did not attend these labs.
Instructional Lab is managed by Bill Lynes.
Course Website including Syllabus:
Resources for Electrical Engineering
Electrical Engineering
Get research recommendations and tips tailored to your subject area via this online guide.
Citation Styles & Tools
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Engineering Library
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computer science.
Electronic Schematic Creation:


Scheme-It
Free. Many symbols. Prepares bill of materials (BOM) PRN. Many objects cannot be labeled flexibly.
1
Electronic Schematic Creation & Calculations: Circuit-Lab
Cannot add subscripts to labels; drawing arrows for voltage labeling clumsy; clunky; Requires student
registration for specific EE course etc., otherwise costs.
Documentation
Book chapters included in the course {and/or discussed in this summary}
Bold = substantial course coverage by instructor
Parentheses indicate coverage by MCM
Chap 1: History of Power Systems {MCM selections completed}
Chap 2: Basic Components of Power Systems {MCM selections completed}
Chap 3: Energy Resources {MCM selections completed}
1
Students at UW are eligible for CircuitLab Student Edition.
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Chap
Chap
Chap
Chap
Chap
Chap
Chap
Chap
Chap
Chap
Chap
Chap
4: Power Plants {MCM selections completed}
5: Environmental Impact of Power Plants {MCM selections completed}
6: Renewable Energy [Solar, Wind, Geothermal, Biomass, Hydrokinetic] {Omitted}
7: Alternating Current Circuits {MCM selections completed}
8: Three-Phase Systems {MCM selections completed}
9: Electric Safety {MCM selections completed}
10: Power Electronics {MCM selections completed}
11: Transformers {MCM selections completed}
12: Electric Machines {MCM selections completed}
13: Power Quality {Not studied in this 300 level class, MCM selections completed}
14: Power Grid and Blackouts {Briefly discussed in class, MCM selections completed}
15: Future Power Systems {Not studied in class, MCM selections completed}
History and Basic Science
Notable Persons in the History of Electricity
This section derives in part from chapter 1.
Thales of Miletus (600 BCE): static electricity from amber (ἤλεκτρον =elektron) when rubbed by fur
William Gilbert (24 May 1544 – 30 November 1603), book De Magnete (1600), originated “electricity”, father
of electricity & magnetism.
Alessandro Giuseppe Antonio Anastasio Volta (18 February 1745 – 5 March 1827): Voltaic pile. Volt is the
SI unit of electric potential.
Hans Christian Ørsted (14 August 1777 – 9 March 1851): discovered that electric currents create magnetic
fields, deflecting a compass needle. Oersted is the CGS unit of the magnetic field strength (auxiliary magnetic
field H).
André-Marie Ampère (20 January 1775 – 10 June 1836): French physicist and mathematician who was one
of the founders of the science of classical electromagnetism, which he referred to as "electrodynamics".
Ampere’s Law. Ampere is the SI unit of current.
Georg Simon Ohm (16 March 1789 – 6 July 1854): German physicist and mathematician. Ohm found that
there is a direct proportionality between the potential difference (voltage) applied across a conductor and the
resultant electric current. This relationship is known as Ohm's law. The ohm is the SI unit of electrical
resistance.
Michael Faraday (22 September 1791 – 25 August 1867), English scientist who contributed to the fields of
electromagnetism and electrochemistry. His main discoveries include those of electromagnetic induction,
diamagnetism and electrolysis. Built a device that became the basis for the AC motor. His work inspired
James Clerk Maxwell. The derived SI unit of capacitance is the farad.
James Clerk Maxwell (13 June 1831 – 5 November 1879): Scottish scientist in the field of mathematical
physics. His most notable achievement was to formulate the classical theory of electromagnetic radiation,
bringing together for the first time electricity, magnetism, and light as manifestations of the same
phenomenon. Maxwell's equations for electromagnetism have been called the "second great unification in
physics" after the first one realized by Isaac Newton.
With the publication of A Dynamical Theory of the Electromagnetic Field in 1865, Maxwell demonstrated that
electric and magnetic fields travel through space as waves moving at the speed of light.
Hippolyte Pixii (1808–1835) , instrument maker from Paris. In 1832 he built an early form of alternating
current electrical generator, based on the principle of magnetic induction discovered by Michael Faraday.
Pixii's device was a spinning magnet, operated by a hand crank, where the North and South poles passed over
a coil with an iron core. ... introducing a commutator, which produced a pulsating direct current.
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Antonio Pacinotti (17 June 1841 – 24 March 1912) was an Italian physicist, improved DC generator
(dynamo) and invented transformer with 2 sets of windings about common core. AC in one winding induced
AC in the other.
John Ambrose Fleming (1849–1945), English electrical engineer and inventor of the Fleming Valve
(thermionic vacuum tube diode). Stated Fleming’s left hand rule: When current flows in a wire, and an
external magnetic field is applied across that flow, the wire experiences a force perpendicular both to that field
and to the direction of the current flow. A left hand can be held ... so as to represent three mutually
orthogonal axes on the thumb (thrust), first finger (magnetic field) and middle finger (current). The right and
left hand are used for generators and motors, respectively.
Lee de Forest (August 26, 1873 – June 30, 1961)American inventor, self-described "Father of Radio", and a
pioneer in the development of sound-on-film recording used for motion pictures. His most famous invention,
in 1906, was the three-element "grid Audion", which, although he had only a limited understanding of how it
worked, provided the foundation for the development of vacuum tube technology.
Julius Edgar Lilienfeld (April 18, 1882 – August 28, 1963), Austro-Hungarian-born American physicist and
electronic engineer. Lilienfeld is credited with the first patents on the field-effect transistor (1925) and
electrolytic capacitor (1931).
Thomas Alva Edison (February 11, 1847 – October 18, 1931): Light bulb, carbon microphone, DC power
plant and distribution, sound recording, motion pictures, fluoroscope, etc.
Nikola Tesla (10 July 1856 – 7 January 1943) Serbian American inventor, electrical engineer, mechanical
engineer, physicist, and futurist best known for his contributions to the design of the modern alternating
current (AC) electricity supply system. Battle of AC vs. DC with Edison. The tesla is the derived SI unit of
magnetic field.
Voltage
“Voltage is a measure of electric potential, ... a type of potential energy, and refers to the energy that could be
released if electric current is allowed to flow... One volt is defined as the difference in electric potential
between two points of a conducting wire when an electric current of one ampere dissipates one watt of power
between those points. It is also equal to the potential difference between two parallel, infinite planes spaced 1
meter apart that create an electric field of 1 newton per coulomb. Additionally, it is the potential difference
between two points that will impart one joule of energy per coulomb of charge that passes [between the two
points]. Voltage can be expressed in terms of SI base units (m, kg, s, and amperes A) as
“Voltage for alternating current almost never refers to the voltage at a particular instant, but instead is the
root mean square (RMS) voltage... In most cases, the fact that a voltage is an RMS voltage is not explicitly
2
stated, but assumed.
Voltages vary from a few mV in nerve conduction and ECGs to > 1 GV in lightning
3
arising from positively charged cloud tops.
Current and Charge
Ampère's force law states that there is an attractive or repulsive force between two
parallel wires which each carry an electric current. This force is used in the formal
4
definition of the ampere.” The ampere is “the basic unit of electrical current in the
2
3
4
Quoted and paraphrased from https://en.wikipedia.org/wiki/Volt including diagram
https://en.wikipedia.org/wiki/Lightning#Positive_and_negative_lightning and
http://www.srh.noaa.gov/jetstream//lightning/positive.htm
https://en.wikipedia.org/wiki/Ampere incl. diagram and paraphrased text
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International System of Units (SI), equivalent to one coulomb per second, formally defined to be the constant
current [i.e., equal in amount and direction] which if maintained in two straight parallel conductors of infinite
length, of negligible circular cross section, and placed one meter apart in vacuum, would produce between
5
these conductors a force equal to 2 × 10−7newton per meter of length.”
The SI unit of charge, the coulomb, is “equal to the quantity of charge transferred in one second across a
6
conductor in which there is a constant current of one ampere.” In general, charge Q is determined by steady
current I flowing for a time t, specifically Q = I·t.
One coulomb (of positive charge) ≈ 6.241509•1018•(charge of proton)
One negative coulomb (i.e., of negative charge) ≈ 6.241509•1018•(charge of electron).
It may also be said that one coulomb is ≈ the magnitude (absolute value) of electrical charge in 6.241509•1018
7
protons or electrons.
Relating Voltage, Current, and Power 8
For DC power:
where
P =VI
P = power consumed by a load (in watts, where 1 W = 1 joule/sec = 1 kg m2 s-3).
W (often after a number) is the abbreviation for watts of power
V = Voltage across a load (volts, where 1 V = 1 kg·m2·s−3·A−1).
V in upper case is used (often after a number) as the abbreviation for volts
I = Current (amperes).
A (often after a number) is the abbreviation for amperes of current
In the textbook EEAI3, P V I represent rms magnitude values for AC and p v i represent instantaneous values.
For AC Power, the formula applies for instantaneous p, v, and i (with complications to follow).
Resistance and Conductance, Resistance of a Wire (Pouillet's law)
Resistance is expressed in ohms and is in many cases approximately constant within a certain range of
9
voltages, temperatures, and other parameters. The units of resistance may be expressed as
where A = amperes, C = coulombs, F = farads, J = joules, s = seconds, S = Siemens, V = volts, W = watts
Resistance of a wire (or other uniform homogeneous conductors with uniform cross section) is given by
Pouillet's law:
where
5
6
7
8
9
R 𝑤𝑤𝑤𝑤 = ρ
l
A
Rwire = Resistance of wire or conductor (Ω ohms)
ρ=
Resistivity of the wire or conductor material (Ω-m)
l=
Length of wire or conductor (m)
A=
Wire or conductor uniform cross sectional area (m2)
http://dictionary.reference.com/browse/ampere
http://dictionary.reference.com/browse/coulomb?s=t
https://en.wikipedia.org/wiki/Coulomb
Course lecture 1.pptx
https://en.wikipedia.org/wiki/Ohm including diagram and some paraphrases text.
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A cube with faces of 1m and with resistance of 1Ω across opposite face sheet contacts has resistivity ρ = 1
ohm-m.
Electrical conductivity σ = 1/ρ (expressed in SI as siemens / m (S/m) where S = Ω-1 = I/V
Selected resistivities at 20 ºC:
10
Substance
Resistivity ρ (ohm-m)
C (Graphene)
1.00×10−8
Cu Copper
1.68×10−8
Ag Silver
1.49×10−8
Au Gold
2.44×10−8
Al Aluminum
2.82×10−8
W Tungsten
5.60×10−8
Steel, Carbon (1010)
1.43×10−7
Steel, Stainless
18% Cr/ 8% Ni austenitic
6.90×10−7
Carbon, Amorphous
5.00×10−4 to 8.00×10−4
Water, Sea
2.00×10−1
Water, Drinking
2.00×101 to 2.00×103
Air
1.30×1016 to 3.30×1016
Ohm’s Law (relating V, I, and R) and Power P
Ohm’s law (and its variations) relates V, I, and R. We add here the definition of Power P = V I, and the
11
resulting relationships among P, V, I, and R.
Current is proportional to V and inversely proportional to R, specifically I = V/R
where
I = Current (amperes)
V = Voltage (volts)
R = Resistance (ohms)
In the following VIRP wheel, power consumed by a static resistance is also shown.
10
https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
https://commons.wikimedia.org/wiki/File:Ohm's_Law_Pie_chart.svg , diagram slightly modified MCM,
instantaneous quantities
11
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Voltage Divider Circuit Showing Voltage Drop from Line Resistance 12
In the following circuit having only static resistances, the current I passes thru the wire resistance and the
12
ibid.
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Thus, the greater the wire resistance, the lower the current and the voltage attained across the load.
Alternating Current Phases and Analysis
Material in this AC section derives in part from chapter 1, chapter 2, and chapter 7.
AC Nomenclature and Symbols
Nomenclature and symbols used by the textbook
13
Note that instantaneous quantities i and v are expressed in lower case, non-RMS averages and max values
are spelled out, RMS magnitudes of I and V and magnitude of Z are shown as unadorned upper case, and
� and Complex quantities S� and Z� are written with a bar over the upper case letter (and have
Phasors I̅ and V
rms values in magnitude). V in upper case is also used (after a number) as the abbreviation for volts, A (after
a number) is the abbreviation for amperes of current, and W (after a number) is the abbreviation for watts of
power. Average voltage is typically 0 for symmetrical sine wave AC.
13
EEAI3 p. 213
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Alternating Current Waveform Equation
where
v = Vmax sin ωt
v = instantaneous voltage
ω = angular frequency where ω = 2πf = 2π/T
f = waveform frequency = ω/2π = 1/T
T = waveform period = 1/f = 2π/ω
(Volts)
(Hz or s-1)
(s)
For most US power calculations, ω = 2πf = 2π*60 ≈ 376.991 radians/s ≈ 377 radians/s. Note that ωt has
units of radians (or is sometimes expressed in degrees)
RMS AC Voltage V
This is given by the sqrt of 1/T times the integral of the square of the instantaneous voltage v over a complete
period of duration T. The RMS may be calculated for any periodic waveform that is defined mathematically.
14
The derivation for periodic sinusoidal waveforms may be given as follows:
14
http://www.raeng.org.uk/publications/other/8-rms
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Note: In this derivation taken from the web, if one instead simply integrated over exactly one period T, the
integral of the cos 2ωt term would be over exactly 2 periods and thus would be zero, yielding the same final
result.
All AC voltages in US household and industrial power circuits and equipment, unless otherwise stated, are
15
expressed in rms values. Thus, nominal 120 V is 120 V rms, so Vmax = 120√2 = 169.7 volts. Voltages at wall
socket active single plugs varies from +170 to -170 V relative to ground potential.
Vmax values tend to vary somewhat due to transients, varying loads, and harmonics, more so than V (i.e.,
Vrms). It follows that Vrms = Vmax /√2.
US AC frequencies are 60 Hz, Europe and other countries are often 50 Hz.
15
EEAI3 p. 214-215
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Phasors, Complex Impedance, and Phase Shifts from Inductors and Capacitors
Phasors
A phasor [from “phase vector”] is a graphical representation which depicts the magnitude and phase shift of
an AC waveform while hiding the instantaneous location within the cycle represented by the sine or cosine ωt
� = A∠θ, where A is the magnitude and θ is the angle with
term. They are represented in angle notation by A
respect to the reference (positive for leading, negative for lagging). These may be converted to complex
numbers to analyze how phasors for R, C, and L add, subtract, multiply, etc.
Phasor complex arithmetic is done as follows (where θ1 is the phase angle for A, etc.):
� = A∠(θ1 ) = A[cosθ1 + j sinθ1 ]=X+jY
A
Multiplication:
where j = √−1, and X and Y are real and imaginary components, resp.
(the traditional math symbol i=√-1 is not used in EE to avoid confusion with current)
Division:
Subtraction
Complex conjugate:
Inverting a phasor:
� �B = AB∠(θ1 + θ2 )
A
A
�
�
B
A∠θ
= B∠θ1 =
2
A
B
∠(θ1 − θ2 )
� = A[cosθ1 + j sinθ1 ] + B[cosθ2 + j sinθ2 ]
𝐴̅ + B
= (Acosθ1 + Bcosθ2 ) + j (Asinθ1 + Bsinθ2 )]
� = A[cosθ1 + j sinθ1 ] − B[cosθ2 + j sinθ2 ]
𝐴̅ − B
= (Acosθ1 − Bcosθ2 ) + j (Asinθ1 − Bsinθ2 )]
if A = X + jY: A⋆ = X − jY
1
�
A
X
Y
= X2 +Y2 − j X2 +Y2
A phasor diagram according to our textbook shows the voltage as a reference along the traditional horizontal
x-axis, with length proportional to rms value. (Judging by the diagrams below, placing voltage on the x-axis is
not a universal convention.) By convention, the direction of rotation in time is counterclockwise, so a lag
such as a current lag is shown as a current arrow rotated in the clockwise direction relative to the reference
16
quantity (here voltage), and a current lead is shown as a counterclockwise current arrow rotation. For either
case, the range of lag or leading angles is by convention 0 ≤ i ≤ 180º. (A lag of more than 180 degrees would
more likely be described as a lead of less than 180 degrees).
Resistors
For a pure resistive (Ohmic) element with resistance R (ohms Ω), the instantaneous voltage across and
current through the resistor (v and iR) are:
v = Vmax sin ωt = iR R
V
iR = max�R sin ωt
17
Phase and Phasor diagram are shown below (where Im = Imax).
This resistance does not cause a phase shift
and instantaneous iR is in phase with v. The phasor shows I and V pointing in the same direction. (These
diagrams from the web use V and I for instantaneous values.)
16
17
EEAI3 p. 218 etc.
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Inductors
“The henry (symbol H) [plural henries per NIST] is the unit of electrical inductance in the International System
of Units. The unit is named after Joseph Henry (1797–1878), the American scientist who discovered
electromagnetic induction... The units may be expressed as
where A = amperes, C = coulombs, F = farads, H = Henries, J = joules, s = seconds, S = Siemens, T = teslas
18
(magnetic flux density or magnetic field strength), V = volts, W = watts, Wb = webers (magnetic flux).
The magnetic permeability [μ0] of a classical vacuum is defined as exactly 4π×10−7 N/A2 or H m-1 (henry per
19
metre).
Inductance is often symbolized as L. For a pure inductive element or load (with no resistance or capacitance)
having inductance L (in henries H), the instantaneous v across the inductor and instantaneous i through it
are:
dI
v = Vmax sin ωt = L dt𝐿
V
V
iL = − max�ωL cos ωt = − max�X cos ωt
L
The quantity XL ≡ ωt is the magnitude of the inductive reactance of the inductor.
This inductor causes a phase shift and iL is not in phase with v. Rather, iL lags the voltage by 90º (or
equivalently v leads iL by 90º).
18
19
https://en.wikipedia.org/wiki/Henry_%28unit%29 including diagram and paraphrased text.
https://en.wikipedia.org/wiki/Vacuum_permeability
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The phasor diagram above shows I lagging V by 90 degrees (again, lag is in the counterclockwise direction).
The inductor resists the buildup of current in response to an applied voltage, thus a time delay exists before
current reaches a maximum. “According to Lenz's law the direction of induced e.m.f [electromotive force] is
always such that it opposes the change in current that created [the e.m.f.] As a result, inductors always
20
oppose a change in current, in the same way that a flywheel oppose a change in rotational velocity.”
Inductive reactance is an opposition to the change of current through an element.
“Because inductors store the kinetic energy of moving electrons in the form of a magnetic field,
they behave quite differently than resistors (which simply dissipate energy in the form of heat)
in a circuit. Energy storage in an inductor is a function of the amount of current through it...
Inductors react against changes in current by dropping voltage in the polarity necessary to
oppose the change. When an inductor is faced with an increasing current, it acts as a load:
dropping voltage as it absorbs energy (negative on the current entry side and positive on the
current exit side, like a resistor). When an inductor is faced with a decreasing current, it acts
as a source: creating voltage as it releases stored energy (positive on the current entry side and
negative on the current exit side, like a battery). The ability of an inductor to store energy in
the form of a magnetic field (and consequently to oppose changes in current) is called
21
inductance.”
Capacitors
One farad is defined as the capacitance of a capacitor across which, when charged with one coulomb of
electricity, there is a potential difference of one volt. Conversely, it is the capacitance which, when charged to
a potential difference of one volt, carries a charge of one coulomb. The units of capacitance are given by
20
21
https://en.wikipedia.org/wiki/Inductor
diagrams slightly modified by MCM
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where A = amperes, C = coulombs, F = farads, H = Henries, J = joules, s = seconds, S = Siemens, V = volts,
22
W = watts.
Capacitance is often symbolized as C.
For a purely capacitive element or load (with no resistance or inductance) having capacitance C (in farads F),
the instantaneous v across the capacitor and i into it are:
v = Vmax sin ωt =
Integrating,
dv
i = C dt
1
C
∫ iC dt
iC = ω C Vmax cos ωt =
Vmax
�X cos ωt
C
The quantity XC ≡ 1/ωt is the magnitude of the capacitive reactance of the capacitor. Capacitive reactance
is an opposition to the change of voltage across an element.
This capacitor causes a phase shift and iC is not in phase with v. Rather, iC leads the voltage by 90º (or
equivalently v lags iC by 90º). The current must flow in before voltage is built up across the capacitor plates.
The phasor diagram shows I lagging V by 90 degrees (again, lag is in the counterclockwise direction).
“When the voltage across a capacitor is increased, it draws current from the rest of the circuit,
acting as a power load. In this condition the capacitor is said to be charging, because there is
an increasing amount of energy being stored in its electric field. Note the direction of electron
current with regard to the voltage polarity [in the diagram to follow]. Conversely, when the
voltage across a capacitor is decreased, the capacitor supplies current to the rest of the circuit,
acting as a power source. In this condition the capacitor is said to be discharging. Its store of
energy—held in the electric field—is decreasing now as energy is released to the rest of the
23
circuit. Note the direction of electron current with regard to the voltage polarity.”
22
23
https://en.wikipedia.org/wiki/Farad including diagram and paraphrased text
diagrams slightly modified by MCM
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Complex Impedance
Total Reactance
�
X = ���
XL + ���
XC = XL ∠ + 90° + XC ∠ − 90° = j(XL − XC ) in phasor & complex notation, resp.
The magnitude of Total Reactance X = ωL - 1/ωC.
XL , and
where XL ≡ ωt is the magnitude of the inductive reactance ���
XC
XC ≡ 1/ωt is the magnitude of the capacitive reactance ���
These are all expressed as ohms. Magnitudes XL and XC are both positive scalar quantities by convention, but
the minus sign in the right part of the formula for total magnitude arises from the negative (lagging) phasor
angle for X C ∠ − 90°. When magnitude X is positive, the total reactance is said to be inductive; when X is
negative, the total reactance is said to be capacitive.
Total impedance in ohms Ω for elements arranged in series (computed by addition of phasors) is
�L + X
�C
Z� = R + X
Z� = R∠0° + XL ∠ + 90° + XC ∠ − 90° = R + j(XL − XC ) in phasor and complex notation, resp.
where XL ≡ ωt is the magnitude of the inductive reactance ���
XL
XC ≡ 1/ωt is the magnitude of the capacitive reactance
���
XC .
Total impedance for elements arranged in parallel (computed by addition of inverted phasors) is
1
�
Z
1
1
1
= R + X� + X�
L
C
Resonant Frequency: by adjusting ω until XL = XC, the total impedance is equal to the load resistance alone,
24
and the resulting frequency f0 is called the resonant frequency:
f0 = 1�2πLC
Alternatively, the following quantities may be defined and used:
Conductance
1
G = R (mhos = siemens. Note that G and R are real numbers)
Inductive Susceptance
���L = 1 (mhos = siemens)
B
����
X
Capacitive Susceptance
24
25
EEAI3 p. 225
EEAI3 p. 226
Page 16 of 116
25
L
�B��C� = 1 (mhos = siemens)
����
X
C
�
���L + �B��C� = G + j(BC-BL) (mhos = siemens)
Y=G+B
!EnergySystems_EE351_MCM_Fall2015.docx
17 May 2016
Power
For sinusoidal waveforms, instantaneous power ρ = vi = VI [cos(θ) - cos(2ωt-θ)]
where θ is the impedance phase angle.
For a purely resistive load, θ=0 and ρ = vi = VI [1 - cos(2ωt-θ)], which is always positive
For a purely inductive load, θ=90 degrees. ρ = -VI [sin(2ωt)], which oscillates symmetrically between positive
and negative values. The inductor consumes power as the voltage rises in the first 1/4 of the cycle, and
returns power back in the 2nd 1/4 of the cycle, etc. On the average, the pure inductor does not consume any
energy—it is “wattless”.
For a purely capacitive load, θ=-90 degrees. ρ = VI [sin(2ωt)], which oscillates symmetrically between positive
and negative values. The capacitor returns power as the voltage rises in the first 1/4 of the cycle, and returns
power back in the 2nd 1/4 of the cycle, etc. On the average, the pure capacitor does not consume any
XL + �
XC , the phase angle is not 0 and the average
energy. For loads that combine various amounts of R + �
26
sum of instantaneous power is non-zero.
The power that produces energy is the called active power or real power, expressed in watts W, and given by
P = VI cos(θ), where θ = overall phase angle. When θ=0, P is simply VI watts (where V and I are both rms,
approximately 0.707·Vmax and 0.707·Imax, respectively).
In contrast, the power that consumes or produces no net energy over multiple cycles is called reactive power
or imaginary power. It is defined as Q ≡ V·I sin θ, and expressed in Voltampere reactive VAr, kilovoltampere
reactive kVAr, etc. θ = overall phase angle.
For an inductive load plus a resistance, inductive reactive power QL = I2XL, the current lags the voltage by θ,
and the inductive reactive power leads the real power by 90º.
For a capacitive load plus a resistance, capacitive reactive power QC = I2XC, the current leads the voltage by θ,
and the capacitive reactive power lags the real power by 90º.
�≡V
� ⋅ I̅∗ = P + jQ = P + j(QL − QC ), expressed as voltampere
Complex power phasor (aka apparent power) S
VA, kVA, etc. With this notation, the magnitudes of reactive power QL of an inductor and QC of a capacitor are
both positive but because of the phase angles, that of the capacitor appears with a minus sign as discussed
above.
Power Factor pf
=
P
S
=
R
Z
= cos(θ) may be lagging or leading depending on the angle of I wrt V: When I leads
V, the pf is leading. Reactive power does not do work (thus it does not generate revenues to the utility), and
its presence can cause problems:
It increased losses in the transmission line (due to increased current with I2R losses),
It reduces spare capacity of the line (due to increased current), and
It reduces the voltage across the load.
VS
2
� Rwire 2
X
��
� + �1 + wire �
XL
XL
The load voltage falls when XL decreases (more reactive load is added). Only with infinite XL=∞ (no reactive
27
Power factor correction may be introduced into transmission and distribution lines and other circuits in the
form of added parallel capacitance across the load, in order to reduce the power factor angle and offset the
28
inductive reactance present.
26
27
28
EEAI3 p. 228-230
EEAI3 p. 233-236
EEAI3 p. 238-240
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𝜏
Energy Consumed: This is simply 𝐸 = ∫0 𝑃𝑃𝑃 where P is instantaneous real power (i.e., adjusted for power
factor) and τ is the time interval of interest. For discrete power levels, the sum rather than the integral
29
applies.
Three-Phase Systems
(This is a complex subject and I have provided only limited discussion, partly derived from chapter 8.) These
systems are common in electrical generation, transmission, transformers, and industrial and commercial
applications (including manufacturing, hospitals, and farming). 3-Phase current is generated in generators
typically with 3 coils in the stator, each providing a phase of voltage as the magnetized rotor spins within.
The 3 phases generated are “balanced” if the waveform is sinusoidal, the magnitudes of the rms voltages of
30
the phases are equal, and the phases are separated by 120º.
In 3-phase power generation, 3 phases of voltage
are generated with phases 120º apart. In feeding a
balanced and linear load, the sum of the
instantaneous currents of the three conductors is
zero. The current in each conductor is equal in
magnitude to, but with the opposite sign of, the
sum of the currents in the other two. The return
path for the current in any phase conductor is the
31
other two phase conductors.
A Wye connected generator provides 3 lines plus a
Neutral conductor. A Delta connected generator
32
provides 3 lines and has no Neutral conductor.
The magnitude of line to line (phase to phase)
33
voltage VLL is VL-N·√3.
The phase voltages are all equal in rms magnitude V but
only differ in their phase angle. The three windings of
the coils are connected together at points, a1, b1 and c1
to produce a common neutral connection for the three
individual phases. Then if the red phase is taken as the
reference phase, each individual phase voltage can be
34
defined with respect to the common neutral.
In phasor notation relative to a2 (and with positive
angles in clockwise direction), the phases are
V ∠ 0°
Phase a2 (Red or Phase 1, va2a1)
V ∠ +120°
Phase b2 (Blue or Phase 2, vb2b1)
V ∠ –120°
Phase c2 (Yellow or Phase 3, vc2c1)
In 3-phase power transmission, the 3 phases of the wye or delta source are connected to 3 (often bundled)
conductors which transmit the power over distance, with the neutral of the generator [for Wye generators]
35
connected to ground (Earth).
29
30
31
32
33
34
35
EEAI3 p. 242-4
EEAI3 p. 252
https://en.wikipedia.org/wiki/Three-phase_electric_power including diagram
EEAI3 p. 250
EEAI3 p. 254
http://diodetech.blogspot.com/2013/07/phasor-diagram.html Text paraphrased plus diagram
EEAI3 p. 252,
also http://electronics.stackexchange.com/questions/124817/why-are-there-only-3-wires-on-this-power-line
Page 18 of 116
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In some cases, the source of power might be a balanced wye yet the load is in a balanced delta
36
configuration.











“Three phase power transmission has become the standard for power distribution. Three phase
power generation and distribution is advantageous over single phase power distribution [because they
transmit 3 times the power as single-phase lines].
Three phase power distribution requires lesser amounts of copper or aluminium for transferring the
same amount of power as compared to single phase power
The size of a three phase motor is smaller than that of a single phase motor of the same rating.
[Motors of higher HP are available with 3-phase.]
Three phase motors are self-starting as they can produce a rotating magnetic field [a very important
advantage]. The single phase motor requires a special starting winding as it produces only a pulsating
magnetic field. [3-phase motors do not spark on startup.]
In single phase motors, the power transferred in motors is a function of the instantaneous current
which is constantly varying. Hence, single phase motors are more prone to vibrations. In three phase
motors, however, the power transferred is uniform throughout the cycle and hence [motor] vibrations
are greatly reduced.
The ripple factor of rectified DC produced from three phase power is less than the DC produced from
single phase supply. [Thus, with 6 peaks per cycle rather than 2 peaks, 3-phase is a steadier source
of power.]
Three phase motors have better power factor regulation.
Three phase generators are smaller in size than single phase generators as winding phase can be more
efficiently used. [Equivalently, a 3-phase
generator generates more power than a single-phase
37
generator occupying the same volume.]”
Both 3-phase and single phase equipment can be powered from a 3-phase supply, but not the
opposite.
The total three-phase power supplied to a balanced three-phase circuit remains constant.
3-phase
power is more reliable: when one phase is lost, the other two phases can still deliver some
38
power.


39
Electrical supply, control, and end-devices are often more complex
and expensive. [However, costs
40
for motors and for installation of equipment are often lower.] Three transformers are needed for
voltage conversion for Wye 3-phase. Although only two are needed for delta 3-phase, but you cannot
41
obtain as much power from a given size transformer as you can with the delta connection.
Failure of a 3-phase transformer is full failure. In contrast, when single single-phase transformers are
used to convert 3-phase power, failure of one of the single-phase transformers leaves 2 single-phase
42
transformers still operational.
36
EEAI3 p. 63
http://www.electrotechnik.net/2010/11/advantages-of-three-phase-power-over.html , also EEAI3 p. 247
38
EEAI3 p. 247
39
http://electrical-engineering-portal.com/single-phase-power-vs-three-phase-power
40
41
https://fairfld61.files.wordpress.com/2010/07/amta4-5-comparing-single-phase-and-three-phasesystems.ppt
42
37
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3-Phase Circuit Diagrams:
The following show in schematic form the generation and delivery to loads of 3-phase power in both Wye (“Y”
43
or “star”) and Delta load configurations:
The following diagrams from another source show voltages across line to line and line to neutral for
44
representative single phase and 3-phase Wye load (4- and 5-wire) and Delta load configurations:
Single phase 120V “house current” with safety
enhancing neutral to Earth Ground connection
(dotted line). 120 volt AC Voltage “Vac L-N” is “Line
to Neutral” (aka “Phase to neutral”, here Phase A to
Neutral). “Neutral is a circuit conductor that
normally carries current, and is connected to ground
45
(earth) at the main electrical panel.”
Single phase 120/240V “house current” or “split
phase”. This configuration has 2 voltage hot “lines”
(Phase A and Phase B here) that have phase 180º
apart. Safety enhancing neutral to ground
connection (dotted line) also shown. 120V is
available from Phase A or B to Neutral and 240 volt
AC Voltage “Vac L-L” is “Line to Line” (aka “Phase to
Phase voltage”, here Phase A to Phase B).
43
https://en.wikipedia.org/wiki/Three-phase_electric_power
Ametek Programmable Power, www.programmablepower.com/support/FAQs/DF_AC_Distribution.pdf , all
images slightly modified MCM, text paraphrased
45
https://en.wikipedia.org/wiki/Ground_and_neutral
44
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3-phase 4-wire Wye (i.e., having Y-shaped loads and
phases): This load configuration has 3 “current
carriers” (aka “lines” or “phases”) which are 120º
apart in phase. The fourth conductor is the “neutral”
wire, which carries little or no current if the 3 phases
are balanced (matched) in load. This 208Y/120 (aka
120/208Vac or 208Y/120 Wye ) configuration is
common in the US. The 208 L-L rms voltage value
(voltage across any 2 “lines”) derives from
VL-N·√3=120√3. There is no Earth Ground here.
The 240V Split Phase Delta (aka dog leg or
stinger leg) is one of several possible Delta load
configurations (named for the delta or triangular
shape of the loads and phases). Delta
configurations are less common than Wye.
There is no Neutral. One load is center tapped
to provide two phases with 120Vac and a High
Leg which provides 208Vac in addition to 240
Vac.
46
Same but showing a 5th wire, the Earth Ground,
which is usually connected to neutral at the main
electrical (circuit breaker) panel. This is the usual
Wye load configuration in the US.
Computation of balanced 3-phase line-to-line
46
voltage VL-L in terms of phase voltage VL-N:
VL−L = √3 × VL−N
The line-to-line voltage—for example VA-B for
transmission lines—leads the phase voltage VA
by 30º. (Note the order of subscripts).
http://electronics.stackexchange.com/questions/92678/three-phase-power-supply-what-is-line-to-line-voltage
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3-phase Current
represents a group of houses such that the resultant impedances are approximately equal.) The load
� are associated with a impedance (phase shift) angle φ that is the same for each load. For a
impedances Z
given line or phase (a), the current with respect to the phase voltage is given by:
Ia̅ =
� an
V
�an
Z
=
� an
V
�
Z
=
� ph ∠θ
V
Z∠φ
=
Vph
Z
∠(θ − φ)
where Vph is the rms voltage of phase a. Thus, the phase current lags or leads the voltage by φ. The other
phase currents are separated by 120º in phase. Line currents are equal to the corresponding currents of the
loads. All 3 phase currents are equal in magnitude. By Kirchoff’s current rule, the sum of the phasors of the
phase currents is 0:
In̅ = Ia̅ + Ib̅ + Ic̅ = 0
Thus, for Wye systems, the neutral conductor carries 0 current. The neutrals at the source and loads can be
47
connected to local earth grounds.
Delta: For Delta connected loads, the line-to-line currents are given by:
̅ = Ia̅ + Ica
̅ etc.
Iab
In balanced systems, the loads are equal and the line-to-line voltages are equal, so the load current are also
48
equal.
It is possible to have mixed circuits—such as a Delta source but Wye load or vice versa—or even more
complexly mixed arrangements.
It is also possible to find a Wye load connection which is equivalent to a Delta load connection and can
therefore be used to represent it for the purpose of making calculations. The opposite is also possible, i.e.,
finding a Delta configuration equivalent to a Wye configurations. This mathematical technique is called a
Wye-Delta transformation (or Y-Δ transform), or more precisely either a Δ-load to Y-load transformation or a
49
3-phase Power
The power consumed in a balanced 3-phase load is the sum of the powers in each load. For each phase,
Real power Pph = Vph Iph cosθ
Reactive power Q ph = Vph Iph sinθ
where θ is the power factor angle (angle between load voltage magnitude Vph and load current magnitude Iph)
Total Wye 3-phase real power is 3··Pph., etc. For balanced loads, the power may be expressed as
Real power Ptot
= 3 ∙ P𝑝ℎ = 3Vph Iph cosθ = 3
VLL
I cosθ
√3 ph
= √3VLL IL cosθ
Reactive power Q tot = √3VLL IL sinθ
where VLL is line-to-line (phase to phase) rms voltage magnitude and IL is line (phase) current.
Total Delta load 3-phase power is also given by
Real power Ptot = √3VLL IL cosθ
Reactive power Q tot = √3VLL IL sinθ
50
Thus θ is the angle of the load impedance)
47
48
49
50
EEAI3
EEAI3
EEAI3
EEAI3
p.
p.
p.
p.
Page 22 of 116
258-9
260
265 and https://en.wikipedia.org/wiki/Y-%CE%94_transform
269
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17 May 2016
Energy Resources and Overall Energy Utilization
This is a limited summary derived in part from chapter 3, with some statistics updated from other sources.
The International Energy Agency (IEA) summary of energy statistics may be found here.
51
Primary Energy Sources
Primary energy sources are raw resources which are eventually transformed into secondary more convenient
and/or usable energy carriers (such as electricity). Primary sources include non-renewable primary sources
(fossil and mineral fuels such as uranium and thorium), along with renewable primary sources such as
hydropower. “Primary energy is the energy embodied in natural resources prior to undergoing any humanmade conversions or transformations. Examples of primary energy resources include coal, crude oil,
52
sunlight, wind, running rivers [i.e., hydropower in the broad sense], vegetation, and uranium.” After
conversion, the three major primary energy sources—fossil fuels, nuclear, and hydroelectric—contribute
53
>99% of world electric energy generation.
In somewhat greater detail, primary energy sources consist of
Primary Fossil Fuels: These are coal, crude oil, and natural gas
Primary Nuclear Fuels: The fissile isotopes (i.e., fissionable radioisotopes found in quantities in nature) are
238U and 235U. The fertile (non-fissile) radioisotope of Thorium 232Th is also a primary fuel found in nature.
54
Plutonium isotopes do not occur naturally in significant amounts.
Someday, primary fusion fuel, namely deuterium [2H or D] (when combined with synthetic tritium 3H), may
55
become commercially viable for electrical energy-generation. ]
Primary Renewable Resources: These include solar photons, hydropower (in the broadest sense), wind;
biomass; and geothermal reservoirs.
The following graph shows the relative contributions of the several primary energy sources :
51
52
53
54
55
56
56
IEA, International Energy Agency: Key World Energy Statistics 2014.
http://www.iea.org/publications/freepublications/publication/KeyWorld2014.pdf
http://www.eoearth.org/view/article/155350/
EEAI3 p. 41
http://www.world-nuclear.org/info/current-and-future-generation/thorium/
http://fusionforenergy.europa.eu/understandingfusion/merits.aspx , also
https://www.iter.org/sci/fusionfuels
http://www.iea.org/publications/freepublications/publication/KeyWorld2014.pdf , slightly modified MCM
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Here, mtoe are millions of tonnes of oil equivalent (see below).
Conversion of Primary Sources to Secondary Energy Carriers
[Thermodynamic Terminology has not been summarized here.] The Gibbs free energy G is the energy
associated with a chemical reaction that can be used to do work. The free energy of a system is the sum of its
enthalpy (H) plus the product of the temperature (Kelvin) and the entropy (S) of the system. The Gibbs free
energy of the system is a state function because it is defined in terms of thermodynamic properties that are
57
state functions. The change in the Gibbs free energy of the system that occurs during a reaction is therefore
equal to the change in the enthalpy of the system minus the change in the product of the temperature times
the entropy of the system, or
∆G = ∆H − ∆(TS) or,
∆G = ∆H − T∆S (for constant T)
Primary energy sources are converted to more readily usable secondary carriers of energy.
A major intermediate carrier is thermal energy, typically in the form of steam and/or enthalpy, which are
used for providing heating and for turning steam turbines for electrical power generation.
The secondary sources (carriers) include the following:
From Fossil Fuels: Crude oil can be refined to fuel oil and other refined fuels, which ultimately is used to
provide thermal energy or power internal combustion engines. Coal, oil, and natural gas are converted
through burning to yield thermal energy, which can give rise to mechanical work or generation of
58
electricity.
57
58
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch21/gibbs.php
https://en.wikipedia.org/wiki/Primary_energy
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From Nuclear Fuels: Thermonuclear fission of primary fuel radioisotopes (238U, 235U, and 232Th) and certain
59
synthesized radioisotopes (especially 239Pu, 240Pu, and 238Pu, ) makes thermal energy which is used to
60
generate electricity.
From Renewable Resources:
• Solar energy provides
(1) thermal energy , some of which is used for generation of electricity
61
(2) photovoltaic electricity (PV);
• Hydropower (including river flow, tidal excursion and wave action) generates mechanical work and/or
62
hydroelectric HE power;
63
• Wind generates mechanical work or electricity;
64
65
• Biomass (crop and forest residue, wood, ? charcoal, other waste, biogas [methane], celluosic ethanol )
generate thermal energy and/or electricity
• Geothermal generates thermal energy and/or electricity.
59
60
61
62
63
64
65
https://en.wikipedia.org/wiki/Plutonium and
http://www.world-nuclear.org/info/nuclear-fuel-cycle/fuel-recycling/plutonium/
http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Introduction/Physics-of-Nuclear-Energy/
http://www.nrdc.org/energy/renewables/solar.asp
http://www.nrdc.org/energy/renewables/hydropower.asp
http://www.nrdc.org/energy/renewables/wind.asp
http://www.nrdc.org/energy/renewables/biomass.asp
https://en.wikipedia.org/wiki/Cellulosic_ethanol
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Utilization of Energy Resources in the US in 2014 66
“Rejected energy increased to 59 quads in 2013 from 58.1 in 2012, rising in proportion to the total energy
consumed. ‘Not all of the energy that we consume is put to use’, [A. J.] Simon explained. ‘Heat you feel when
you put your hand on your water heater and the warm exhaust from your car's tailpipe are examples of
rejected energy.’ Comparing energy services to rejected energy gives a rough estimate of each sector's energy
67
efficiency.”
Note: A quad is a unit of energy equal to 1015 BTU, or 1.055 × 1018 joules (1.055 exajoules or EJ), or 293.08
68
Terawatt-hours (TWh). The name quad derives from 1015 = 1 Peta = 1000 x (1,0004) = 1 short-scale
quadrillion = 1 thousand trillion = 1 thousand thousand billion, etc. “Today, the United Kingdom officially
69
uses the short scale [like the US], but France and Italy use the long scale.”
In 2010, 4125 TWh of electrical energy were generated in the US, mostly from fossil fuel, especially coal,
the diagram above shows that natural gas by 2014 exceeds coal in quads of electrical energy production
(reflecting increased gas production from fracking).
70
but
According to the US Energy Information Administration, world electricity generation in 2012 was 21,532
billion kWh, compared to 4,048 billion kWh for the US. Installed generating capacity in 2012 was 1,063
Million kW [1.063 TW] in the US versus 5,550 Million kW [5.550 TW] for the world. While the US has risen
66
67
68
69
70
https://flowcharts.llnl.gov/
https://www.llnl.gov/news/americans-using-more-energy-according-lawrence-livermore-analysis
https://en.wikipedia.org/wiki/Long_and_short_scales
EEAI3 p. 41
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only a little, Asia shows rapid rise in electricity generation, increasing from 4,469 billion kWh in 2002 to
8,762 in 2012. Total primary energy consumption for all types of energy for 2012 in the US was 95
71
quadrillion BTUs, compared to 524 for the entire world.
The textbook author computes that per capita annual consumption of electricity in 2012 was 13.3 MWh for
the US, 2.0 MWh for the remainder of the world, and 2.5 MWh for the whole world including the US. The
72
high consumption in the US reflects not just high living standards but also an advanced industrial base.
The following graph depicts global (world) energy consumption of all harnessed types from all sources
(biomass, coal, oil, natural gas, nuclear, hydro, and other renewables) during the period 1800 to 2013.
73
Clearly, total energy use has been rising nearly exponentially, most strikingly that of fossil fuels:
The various forms of energy are here expressed in MTOE/a, that is Million Tonnes of Oil Equivalent. The /a
74
in “MTOE/a” signifies total consumption (totaled for all humans) rather than per capita consumption. One
tonne of a substance is one metric ton or 1000 kg (approximately 2,205 lb., thus larger than a US ton of 2000
75
lb.). The tonne is confusingly slightly less than a UK ton (which is 2240 lb.). One tonne of crude oil is said
to release energy when burned of 41.9 GJ = 11.63 MWh = 39,683,207 BTU. One Mtoe represents 11.63x106
MWh. The final total peak value in the graph above of about 14,000 Mtoe represents 1.63x1011 MWh annual
equivalent consumption.
I will not attempt to summarize individual details about the various fossil fuels here. Many of the harmful
effects of toxic byproducts are well known, including release of the greenhouse gas CO2, CO, SO2, NOx, black
carbon (soot), and carcinogenic and/or otherwise deleterious substances. These latter substances include
benzene; petroleum coke (which contains toxic dusts with many compounds and heavy metals);
71
http://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=2&pid=2&aid=12
EEAI3 p. 42-4
73
http://fractionalflow.com/2014/10/10/the-powers-of-fossil-fuels/
74
Robert Bent, Lloyd Orr, Randall Baker, Energy: Science, Policy, and the Pursuit of Sustainability, 2002,
Island Press, p. 38
75
https://en.wikipedia.org/wiki/Ton and https://en.wikipedia.org/wiki/Tonne
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formaldehyde; polycyclic aromatic hydrocarbons (PAH); mercury; silica and other dusts; radon; and
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hydrofluoric acid HF, etc.
The nuclear power industry also does not have an unblemished record, and environmental contamination
with radioisotopes from reactors has been of great concern since Three-Mile Island (1979), Chernobyl (1986),
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and the Fukushima Daiichi nuclear disaster (2011).
Overall Electrical Generation in the US and World
78
The US EIA (U.S. Energy Information Administration) provides these overall statistics for Electrical
Generation, expressed in multiples of Watt-hours (Wh).
US Annual Totals
[Giga G = 109, Tera T= 1012, Peta = 1015]
2002: 3,858 billion kWh = 3.858 x 103 x 109 x 103 Wh = 3,858 x 1012 Wh = 3,858 TWh
2012: 4,048 billion kWh = 4.048 x 103 x 109 x 103 Wh = 4,048 x 1012 Wh = 4,048 TWh
World Totals
2002: 15,393 billion kWh = 15.393 x 103 x 109 x 103 Wh = 15,393 x 1012 Wh = 15,393 TWh
2012: 21,532 billion kWh = 21.532 x 103 x 109 x 103 Wh = 21,532 x 1012 Wh = 21,532 TWh
The first of the following graphs shows the EIA’s statistics on electric power generation in the US, the graph
extending from 2001 to 2014. The table show US electrical energy generation from 2009 to 2014. All values
are expressed in thousands of MWh, thus in GWh. It is clear that most of US electrical power is generated
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from coal (though declining), nuclear energy (relatively constant), and natural gas (increasing). Hydroelectric
(fairly steady) and wind (increasing) make still small overall contributions.
The second table shows the EIA’s statistics on electric power generation for the entire world, the data
extending from 2008 to the most recently available year, 2012, and demonstrating how global electricity
76
77
78
79
http://planetsave.com/2013/12/07/pollution-air-pollution-water-pollution-health-problems/
https://en.wikipedia.org/wiki/List_of_civilian_nuclear_accidents
http://www.eia.gov/cfapps/ipdbproject/iedindex3.cfm
http://www.eia.gov/electricity/data/browser and
http://www.eia.gov/cfapps/ipdbproject/iedindex3.cfm graphs and tables specified & modified by MCM
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Units above are thousands of MWh = GWh
US Electrical Energy Generation 2002 to 2014 (units are thousands of MWh = GWh)
Total World Electrical Energy Generation 2008 to 2012 (units are TWh, note decimal point)
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Overview of AC Electrical Generation, Transmission and Distribution
Nikola Tesla conceived and championed our current AC electrical distribution system.
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A modern diagram of our electrical system follows. This shows or implies:
• original voltage generated at the electrical plant (typically 11 to 13 kV, 3-phase),
• step-up to high voltages (138 to 765 kV, 3-phase) by transmission transformer
for long distance primary transmission, possibly with transmission voltage
industrial customer in this voltage range,
• step-down to lower voltages (e.g., 26 to 69 kV, 3-phase) at distribution transformer
for secondary transmission with possible subtransmission customer in this voltage range,
• step-down to 4 kV to 13 kV, 3-phase at distribution transformer for primary distribution, and
• step-down to 120 to 240 V at service transformer for distribution
to residential customers (mostly single phase) and
industrial or commercial customers (mostly 3-phase, voltages may be somewhat higher)
Electrical Generation (discussed under individual modes of generation)
Electrical Transmission (discussed in its own section below)
Electrical Distribution
Electrical power is delivered to residences, businesses, etc. by the local electric power company (aka power
utility, energy service company). For residences and small businesses, it is delivered via a distribution system,
which includes primary distribution lines, distribution substations ,distribution transformers (pole mounted,
pad mounted, or located inside a structure), and secondary distribution split-phase (single phase 120/240V)
81
lines reaching the home (via an overhead service drop or underground service lateral), etc. The customer’s
responsibility begins at the output of the electric meter. Much of the material pertaining to home electrical
distribution is discussed below under Electrical Safety.
Hydroelectric Power Plants
See also earlier tables on electrical generation in the US and the world. (This discussion draws in part on
chapter 3 and chapter 4.) Adverse environmental effects of hydroelectric plants are mentioned briefly in
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chapter 5.
80
http://www.electricaltechnology.org/2013/05/typical-ac-power-supply-system-scheme.html
81
https://en.wikipedia.org/wiki/Service_drop
82
EEAI3 p. 96
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Hydroelectric Power Plant (HE PP) Capacity and Production
The following diagram shows Current Hydroelectric Capacity in the United States by state (developed,
83
excluded, other, and feasible), showing the dominance of WA, CA, ID, and OR.
Largest hydroelectric plants in the world (compared to selected US plants)
Three Gorges, Yangtze R in Hubei Province, China:
Itaipu (Paraná River, across the Brazil-Paraguay border):
Guri (Venezuela)
Grand Coulee, WA:
Hoover, Colorado River, on the border between AZ and NV.:
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https://wiki.uiowa.edu/display/greenergy/Hydroelectric+Power
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22.5 GW (completed 2010)
14.0 GW (completed 1983)
10 GW (completed 1986)
6.8 GW (completed 1942)
2.0 GW (generation began 1936)
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Terminology
Hydropower: To my way of thinking (and definitions vary),
hydropower is water power, “power derived from the energy of
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falling water or fast running water”. It depends on the
hydrologic cycle, in which the Sun evaporates sea and fresh
water, the water precipitates as rain or snow, and the water flows
in liquid form in rivers to return to the sea. Hydropower includes
hydroelectric power (in fact some consider these terms
85
synonymous) , but I prefer to regard it as a broader term that
includes all forms of power harnessed from flowing water. Old
technologies such mechanical rotation of a wheel by flowing river
water (used in grinding mills, saw mills, and mechanical wheel
86
water pumps such as the noria, depicted to the right ), power
87
captured from river turbines, tides and sea currents, as well as
hydroelectric power, etc.
Hydroelectric Power specifically applies to conversion of the
potential and/or kinetic energy of flowing water into electricity.
The flow of water arises ultimately from solar energy, which is a renewable resource, but installed large-scale
hydroelectric power generation in the US is relatively fixed in capacity currently, due to important
environmental constraints. Thus, most authors do not consider it “renewable”, at least in the US. Although
the installed base in the US of HE PPs is relatively fixed and not expanding, new plants have been or will be
built in recent decades in China (Three Gorges), Brazil/Paraguay (Itaipu), Vietnam, Ethiopia, etc. Small scale
hydrokinetic power generation is considered renewable.
The earliest was built across the Fox River in Wisconsin, first operating in 1882.
Types of HE PPs
1. Impoundment HE PPs
For example, Grand Coulee Dam. These typically generate the greatest amounts of electricity. They use a
dam to create a lake or reservoir. Water under pressure feeds through one of more penstocks to turbines
located at a lower level. A governor can regulate the rate of water flow presented to the turbines, and thus the
power output, in order to match loads. Turbines are discussed further below. These can have a substantial
88
environmental impact. .
84
85
86
87
88
https://en.wikipedia.org/wiki/Hydropower
http://www.merriam-webster.com/dictionary/hydropower
https://en.wikipedia.org/wiki/Noria
http://energy.gov/eere/water/water-power-program
EEAI3 p. 55, also http://www.usbr.gov/power/edu/pamphlet.pdf and
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Power generated in an Impoundment HE PP
is a function of both water head and actual
flow rate. The different colors represent
different water pressures (“head” in m)
Impoundment HE PP. Many HE PPs have a dam, reservoir,
and one or more sets of: control gate (aka governor), penstock
(carrying water to the turbine), turbine connected to
generator, and outflow channel.
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When water flows in the penstock, the static pressure at the turbine inflow Pr0 (i.e., pressure for the blocked
no flow condition) is reduced (by viscosity, frictional losses, and turbulence), so that the actual pressure at
90
the turbine inflow Pr < Pr0 , and the head at the turbine is now designated the effective head h, where h < H.
In additional to penstock losses of power, there is power loss occurring at the conversion of water energy to
turbine rotational energy, and in the generator’s conversion of rotational energy to electrical output. Overall
efficiency of power plant generation is given by the ratio of electrical power generated to PE + KE at the water
intake. This ratio is given by
where
𝑃𝑜𝑜𝑜
= 𝜂𝑡𝑡𝑡𝑡𝑡 = 𝜂𝑝 𝜂ℎ 𝜂𝑡 𝜂𝑔
𝑃𝑝−𝑖𝑖
ηp = penstock power transmission efficiency (0-1)
ηh = penstock to turbine blade power conversion efficiency (0-1)
ηt = turbine to generator power transmission efficiency (0-1), and
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ηg = generator mechanical to electrical power conversion efficiency (0-1).
Estimates of overall electrical energy generation efficiency ηtotal of modern HE PPs vary from as high as 8092
90% or even 95% to as low as 50%-60% (the lower figures are especially applicable to small plants).
However, the sources of this information are not always clear as to exactly what computation is being used.
89
90
91
92
https://wiki.uiowa.edu/display/greenergy/Hydroelectric+Power
EEAI3 p. 67
EEAI3 p. 69
https://wiki.uiowa.edu/display/greenergy/Hydroelectric+Power
http://www.usbr.gov/power/edu/pamphlet.pdf
90%
http://www.mpoweruk.com/hydro_power.htm
95%
http://www.reuk.co.uk/Calculation-of-Hydro-Power.htm 50-60%
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2. Pumped Storage HE PPs: These help with load
balancing and more efficient power generation at HE
installations. When electrical demand is low and extra
electrical power is available, the power is used to pump
water to an upper level water reservoir (or to raise the
surface level of the reservoir). When electrical demand is
high, the extra water is available to add to the head for
additional power generation. The relatively low energy
density of pumped storage systems requires either a very
large body of water or a large variation in height, and
this creates specific geographic constraint on suitable
sites and can have a substantial environmental impact.
The diagram shows a representative pattern at an
unspecified site of pumping water (green) in off hours,
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and generating top power in times of higher demand.
In some cases, reversible Francis turbines are used for
pumping.
3. Diversion HE PPs: These do not require a reservoir but utilize strong river currents to create a relatively
low head that drives turbines for modest power output. E.g., Fox River in Wisconsin.
http://www.buzzle.com/articles/how-efficient-is-hydroelectric-power-generation.html
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https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity and EEAI3 p. 54.
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50% to 90%
17 May 2016
Categories of turbines and how they are selected
“An impulse turbine [e.g., Pelton] is generally suitable for high head, low flow applications... Reaction
turbines are generally used for sites with lower head and higher flows than compared with the impulse
94
turbines.”
The following graph shows one author’s interpretation of optimal ranges for different types of turbine and
thus how a particular type of turbine is chosen, namely: Francis, Pelton, and Kaplan, CrossFlow [impulse]
and Turgo [impulse]. The parameters considered in the diagram are Head of pressure at the turbine (m) and
95
Flow rate of water (m3/s), as well as output megawatts of the turbine (or power plant?).
Impulse Turbines (mostly Pelton)
Impulse turbines operate on kinetic energy of water rather than pressure. They are mostly of the Pelton type,
which utilize 1 or more jets of water directed in air against split buckets (cups, vanes) attached to the runner
of the turbine. They are optimal for high head lower flow situations.
For Pelton turbines, the change of momentum of the water injected and reflected back in more-or-less the
opposite direction yields a net linear force on the cups which may be theoretically as great as
96
(approximately)
Fc = 2
mi
t
(vi − vc )
where Fc = net force on a single cup in tangential direction (that of the jet)
mi/t = mass (kg) of water in the jet emitted per time interval t
vi = velocity of the incident jet relative to the cup
vc = linear velocity of the cup relative to the stationary enclosure.
As energy may be force x distance and power may be given by force times speed, the power acquired by the
cup Pc is
Pc = Fc vc
It can be shown that maximum power is delivered when cup (runner) speed is 1/2 of the incident jet speed vi.:
94
95
96
http://energy.gov/eere/water/types-hydropower-turbines
https://commons.wikimedia.org/wiki/File:Water_Turbine_Chart.png by anon. author “Tonigonenstein”
All computations for Pelton turbines are from EEAI3 p. 57-61
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vi = vc
in which case, maximum power captured is
Pc−max =
mi
t
vi 2
In this maximum power capture condition, the full KE of the incident jet is captured.
Expressing power in terms of volume flow rate rather than mass flow rate,
Pc = 2
voli
t
δ(vi − vc )vc = 2fδ(vi − vc )vc
where f = volume flow rate in jet (m3/s) = Avi (where A is cross section of jet)
δ = water density kg/m3
The maximum power is delivered when
1
Pc−max = 2 fδvi 2
Pelton turbines are depicted in the following two images:
Shown above is a horizontally mounted Pelton turbine showing 5 injection jets within the turbine casing.
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Shown above is a vertically mounted Pelton turbine runner with stainless steels cups and a single adjacent jet
97
nozzle. The turbine casing has been removed.
Other types of impulse turbine include the Cross-Flow
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and Turgo.
99
Reaction Turbines
These are completely immersed in water and are said to operate more on pressure rather than kinetic energy.
However, the Francis turbine is said to combine impulse and reaction characteristics. According to the
textbook EEAI3, Francis are suitable for 80 to 500 m heads, whereas Kaplan are suitable for lower heads of
1.5-80m.
Francis Turbine
Francis turbines are high efficiency, operate well over a wide range of operating conditions and are widely
used in HE PP, contributing 60% of global hydropower capacity. The fixed blades (aka buckets or vanes) are
complexly shaped like airfoils, and experience both an impulse as well as a lift force (via Bernoulli effect).
These are thus mixed impulse and reaction turbines. The water enters the spinning blades more or less
radially and exits below axially. Flow in the spiral casing (scroll case) surrounding the blades has
continuously decreasing cross section, so that as water is directed into the turbine blades, the cross sectional
decrease keeps the water flow velocity nearly uniform. Stay vanes (fixed vanes, aka wicket gates) and guide
vanes (fixed in vertical axis but having adjustable variable angle) redirect flow toward the rotating blades. The
variable guide vanes are used to control how much water is injected and thus can control power output of the
turbine and therefore the generator to match power demand. They also control inlet flow angles to keep the
angle of attack optimal.
The low pressure side where water exits below is subject to cavitation (because local pressure at the exit side
drops below the saturation vapor pressure of water) and severe erosional damage can result. Thus, the
exiting draft tube requires careful design attention, including a gradually increasing cross-sectional area for
97
98
99
both images extracted from this article and the 2nd was modified slightly by MCM
http://energy.gov/eere/water/types-hydropower-turbines
https://en.wikipedia.org/wiki/Turgo_turbine
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101
cavitation in rotating Francis turbines.
100
The following images depict several types of
Assuming pressure energy is the dominant component (and therefore that KE can be neglected), the energy
imparted to the blades is given by:
1
Eblades = (Pr1 − Pr2 )vol + 2 m(v12 − v22 ) ≈ (Pr1 − Pr2 )vol ≈ Pr1 vol
where Pr1 is the pressure just before encountering the blades
Pr2 is the pressure just after encountering the blades (assumed to be very low)
v1 is the water velocity just before encountering the blades
v2 is the water velocity just after encountering the blades
vol is the volume of water causing the energy deposition
The power imparted to the blades is therefore
P𝑏𝑏𝑏𝑏𝑏𝑏 ≈ Pr1
vol
𝑡
≈ 𝑃𝑟1 𝑓
where f is the penstock flow rate in m3/s
100
101
http://www.learnengineering.org/2014/01/how-does-francis-turbine-work.html etc.
http://www.slideshare.net/saurabh856/cavitation-in-francis-turbine
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Runner with blades of a Francis turbine installed in the Sanxia (Three Gorges Dam) power plant in Yichang,
Hubei province. There are 32 main turbine/generator units each at capacity of 700-710 MW (plus two plant
power generators, each with capacity of 50 MW), and total installed capacity of 22,500 MW. This single
102
turbine and its generator have the following specifications:







Turbine Rotational Speed (rpm)
Runner weight (t)
Runner diameter (m)
Generator Stator Bore (m)
Rotor Weight (t) 2,000
Capacity (MW)
71.4/75
80.6
46.3
9.6
18.8
2,000
700-710
Kaplan Turbine
“The Kaplan turbine is a propeller-type water turbine which has adjustable blades. It was
developed in 1913 by the Austrian professor Viktor Kaplan, who combined automatically
wide range of flow and water level... Its invention allowed efficient power production in lowhead applications that was not possible with Francis turbines. The head [of pressure] ranges
from 10–70 meters and the output from 5 to 200 MW. Runner diameters are between 2 and 11
meters. The range of the turbine rotation is from 79 to 429 rpm... Kaplan turbines are now
widely used throughout the world in high-flow, low-head power production... Power is
recovered from both the hydrostatic head and from the kinetic energy of the flowing water. The
design combines features of radial and axial turbines. The inlet is a scroll-shaped tube that
102
http://www.alstom.com/Global/Power/Resources/Documents/Brochures/three-gorges-hydro-powerplant-china.pdf , and
https://en.wikipedia.org/wiki/Three_Gorges_Dam
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wraps around the turbine's wicket gate. Water is directed tangentially through the wicket gate
and spirals on to a propeller shaped runner, causing it to spin... Kaplan turbines are widely
used throughout the world for electrical power production. They cover the lowest head hydro
sites and are especially suited for high flow conditions... Inexpensive micro turbines on the
Kaplan turbine model are manufactured for individual power production designed for 3 m of
head, [but] can work with as little as 0.3 m of head at a highly reduced performance provided
[there is] sufficient water flow... Large Kaplan turbines are individually designed for each site
to operate at the highest possible efficiency, typically over 90%. They are very expensive to
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These turbines may be installed
design, manufacture and install, but operate for decades.”
104
Kaplan turbines are now widely used throughout
with vertical, horizontal, or oblique axis.
105
the world in high-flow, low-head power production.
The Manuel Piar Hydroelectric Power Plant (Tocoma Dam) in Venezuela, scheduled to
open in 2015, has Kaplan turbines that generate the greatest power at nominal head as of
2012. The total installed capacity is 2,300 megawatts at rated head 34.65 m. This capacity
derives from ten Kaplan generator units manufactured by IMPSA, each producing 230
106
megawatts. The diameter of the runner is 8.6 metres (28 ft).
Vertical axis Kaplan turbine showing wicket gates which direct water against the variable pitch airfoil-like
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blades, and shaft connection to generator rotor. Water exits below in this case.
Fossil Fuel Power Plants
108
Fossil Fuel Power Plants are discussed quite briefly in the textbook in chapter 4 and also briefly here. I
109
have discussed the relevant thermodynamic cycles and steam turbine technology in a separate summary.
103
104
105
106
107
108
https://en.wikipedia.org/wiki/Kaplan_turbine
http://www.koessler.com/sites/default/files/produkte/Anlagebl%25C3%25A4tter%2520Kaplan%25202013%2520Englisch.pdf
http://www.hydroquebec.com/learning/hydroelectricite/types-turbines.html
https://en.wikipedia.org/wiki/Tocoma_Dam
https://commons.wikimedia.org/wiki/File:Water_turbine_%28en_2%29.svg
EEAI3 p. 70-75
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The heavy environmental impacts of fossil fuels, including atmospheric pollution from CO2, SO2, NOx, acid
rain, and ozone, as well as ashes, Legionella transmission from cooling towers, etc., are mentioned only briefly
110
I have provided a much more thorough summary pertaining to atmospheric pollution in a
in Chapter 5.
111
separate document.
Such plants depend on heat generated from burning fossil fuels (coal, natural gas, petroleum liquids—diesel,
fuel oil, etc.—and (solid) petroleum coke). The amount of electrical power generated by these plants compared
to hydroelectric and other sources of electrical power generation are shown in the earlier table, “US Electrical
Energy Generation 2002 to 2014”.
Thermal (Thermodynamic) Cycle
Because they depend on a thermal (thermodynamic) cycle, the conversion to electrical energy by burning fuel
in fossil fuel plants is quite inefficient. The heat sink (at TLow, usually a cooling tower) must extract and
release waste heat into the environment, in order for the thermal cycle to succeed.
The following diagram
112
illustrates an idealized Rankine thermodynamic cycle using water/steam as the
working fluid and with simplified and suboptimal operating characteristics.
power consumed by (pump) or provided to the system (turbine).
113
Here,
Q̇ = heat flow rate, Ẇ =
Process 1-2, Isentropic compression by a pump: The working fluid is pumped from low to
high pressure (at state 2). Because the fluid is a liquid at this stage (it lies to the left of the
saturated liquid line in the compressed liquid region), the pump requires relatively little input
energy.
Process 2-3, Constant pressure heat addition in a boiler: The high pressure compressed
liquid enters a boiler where it is heated at constant pressure by an external heat source to
become first a saturated liquid, then a saturated liquid-vapor mixture, then a superheated
vapor (ending at 3, a subcritical state having T3 < Tcr). The input energy Qin required to attain
this state can be calculated graphically, using an enthalpy-entropy chart (aka h-s or Mollier
diagram), or numerically, using steam tables.
Process 3-4, Isentropic expansion in a turbine: The superheated vapor expands through a
turbine, generating power. This decreases the temperature and pressure of the vapor, and
some condensation may occur (as implied in the diagram lower left), though at state 4, there is
and should be at most minimal condensation. The turbine net work output
Wnet,out = Wout - Win
for this process (i.e., net after allowing for pump Workin) can be easily calculated using the
charts or tables.
Process 4-1, Constant pressure heat rejection in a condenser: The slightly wet vapor at 4
then enters a condenser where it is condensed at a constant pressure to become a saturated
liquid-vapor mixture, and finally a saturated liquid (at 1). Heat Qout is given off as a result of
the enthalpy of vaporization resulting from condensation of the vapor.
109
http://www.mcgoodwin.net/pages/thermodynamics.pdf
EEAI3 p. 89-95
111
http://www.mcgoodwin.net/pages/atmscuw458.pdf
112
https://en.wikipedia.org/wiki/User:Andrew.Ainsworth , who also provides the annotation.
113
I have discussed Rankine cycle thermodynamics in much greater detail in
http://www.mcgoodwin.net/pages/thermodynamics.pdf
110
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Idealized Rankine thermodynamic cycle with simplified and suboptimal operating characteristics:
“T-s (Temperature vs. specific entropy) diagram of a basic Rankine cycle using water/steam in
SI units. Data derived from IAPWS IF-97 [The International Association for the Properties of
Water and Steam]... Isobars are at pressures 0.06 bar, 1.01325 bar (1atm), 50 bar, 150 bar
and 221 bar. Temperature rise associated with pump is heavily exaggerated for clarity and
cycle operates between pressures of 50 bar and 0.06 bar...Easiest to think of the cycle starting
at the pump and so input to pump is state 1.”
Actual cycles deviate from the ideal:
“The compression by the pump and the expansion in the turbine are not isentropic. In other
words, these processes are non-reversible and entropy is increased during the two processes.
This somewhat increases the power required by the pump and decreases the power generated
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by the turbine.”
114
https://en.wikipedia.org/wiki/User:Andrew.Ainsworth , who also provides the annotation.
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A slightly more complex Rankine cycle with superheating and reheating is depicted to follow:
The corresponding Rankine cycle with reheat follows:
115
“The purpose of a reheating cycle is to remove the moisture carried by the steam at the final
stages of the expansion process [in the turbine]. In this variation, two turbines work in series.
The first [High Pressure HP Turbine] accepts vapor from the boiler at high pressure. After the
vapor has passed through the first turbine, it re-enters the boiler and is reheated before
passing through a second, lower-pressure, turbine. The reheat temperatures [at 5] are very
close or equal to the inlet temperatures [at 3], whereas the optimum reheat pressure needed
[along 4-5] is only one fourth of the original boiler pressure [attained at 3]. Among other
advantages, this prevents the vapor from condensing during its expansion [in the turbine] and
thereby damaging the turbine blades, and improves the efficiency of the cycle, because more of
the heat flow [in the turbine] occurs at higher temperature... The idea behind double reheating
is to increase the average temperature. It was observed that more than two stages of reheating
are unnecessary, since the next stage increases the cycle efficiency only half as much as the
preceding stage. Today, double reheating is commonly used in power plants that operate
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under supercritical pressure [the diagram does not depict supercritical pressure].”
115
116
https://www.scribd.com/doc/54610589/10/Combined-Reheat-and-Regenerative-Rankine-Cycle (both images)
https://en.wikipedia.org/wiki/Rankine_cycle
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The following pressure - specific enthalpy (P-h) diagram depicts the operation of an idealized Rankine cycle
that is more optimal. It is operating in subcritical pressures and temperatures, and it incorporates
superheating [at states 1 and 3] and reheating [in process 2-3]. The cycle depicted also shows that the ending
turbine state [4] is associated with only slight condensation under the saturation dome, preventing erosion of
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https://www.ohio.edu/mechanical/thermo/Applied/Chapt.7_11/Chapter8a.html
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Types of Turbines (aka “Prime Movers”) used in Thermal Power Plants
Prime Movers (including Turbines) “... are typically Diesel Engines, Gas or Steam Turbines, or Hydro and
Wind Turbines. Prime movers convert oil, gas, coal, wood, uranium, water, wind, etc. into mechanical energy.
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The mechanical [rotational] energy is supplied to the shaft of the generator ”
119
I have made an extensive summary here of the thermodynamics and operation of steam turbines (vapor
power cycle plants), gas turbines (gas power cycles plants), combined cycle plants, and other power cycles
used in power generation. This information includes discussion of thermal efficiencies.
Steam Turbines
Steam turbine plants use the dynamic pressure generated by expanding steam to turn the blades of a
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turbine. Almost all large non-hydro plants use this system, and they are the focus of most of this section.
Gas Turbines
Gas turbine plants use the dynamic pressure from flowing gases (air and combustion products) to directly
operate the turbine. They are often natural gas or oil fueled.
A major selling point for the gas turbine power plant is that it operates at very high temperatures, thus
should be thermodynamically more efficient. (It can also be very clean burning.) The following is from the
Office of Fossil Energy:
“The combustion (gas) turbines being installed in many of today's natural-gas-fueled power
plants are complex machines, but they basically involve three main sections:
• The compressor, which draws air into the engine, pressurizes it, and feeds it to the
combustion chamber at speeds of hundreds of miles per hour.
• The combustion system, typically made up of a ring of fuel injectors that inject a steady
stream of fuel into combustion chambers where it mixes with the air. The mixture is burned at
temperatures of more than 2000 degrees F. The combustion produces a high temperature, high
pressure gas stream that enters and expands through the turbine section.
• The turbine is an intricate array of alternate stationary and rotating aerofoil-section blades.
As hot combustion gas expands through the turbine, it spins the rotating blades. The rotating
blades perform a dual function: they drive the compressor to draw more pressurized air into
the combustion section, and they spin a generator to produce electricity.
Land based gas turbines are of two types:
(1) Heavy frame engines are characterized by lower pressure ratios (typically below 20) and
tend to be physically large. Pressure ratio is the ratio of the compressor discharge pressure
and the inlet air pressure. Aeroderivative engines are derived from jet engines, as the name
implies, and operate at very high compression ratios (typically in excess of 30).
(2) Aeroderivative engines tend to be very compact and are useful where smaller power
outputs are needed. As large frame turbines have higher power outputs, they can produce
larger amounts of emissions, and must be designed to achieve low emissions of pollutants,
such as NOx.
One key to a turbine's fuel-to-power efficiency is the temperature at which it operates. Higher
temperatures generally mean higher efficiencies, which in turn, can lead to more economical
operation. Gas flowing through a typical power plant turbine can be as hot as 2300 degrees F,
but some of the critical metals in the turbine can withstand temperatures only as hot as 1500
to 1700 degrees F. Therefore, air from the compressor might be used for cooling key turbine
components, reducing ultimate thermal efficiency.
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http://electricalengineeringtour.blogspot.com/2012/08/how-prime-movers-works-in-electic-power.html
syntax corrected MCM
119
http://www.mcgoodwin.net/pages/thermodynamics.pdf
120
https://en.wikipedia.org/wiki/Power_station
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One of the major achievements of the Department of Energy's advanced turbine program was
to break through previous limitations on turbine temperatures, using a combination of
able to boost turbine inlet temperatures to as high as 2600 degrees F - nearly 300 degrees
hotter than in previous turbines, and achieve efficiencies as high as 60 percent.
Another way to boost efficiency is to install a recuperator or heat recovery steam generator
(HRSG) to recover energy from the turbine's exhaust. A recuperator captures waste heat in the
turbine exhaust system to preheat the compressor discharge air before it enters the
combustion chamber. A HRSG generates steam by capturing heat from the turbine exhaust.
These boilers are also known as heat recovery steam generators. High-pressure steam from
these boilers can be used to generate additional electric power with steam turbines, a
configuration called a combined cycle.
A simple cycle gas turbine can achieve energy conversion efficiencies ranging between 20 and
35 percent. With the higher temperatures achieved in the Department of Energy's turbine
program, future hydrogen and syngas fired gas turbine combined cycle plants are likely to
achieve efficiencies of 60 percent or more. When waste heat is captured from these systems for
heating or industrial purposes, the overall energy cycle efficiency could approach 80
121
percent.”
(But see below about actual average Heat Rate data currently achieved.)
Additional technologies which have been implemented or hold promise for gas turbines include:
122
123
(1) hydrogen turbines which use hydrogen as fuel, some of which may derive from coal
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(2) coal gasification, which forms a mixture of carbon monoxide, hydrogen and other gaseous
compounds that can be burned
The newer gasification technologies also are aimed at reducing atmospheric pollution by NOx, SOx, and
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particulates:
“The environmental benefits of gasification stem from the capability to achieve extremely low
SOx, NOx and particulate emissions from burning coal-derived gases. Sulfur in coal, for
example, is converted to hydrogen sulfide and can be captured by processes presently used in
the chemical industry. In some methods, the sulfur can be extracted in either a liquid or solid
form that can be sold commercially. In an Integrated Gasification Combined-Cycle (IGCC) plant,
the syngas produced is virtually free of fuel-bound nitrogen [i.e., N found naturally in coal].
NOx from the gas turbine is limited to thermal NOx. Diluting the syngas allows for NOx
emissions as low as 15 parts per million. Selective Catalytic Reduction (SCR) can be used to
reach levels comparable to firing with natural gas if required to meet more stringent emission
levels. Other advanced emission control processes are being developed that could reduce NOx
from hydrogen fired turbines to as low as 2 parts per million.
The Office of Fossil Energy is also exploring advanced syngas cleaning and conditioning
processes that are even more effective in eliminating emissions from coal gasifiers. Multicontaminant control processes are being developed that reduce pollutants to parts-per-billion
levels and will be effective in cleaning mercury and other trace metals in addition to other
impurities.
Coal gasification may offer a further environmental advantage in addressing concerns over the
atmospheric buildup of greenhouse gases, such as carbon dioxide. If oxygen is used in a coal
gasifier instead of air, carbon dioxide is emitted as a concentrated gas stream in syngas at high
pressure. In this form, it can be captured and sequestered more easily and at lower costs. By
121
122
123
124
125
http://energy.gov/fe/how-gas-turbine-power-plants-work slight MCM modifications
http://energy.gov/fe/science-innovation/clean-coal-research/hydrogen-turbines
http://energy.gov/fe/science-innovation/clean-coal-research/hydrogen-coal
http://energy.gov/fe/science-innovation/clean-coal-research/gasification
ibid.
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contrast, when coal burns or is reacted in air, 79 percent of which is nitrogen, the resulting
carbon dioxide is diluted and more costly to separate.”
The following illustrates some of the reaction intermediates and the final gases produced in coal
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gasification:
Gas produced by gasification is sometimes called syngas.
“Syngas, or synthesis gas, is a fuel gas mixture consisting primarily of hydrogen, carbon
monoxide, and very often some carbon dioxide. The name comes from its use as intermediates
in creating synthetic natural gas (SNG) and for producing ammonia or methanol. Syngas is
usually a product of gasification and the main application is electricity generation... Syngas
can be produced from many sources, including natural gas, coal, biomass, or virtually any
hydrocarbon feedstock, by reaction with steam or oxygen. Syngas is a crucial intermediate
resource for production of hydrogen, ammonia, methanol, and synthetic hydrocarbon fuels.
Syngas is also used as an intermediate in producing synthetic petroleum for use as a fuel or
lubricant... Syngas is combustible and often used as a fuel of internal combustion engines. It
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has less than half the energy density of natural gas.”
Internal Combustion Reciprocating Engine Turbines
These do not include gas turbines. They are usually fueled by diesel oil, heavy oil, natural gas, and landfill
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gas, and play an ancillary role.
Combined Cycle Plants
“Combined cycle plants have both a gas turbine fired by natural gas, and a steam boiler and steam turbine
which use the hot exhaust gas from the gas turbine to produce electricity. This greatly increases the overall
126
image slightly modified by MCM
127
https://en.wikipedia.org/wiki/Syngas
128
https://en.wikipedia.org/wiki/Power_station
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efficiency of the plant, and many new baseload power plants are combined cycle plants fired by natural
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gas.”
Efficiency of Thermal Power Plants
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Energy Content of Fuels (Thermal Energy Constants):
The thermal energy contained in fossil fuels may be expressed as Thermal Energy Constants, defined as the
amount of thermal energy produced (in BTUs) per kg of burned fuel.
1 BTU ≈ 1.055 kJ ≈ 1 kJ (exact definitions of the BTU vary).
Typical TEC values (from the textbook EEAI3) are: Petroleum liquid 45,000 BTUs/kg, Natural Gas 48,000,
Coal 27,000 and Dry Wood 19,000. Much of the heat energy generated by burning is lost as waste heat at the
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cooling tower, so overall system efficiencies are low, often well below 50%.
Heat Rate:
The EIA (U.S. Energy Information Administration) gives the following discussion regarding the efficiency of
different types of power plants, expressed as heat rates:
“One measure of the efficiency of a generator or power plant that converts a fuel into heat and
into electricity is the heat rate. The heat rate is the amount of energy used by an electrical
generator or power plant to generate one kilowatthour (kWh) of electricity. The U.S. Energy
Information Administration (EIA) expresses heat rates in British thermal units (Btu) per net
kWh generated. Net generation is the amount of electricity a power plant (or generator)
supplies to the power transmission line connected to the power plant. Net generation accounts
for all the electricity that the plant itself consumes to operate the generator(s) and other
equipment, such as fuel feeding systems, boiler water pumps, cooling equipment, and pollution
control devices... To express the efficiency of a generator or power plant as a percentage, divide
the equivalent Btu content of a kWh of electricity (which is 3,412 Btu) by the heat rate. For
example, if the heat rate is 10,500 Btu, the efficiency is 33%. If the heat rate is 7,500 Btu, the
efficiency is 45%... EIA only publishes heat rates for fossil fuel-fired generators and nuclear
power plants... There is a discussion of the method that EIA uses to estimate the amount of
energy consumed to generate electricity with renewable energy sources in Alternatives for
Estimating Energy Consumption, which includes a table with estimates for the conversion
efficiencies of noncombustible renewable energy sources (geothermal, hydro, solar, and wind
132
energy).”
129
130
131
132
ibid.
http://www.mcgoodwin.net/pages/thermodynamics.pdf
EEAI3 p. 71-72
http://www.eia.gov/tools/faqs/faq.cfm?id=107&t=3
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The EIA provides the following heat values by year for the stated energy sources (lower values mean greater
133
efficiency):
“Coal includes anthracite, bituminous, subbituminous and lignite coal. Waste coal and
synthetic coal are included starting in 2002... Petroleum includes distillate fuel oil (all diesel
and No. 1 and No. 2 fuel oils), residual fuel oil (No. 5 and No. 6 fuel oils and bunker C fuel oil,
jet fuel, kerosene, petroleum coke, and waste oil. Included in the calculation for coal,
petroleum, and natural gas average operating heat rate are electric power plants in the utility
and independent power producer sectors. Combined heat and power plants, and all plants in
the commercial and industrial sectors are excluded from the calculations. The nuclear average
heat rate is the weighted average tested heat rate for nuclear units...”
As stated in the discussion above, the efficiency of these fuels in the most recent year (2013) compared to the
equivalent Btu content of a kWh of electricity is readily calculated to be 33% for coal, 32% for petroleum, 43%
for natural gas, and 33% for nuclear energy, much lower than typical values for hydroelectric power.
Clearly, heat values have not improved much in the past 10 years, with the exception that natural gas heat
values have improved by 14%.
Looking at 2013 (the most recent EIA data), the heat values for various prime movers are shown as follows:
133
134
http://www.eia.gov/electricity/annual/html/epa_08_01.html including quote that follows immediately.
http://www.eia.gov/electricity/annual/html/epa_08_02.html data selected and edited by MCM
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17 May 2016
We may conclude for 2013 and comparing to the efficiency of the steam generator (about 34% efficiency for all
energy sources):
• the gas turbine burning petroleum is especially inefficient (only 25% efficiency), but the inefficiency is less
pronounced when burning natural gas (30%). But see above about how gas turbines should have high
efficiency.
• the internal combustion process has about the same efficiency as the steam generator (with 33%), somewhat
better with natural gas (36%), and
• that the combined cycle when burning petroleum has about the same efficiency as the steam generator (with
34%), but is significantly better when burning natural gas (efficiency 45%).
The last item is explained as follows: “In electric power generation a combined cycle is an assembly of heat
engines that work in tandem from the same source of heat, converting it into mechanical energy, which in
turn usually drives electrical generators. The principle is that after completing its cycle (in the first engine),
the working fluid of the first heat engine is still low enough in its entropy that a second subsequent heat
engine may extract energy from the waste heat (energy) of the working fluid of the first engine... In stationary
power plants, a widely used combination is a gas turbine (operating by the Brayton cycle) burning natural gas
or synthesis gas from coal, whose hot exhaust powers a steam power plant (operating by the Rankine cycle).
This is called a Combined Cycle Gas Turbine (CCGT) plant, and can achieve a best-of-class real [HHV=Higher
Heating Value] thermal efficiency of around 54% in base-load operation, in contrast to a single cycle steam
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power plant which is limited to efficiencies of around 35-42%.”
A coal fired thermal power plant is illustrated to follow:
135
136
136
https://en.wikipedia.org/wiki/Combined_cycle
https://en.wikipedia.org/wiki/Thermal_power_station
images by https://en.wikipedia.org/wiki/User:BillC , modified minimally by MCM:
https://commons.wikimedia.org/wiki/File:PowerStation3.svg and
https://en.wikipedia.org/wiki/File:PowerStation2.svg
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The person contributing this image offers the following additional key and explanation [minor alterations by
MCM]:
“1. [Hyperboloid wet probably natural draft] cooling tower. 2. Cooling water pump. 3.
Transmission line (3-phase). 4. Unit transformer (3-phase). 5. Electric generator (3-phase). 6.
Low pressure turbine. 7. Condensate extraction [boiler feed] pump. 8. Condenser. 9.
Intermediate pressure turbine. 10. Steam governor valve. 11. High pressure turbine. 12.
Deaerator. 13. Feed heater. 14. Coal conveyor. 15. Coal hopper. 16. Pulverised fuel mill. 17.
Boiler drum. 18. Ash hopper. 19. Superheater. 20. Forced draught fan. 21. Reheater. 22. Air
intake. 23. Economiser. 24. Air preheater. 25. Precipitator. 26. Induced draught fan. 27.
Chimney stack. [28. Feed pump between deaerator and feed heater, located differently on
image with key].
Coal is conveyed (14) from an external stack and ground to a very fine powder by large metal
spheres in the pulverised fuel mill (16). There it is mixed with preheated air (24) driven by the
forced draught fan (20). The hot air-fuel mixture is forced at high pressure into the boiler
where it rapidly ignites. Water of a high purity flows vertically up the tube-lined walls of the
boiler, where it turns into steam, and is passed to the boiler drum, where steam is separated
from any remaining water. The steam passes through a manifold in the roof of the drum into
the pendant superheater (19) where its temperature and pressure increase rapidly to around
200 bar and 570°C, sufficient to make the tube walls glow a dull red. The steam is piped to the
high pressure turbine (11), the first of a three-stage turbine process. A steam governor valve
(10) allows for both manual control of the turbine and automatic set-point following. The steam
is exhausted from the high pressure turbine, and reduced in both pressure and temperature, is
returned to the boiler reheater (21). The reheated steam is then passed to the intermediate
pressure turbine (9), and from there passed directly to the low pressure turbine set (6). The
exiting steam, now a little above its boiling point, is brought into thermal contact with cold
water (pumped in from the cooling tower) in the condenser (8), where it condenses rapidly back
into water, creating near vacuum-like conditions inside the condenser chest. The condensed
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water is then passed by a condensate pump (7) to a deaerator (12), then pumped by feedwater
pump (28) and pre-warmed, first in a feed heater (13) powered by steam drawn from the high
pressure set, and then in the economiser (23), before being returned to the boiler drum. The
cooling water from the condenser is sprayed inside a cooling tower (1), creating a highly visible
plume of water vapor, before being pumped back to the condenser (8) in cooling water cycle.
The three turbine sets are sometimes coupled on the same shaft as the three-phase electrical
generator (5) which generates an intermediate level voltage (typically 20-25 kV). This is stepped
up by the unit transformer (4) to a voltage more suitable for transmission (typically 250-500
kV) and is sent out onto the three-phase transmission system (3).
Exhaust gas from the boiler is drawn by the induced draft fan (26) through an electrostatic
precipitator (25) and is then vented through the chimney stack (27).”
Nuclear Power Plants
These are discussed in the textbook, chapter 4, p. 75-86. This topic warrants much more attention than I
have yet been able to give to it, particularly the environmental issues; waste disposal; risks of coolant loss
with overheating, hydrolysis at 1200°C, and fuel rod
melting at 2400°C; and potential for adverse use by
terrorists or other aggressors. Chapter 5 deals in part
with nuclear waste disposal and environmental
137
contamination.
Such plants depend on heat generated by nuclear
fission (fusion is not yet a viable option), which is used
to turn water into steam to drive steam turbines.
Worldwide, there are about 400 commercial nuclear
138
power plants (generating a total in 2014 of 2,410
TWh). Nuclear provides 10.6% of global domestic
139
electrical energy generation (2013 data from IEA) or
140
19.5% in 2014.
141
There are 99 operational power reactors in 61 commercial power plants in the US.
Typical generating
142
capacity per US reactor in 2014 ranges from 5 to 12 TWh (i.e., billions of kWh), with an average in 2010 of
143
7.8 TWh per reactor (i.e., 7,759,000 MWh).
U.S. electricity generated from nuclear energy in 2014 totaled 797 billion kWh (797 TWh), which comprised
144
19.5% of total US electricity generation (4,092 TWh).
In Washington state as of 2013, the boiling water reactor in the Columbia Generating Station 2 near Richland
annually generates 8.5 billion kWh (8.5 TWh), comprising 7.5% of Washington electricity generation.
145
There has been
Hydroelectric provided 68.8%, natural gas 10%, coal 5.9%, and renewable and other 7.8%.
146
little growth in recent years in nuclear generation of electricity in the US (see graph).
137
138
139
140
141
142
143
144
145
146
EEAI3 p. 97
http://www.world-nuclear.org/info/Facts-and-Figures/Nuclear-generation-by-country/
https://www.iea.org/publications/freepublications/publication/key-world-energy-statistics-2015.html
http://www.world-nuclear.org/info/facts-and-figures/nuclear-generation-by-country/
EEAI3 p. 75 and http://www.eia.gov/tools/faqs/faq.cfm?id=207&t=3
http://www.eia.gov/nuclear/reactors/stats_table1.html
computed by MCM from http://www.eia.gov/nuclear/reactors/stats_table1.xls
http://www.nei.org/Knowledge-Center/Nuclear-Statistics/US-Nuclear-Power-Plants and
http://www.world-nuclear.org/info/country-profiles/countries-t-z/usa--nuclear-power/
http://www.nei.org/CorporateSite/media/filefolder/Backgrounders/Fact-Sheets/Washington-State-Fact-Sheet-2014_1.pdf
http://www.eia.gov/nuclear/generation/index.html
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148
Reactors are typically boiling water reactors BWR (35 in the US) or pressurized water reactors PWR (65 in
the US). In BWR, water that moves through the reactor core is allowed to boil into steam that is used to turn
the turbine directly. In contrast, PWRs keep water under pressure so that it heats, but does not boil. Water
from the reactor [radioactive] and the water in the steam generator that is turned into steam never mix..
Fuel
The primary fuels used in power reactors are the fissile isotopes of uranium: 235U enriched to 3 to 5%, with
the balance of uranium as the essentially non-fissile isotopes 238U and 234U. Some reactors can breed 239Pu
from fertile isotopes such as 238U and 232Th. A fissile (fissionable) isotope is “capable of sustaining a nuclear
fission chain reaction... with neutrons... The predominant neutron energy may be typified by either slow
neutrons (i.e., a thermal system [as with 235U]) or fast neutrons [as with 238U though much less probable].
Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear
149
explosives.”
The fission of
235U
releases energy as follows:
150
“The number of neutrons and the specific fission products from any fission event are governed by statistical
probability... However, conservation laws require the total
number of nucleons and the total energy to be conserved.
The fission reaction in U-235 produces fission products
such as Ba, Kr, Sr, Cs, I and Xe with atomic masses
distributed around 95 and 135. Examples may be given of
typical reaction products, such as:
U-235 + n  Ba-144 + Kr-90 + 2n + about 200 MeV
U-235 + n  Ba-141 + Kr-92 + 3n + 170 MeV
U-235 + n  Zr-94 + Te-139 + 3n + 197 MeV
In such an equation, the number of nucleons (protons +
neutrons) is conserved, e.g. 235 + 1 = 141 + 92 + 3, but a
small loss in atomic mass [the mass deficit] may be shown
to be equivalent to the energy released [through E = mc2].
Both the barium and krypton isotopes subsequently decay
and form more stable isotopes of neodymium and yttrium,
with the emission of several electrons from the nucleus
(beta decays). It is the beta decays, with some associated
gamma rays, which make the fission products highly
Probability yields from fission (shown as % probability)
233
235
239
for U, U, Pu, and a U-Pu mixture.
Horizontal axis is atomic mass number
(i.e., nucleon number A = Z + N)
235
U peaks on left at A ≈ 95 and on the right at A≈134
The total binding energy released in fission of an atomic
nucleus varies with the precise break up, but averages
about 200 MeV for U-235 or 3.2 x 10-11 joule. [These are
total energy release figures]... That from U-233 is about the same, and that from Pu-239 is about 210 MeV
per fission. (This contrasts with 4 eV or 6.5 x 10-19 J per atom of carbon burned in fossil fuels.)”
A clearer analysis to follow of average fission energy released by 235U fission explicitly deals with the energy
carried away by neutrinos from beta decay. As the table further below shows, “the fission of one atom of U235 generates [an average of ] 202.5 MeV = 3.24 × 10−11 J, which translates to 19.54 TJ/mol, or 83.14
151
TJ/kg.”
147
148
149
150
151
https://en.wikipedia.org/wiki/Fissile_material
http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Introduction/Physics-of-Nuclear-Energy/ quoted & paraphrased MCM
https://en.wikipedia.org/wiki/Uranium-235
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To compare coal to nuclear: The thermal energy content of 1 kg of coal is 29.3 MJ or 2.93 × 107 J.
From
above, the thermal energy content of 235U is 83.14 TJ/kg = 8.314 × 1013 J. On a per weight basis and
neglecting various inefficiencies, 1 kg of 235U is equivalent to 2,837,543 kg of coal, so the ratio is 2.84× 106.
The World Nuclear Association WNA estimates that to produce 1 GW of electricity over a year requires about
27 tonnes of fresh enriched uranium fuel each year. This is needed to keep the gradually depleting 75 tonnes
153
of low enriched uranium in the reactor adequately replenished. The WNA also states,
“An issue in operating reactors and hence specifying the fuel for them is fuel burn-up. This is
measured in gigawatt-days per tonne [GWd/t of enriched fuel] and its potential is proportional
to the level of enrichment. Hitherto a limiting factor has been the physical robustness of fuel
assemblies, and hence burn-up levels of about 40 GWd/t have required only around 4%
enrichment. But with better equipment and fuel assemblies, 55 GWd/t is possible (with 5%
enrichment), and 70 GWd/t is in sight, though this would require 6% enrichment. The benefit
of this is that operation cycles can be longer – around 24 months – and the number of fuel
assemblies discharged as used fuel can be reduced by one third. Associated fuel cycle cost is
expected to be reduced by about 20%.
154
155
The following table clarifies that the energy of the [approximately 6 electron-type ] anti-neutrinos (8.8 MeV,
arising from beta-decays) is carried away and does not contribute to reactor heat generation. A confusingly
similar amount of energy, 8.8 MeV for 235U, is added to the reactor heat when certain of the neutrons that
were released in a fission reaction are finally captured by nuclei but do not themselves lead to new fission.
Thus, although an average of 211.3 MeV of energy in multiple forms including anti-neutrinos are released per
fission, only 202.5 MeV are available to add to reactor heat and therefore electrical generation.
Reactor neutrons are categorized by energy (though definitions seem to vary widely):


152
153
154
155
156
156
A Thermal neutron is a free neutron with a kinetic energy of about 0.025 eV (about 4.0×10−21 J or 2.4
MJ/kg, hence a speed of 2.2 km/s), which is the energy corresponding to the most probable velocity at
a temperature of 290 K...
An Epithermal neutron has 0.025 eV < KE < 1 eV (however, definitions vary)
https://www.euronuclear.org/info/encyclopedia/coalequivalent.htm
http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Introduction/Nuclear-Fuel-Cycle-Overview/
https://en.wikipedia.org/wiki/Uranium-235
http://t2k-experiment.org/neutrinos/sources-and-experiments/
https://en.wikipedia.org/wiki/Neutron_temperature , also
http://www.nuclearglossary.com/suites/nuclearglossary_neutrons.html
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
A Fast neutron is a free neutron with a kinetic energy level close to 1 MeV (100 TJ/kg), hence a speed
157
of 14,000 km/s or higher... [Some authors use 100 keV or even 10 keV as the lower cutoff value. ]
Nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e. 20,000 km/s)...
However the range of neutrons from fission follows a Maxwell–Boltzmann distribution from 0 to about
14 MeV... and the mode of the energy is only 0.75 MeV, meaning that fewer than half of fission
neutrons qualify as "fast" even by the 1 MeV criterion.
The following quoted text and log-log graph describe the probability of fission interactions for 235U and 239Pu.
158
The “fission neutron energy” presumably refers to the range of energy of neutrons given off during fission:
159
This facilitating
(Note: a useful table of all credible isotopes, including radioisotopes, is given here.
assessment of odd vs. even numbers of neutrons.)
“Fission may take place in any of the heavy nuclei after capture of a neutron. However, lowenergy (slow, or thermal) neutrons are able to cause fission only in those isotopes of uranium
and plutonium whose nuclei contain odd numbers of neutrons (e.g. U-233, U-235, and Pu239). Thermal fission may also occur in some other transuranic elements whose nuclei contain
odd numbers of neutrons. For nuclei containing an even number of neutrons, fission can only
occur if the incident neutrons have energy above about one million electron volts (MeV) [“fast”
neutrons]. (Newly-created fission neutrons are in this category and move at about 7% of the
speed of light, while moderated neutrons move a lot slower, at about eight times the speed of
sound.)
The probability that fission or any another neutron-induced reaction will occur is described by
the neutron cross-section for that reaction. The cross-section may be imagined as an area
surrounding the target nucleus and within which the incoming neutron must pass if the
reaction is to take place. The fission and other cross sections increase greatly as the neutron
velocity reduces from around 20,000 km/s to 2 km/s, making the likelihood of some
interaction greater. In nuclei with an odd-number of neutrons, such as U-235, the fission
cross-section becomes very large at the thermal energies of slow neutrons.”
157
158
159
http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Introduction/Physics-of-Nuclear-Energy/
https://en.wikipedia.org/wiki/Table_of_nuclides_%28complete%29
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The following graph, also in log-log format, depicts the fission cross sections for 6 isotopes: the 2 lowermost
curves (with lowest probability, colors black and blue) are for 238U and 232Th, while the upper four, all rather
similar, are for 233U, 235U, 239Pu, and 241Pu.
A summary of fission cross sections for many isotopes may be found here.
161
There is ongoing modest interest in developing reactors that can use the fertile (non-fissile) radioisotope of
Thorium 232Th, which is also a primary fuel found in nature. It is more abundant than uranium, in a reactor
it breeds fissile 233U, and is well suited for molten salt reactors, but the issues appear to be complex and I
162
have not delved much into this subtopic.
160
161
162
http://thorea.wikia.com/wiki/Thermal,_Epithermal_and_Fast_Neutron_Spectra
http://nuclearweaponarchive.org/Nwfaq/Nfaq12.html
http://www.world-nuclear.org/info/current-and-future-generation/thorium/
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Nuclear Power Plant Design
The following diagram depicts a representative Pressurized Water Reactor (PWR) plant:
163
Not shown is the cooling tower to handle the waste heat.
163
http://josiah.berkeley.edu/2008Spring/ER102/Handouts/ER102_nuclear_power_handout.pdf
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Another diagram of a Pressurized Water Reactor (PWR) plant follows:
164
165
RHR = residual heat removal system;
Possibly unfamiliar acronyms :
RHR HX = RHR Heat Exchanger; PZR = Pressurizer; SG = steam generator;
RCP = reactor coolant pump; HP = high pressure [turbine]; LP = low pressure [turbine];
MSR = moisture separator reheater; FW HTR = feedwater heater
I have not discussed the role (for conventional reactors) of
the moderator (for slowing neutrons, usually water H2O, heavy water D2O, or graphite C),
control rods (for controlling the rate of the nuclear chain reaction, especially boron-10, silver-107,
166
 the pressure vessels and tubes, and
 the containment structure.
Reactors can be classified by fuel, moderator, coolant, generation, fuel phase (liquid or solid), or use. Other
167
types of reactors that are or someday may be employed in nuclear power plants include:








164
165
166
167
168
169
Pressurized Heavy Water Reactor (PHWR, CANDU)—in Canada, India, uses 2H deuterium as coolant
and moderator
Advanced Gas-cooled Reactor (AGR & Magnox)—in UK, uses CO2 as coolant and graphite as
moderator. The Magnox Gas-cooled Reactor design was supplanted by the AGR.
Light Water Graphite Reactor (RBMK & EGP)—in Russia, uses water as coolant and graphite as
moderator. RBMK = Reaktor Bolshoy Moschnosti Kanalniy = high-power channel reactor. Chernobyl
was of this design. EGP are small scaled down versions of the RBMK.
168
Fast Neutron Reactor (FBR) —in Russia, uses liquid sodium as coolant and no moderator. More
Liquid-metal fast-breeder reactor (LMFBR)
169
170
Other Advanced Reactors under development: Generation III and Generation IV reactors. The
latter include:
These NRC compiled abbreviations are “in common use in the nuclear industry and regulatory community.”
http://large.stanford.edu/courses/2011/ph241/grayson1/
http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Power-Reactors/Nuclear-Power-Reactors/
http://www.world-nuclear.org/info/Current-and-Future-Generation/Fast-Neutron-Reactors/
https://en.wikipedia.org/wiki/Generation_III_reactor
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o
o
o
o
o
o
Gas-cooled fast reactor GFR
Molten salt reactor MSR
Sodium-cooled fast reactor SFR
Supercritical water reactor SCWR
171
Very-high-temperature gas reactor VHTR (including Pebble-bed reactors PBR).
Hydrogen gas production will be an integral part of the VHTR.
172
A 2014
A detailed 2003 color presentation for the Gen IV reactor candidates is given here.
173
update to the Gen. IV goals, published by the GenIV International Forum (GIF), is given here.
Renewable Energy Resources
Material covered on Solar, Wind, Geothermal, Biomass, and Hydrokinetic electricity generation derives mostly
174
Regrettably, I did not find time to do a summary of this important and far-reaching topic.
from chapter 6.
Electrical Transmission
Material here derives in part from chapter 2, chapter 7, and chapter 8.
US Electric Transmission Grid
Most electrical power is transmitted long distances by means of 3 high voltage conductors carrying 3-phase
AC voltage. There is usually no neutral conductor, though there may be a ground conductor. In recent years,
there has been increasing interest in DC transmission lines for certain situations.
US (lower 48) Power Grid c. 2007
170
171
172
173
174
175
, does not show DC lines
Example of one of the few
176
DC interties in the US.
http://www.world-nuclear.org/info/nuclear-fuel-cycle/power-reactors/generation-iv-nuclear-reactors/
https://en.wikipedia.org/wiki/Generation_IV_reactor and
https://en.wikipedia.org/wiki/Nuclear_reactor#Reactor_types
http://www.engr.utk.edu/nuclear/colloquia/slides/Gen%20IV%20U-Tenn%20Presentation.pdf
EEAI3 p. 99-212.
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Categories of Transmission Voltage
(per IEC 60038 = International Electrotechnical Commission)
Low Voltage
High Voltage
Ultra High Voltage
177
≤ 1000 V
Medium Voltage
35 kV to 230 kV
Extra High Voltage
178
> 800 kV (up to as high as 1150 kV )
1,000 to 35,000 V
>230 kV
Transmission and Distribution Line Conductors 179
Conductors are stranded (made of multiple strands for greater flexibility). Aluminum is not quite as good a
conductor as copper, but it is much lighter and cheaper and thus is preferred.
AAC
AAAC
ACSR
ACAR
175
176
177
178
179
All Aluminum Conductor.
short spans in coastal areas to reduce corrosion.
All Aluminum Alloy Conductor:
good strength and corrosion resistance
Aluminum Conductor Steel Reinforced: stronger for longer spans but galv. steel can corrode.
Aluminum Conductor Aluminum-Alloy Reinforced: reduced corrosion, stronger.
https://commons.wikimedia.org/wiki/File:UnitedStatesPowerGrid.jpg fr. FEMA, ?2007 or earlier,
does not show HVDC lines such as Pacific DC Intertie, Path 27, etc.
https://en.wikipedia.org/wiki/Pacific_DC_Intertie
http://www.electrotechnik.net/2011/03/voltage-classification-lv-mv-and-ehv.html
https://en.wikipedia.org/wiki/Ekibastuz%E2%80%93Kokshetau_high-voltage_line
http://www.southwire.com/support/TransmissionConductoraReviewOfTheDesignandSelectionCriteria.htm
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Bundled High Voltage Conductors
On very high voltage transmission lines with
V > 230 kV, multiple subconductor cables are
bundled together but held apart by (typically)
180
These multiple connected
conducting spacers.
subconductor cables (consisting of many flexible
strands of conducting metal) function like a single
conductor and together carry a single phase of the (typically 3-phase) voltage. They are used to reduce
electric field strength and energy losses (and noise) due to corona discharge. This is because E (electric field)
is roughly a function of V/d where d is the effective overall diameter. The diameter d is effectively increased
by the spacing out of the subconductors. These have lower reactance and electric field, as well as improved
AC skin effect, but at the cost of greater wind resistance and expense.
Typical Double Circuit High Voltage Power Line Configuration and Power Transmitted
In the photo above right (of a power line in England),
181
I infer the following likely characteristics:
Terminology about these HV wires, cables, and conductors can be confusing and inconsistent. I will refer to
what carries a single phase as a conductor; the components of a bundled conductor are subconductors
consisting of multiple strands. A conductor carrying one phase is a line or phase.
A ground / Earth conductor is the single conductor/wire at the very top. There are 2 parallel sets of naked 3phase high voltage lines (i.e., two 3-phase circuits), 6 conductors in all and spaced widely apart. Each 3phase conductor (phase or line) consists of 4 bundled subconductors, with each conductor bundle separated
from the metal tower by long insulators. It is likely that the 2 sets of 3-phase lines depicted here carry exactly
the same voltage and phase because they originate at a common point. (The lines however may be
182
“transposed” along the way to achieve “optimum phasing”.)
Circuits are often doubled to reduce inductive reactance (and resistance if applicable) and thereby increase
183
the combined current carrying capacity. In a rough calculation from the textbook, maximum power of a
transmission line is given by
Pmax =
180
181
182
183
3V0 Ef
X
http://www.electrotechnik.net/2011/02/bundled-conductors-in-tranmission-lines.html
(image slightly modified MCM);
https://en.wikipedia.org/wiki/Electric_power_transmission
EEAI3 p. 448 (in chapter 12)
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V0 = Voltage of the infinite bus to which the transmission line connects
Ef = Equivalent rms field voltage
X = total inductive reactance, combining that from the synchronous generator Xs
and of the transmission line Xl
where
The resistance is said to be negligible compared to the inductive reactance. Presumably, total inductive
reactance X here has factored in any reduction by capacitive reactance.
If V0 = 230 kV, Ef = 210 kV, Xl = 10 Ω, and Xs = 2 Ω, this single 3-phase circuit can carry
Pmax =
3V0 Ef
=
Pmax =
3V0 Ef
=
X
230 × 210
= 4.0 GW
230 × 210
= 6.9 GW
(2+10)
If the transmission line is doubled, the maximum power rises to:
X
(2+
10×10
)
10+10
Doubling the transmission lines in this example produces a 71% increase in Pmax, thus not a full doubling of
Pmax.
Transmission line inductive reactance is also reduced (and thus Pmax raised) by the use of bundling described
above. However, inductive reactance is increased by increasing spacing between the phases, a necessity with
high voltage lines. More details follow
Note: It is not yet entirely clear to me why Ef can be less than V0 and yet the generator imparts energy to the
infinite bus.
Transmission Line Inductive Reactance
Inductive reactance should be reduced as much as possible. The following elegant resource on mathematical
184
analysis of transmission lines, far beyond my skill level, derives the following relationships and provides the
quoted text in this section (which I have attempted to interpret):
Single Conductor
For a single straight wire of infinite length, the combined internal and external inductance is given by
Ltot =
where
µ0
2π
D
ln �GMR� (H/m)
Ltot = Total inductance in H/m of a single conductor carrying A/C
and concentrated at the skin surface
μ0 = vacuum permeability (magnetic constant) = 4π × 10−7 H m-1
D = distance from conductor center to the sampling point (m)
GMR = Geometric Mean Radius for the conductor (m). “GMR = e−1/4 r = 0.7788 r.
GMR can be considered as the radius of a fictitious conductor
assumed to have no internal flux but with the same inductance
as the actual conductor with radius r.”
Two-Wire, Single-Phase Line:
The two wires or conductors A and B are assumed to be parallel, solid, and carrying antiparallel currents.
They are separated by on-center distance D > r, and each conductor has true radius r. They are linked at
point P by magnetic fluxes λAAP, λABP, λBAP, and λBBP. If the sampling point P is considered to be shifted to
infinity, and A and B have identical radii, then total inductance per m for the one-phase system is:
L1−phase system =
µ0
π
D
ln �GMR� (H/m)
184
Manuel Reta-Hernández, Chapter 14 in Electric Power Generation, Transmission, and Distribution, Third
Edition, 2012, entire book available from CRCNetBase through a university proxy. (An earlier 2006 version
without access restriction may be found here.) These resources could provide hours of pleasurable reading.
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L1-phase system = Total inductance in H/m of the combined conductor system carrying A/C
D = on-center distance between the two conductors (m)
GMR = Geometric Mean Radius for each conductor (m)”
where
The inductance for this system is twice that of a single conductor.
Here, the GMR applies to each conductor. If the conductor is stranded, GMRstranded is usually available from
the manufacturer (otherwise the computation is rather involved).
If the conductors are bundled as 4 stranded subconductors per bundle with spacing d (m) between nearest
neighbors, the GMR for the bundle becomes:
4
GMR 4 bundle connectors = 1.09 �GMR stranded d3
where
d = on-center distance between bundle subconductors
GMRstranded = Geometric Mean Radius for each stranded subconductor (m)”
Here, d is greater than GMR. Inspection of this relationship suggests that GMR4 bundle connectors > GMRstranded.
Therefore, the GMR appearing in the L equation is larger, so overall inductance is smaller for bundling.
Balanced 3-Phase Transmission Line with Phases Arranged Symmetrically
In this idealized example, the three conductors A, B, and C are again assumed to be parallel. They are
separated by equal on-center distance D > r. The inductance per m for each phase of the three-phase system
is:
Lphase =
where
µ0
D
ln �GMR
2π
phase
� (H/m)
Lphase= Inductance in H/m of one phase conductor
D = on-center distance between any two phase conductors (m)
GMRphase = Geometric Mean Radius for each phase conductor, bundled or not (m)
This value is the same as for a single conductor. For the three phases, I infer that the total system
inductance would be multiplied by 3, so
L3−phase symmetrical system =
3µ0
2π
D
ln �GMR
phase
� (H/m)
Thus, total system inductance for this 3-phase arrangement is only 1.5 times that of the single phase system.
Although it is usually infeasible to maintain a symmetrical arrangements over long distance, “it is possible to
assume symmetrical arrangement in the transmission line by transposing the phase conductors. In a
transposed system, each phase conductor occupies the location of the other two phases for one-third of the
total line length...”
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Power Electronics
This section is based in part on chapter 10. I have little experience in this field, can only touch on a few of
the many relevant items, and will not attempt to review semiconductor principles in detail. The course Lab 1
dealt with power electronics, but as an auditor I was not to be present while the labs were in progress.
However, the equipment was demonstrated to me by the knowledgeable TA and 2nd year MSEE graduate
student, John J. Sealy. (Incidentally, John advises me that budding experimentalists may obtain a wide
185
186
array of electronic components from Digi-Key and SparkFun. )
The term Power Electronics (PE) has come to mean the application of solid-state [SS] electronics to the control
and conversion of electric power. Electrical energy here is expressed in Watts rather than as bytes or
informational signals, etc.) Use of Power Electronics, including in high voltage applications, has been rapidly
Energy conversion and switching appear integral to power electronics: One author states,
“Power Electronics is the art of converting electrical energy from one form to another in an
efficient, clean, compact, and robust manner for convenient utilisation... In Power Electronics
all devices are operated in the switching mode - either 'FULLY-ON' or 'FULLY-OFF'...
Power Electronics involves the study of
Power semiconductor devices - their physics, characteristics, drive requirements and their protection
for optimum utilisation of their capacities,
 Power converter topologies involving them,
 Control strategies of the converters,
 Digital, analogue and microelectronics involved,
 Capacitive and magnetic energy storage elements,
 Rotating and static electrical devices,
 Quality of waveforms generated,
 Electro Magnetic and Radio Frequency Interference
187
 Thermal Management”
188
Power conversions include:

• AC to DC (Rectifier, Mains power supply unit (PSU), Switched-mode power supply, etc.)
DC to AC (Inverter)
DC to DC (DC-to-DC converter, Voltage Regulator, Linear Regulator, etc.)
AC to AC (Transformer/autotransformer, Voltage converter, Voltage regulator, Cycloconverter,
Variable-frequency transformer
Some of these are demonstrated below.




The precursors to SS power electronics include vacuum tube devices (beginning with vacuum diodes, invented
by John Fleming in 1904) and the transistor (1947). The transistor was named by John R. Pierce of Bell
Labs, who stated, “[The name is] an abbreviated combination of the words ‘transconductance’ or ‘transfer’,
and ‘varistor’. The device logically belongs in the varistor family, and has the transconductance or transfer
189
impedance of a device having gain, so that this combination is descriptive.”
SS PE devices may be divided into three types, on the basis of numbers of semiconducting layers:
Two layer devices such as Diodes
Three layer devices such as Transistors,
Four layer devices such as Thyristors.
There are also hybrid devices: Insulated Gate Bipolar Transistor IGBT and Darlington transistor.
185
186
187
http://www.digikey.com/ for new mainstream industrial parts
https://www.sparkfun.com/ for new and used parts, hobbyist and industrial
Kharagpur. "Power Semiconductor Devices", Module 1, Lesson 1, in
http://www.nptel.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Power%20Electronics/New_index1.html
188
189
https://en.wikipedia.org/wiki/Electric_power_conversion
https://en.wikipedia.org/wiki/History_of_the_transistor
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SS PE devices in converters often perform high speed switching,
Diodes
190
Etymology: di=two + electrode.
There are many types of diodes P-N Junction diodes consist of 2
semiconductor layers, p and n. The diode's behavior in a circuit “is given by its current–voltage characteristic,
or I–V graph... [image to follow] The shape of the curve is determined by the transport of charge carriers
through the so-called depletion layer or depletion region that exists at the p–n junction between differing
191
semiconductors...”
The diode symbol (shown above on the left) includes an arrowhead on the positive anode side directed toward
the negative cathode, and indicating the direction that conventional (positive charges) current passes freely.
The I–V graph shows that when anode to cathode voltage across the diode VAK is biased negative, essentially
no current (or just a trickle, Is) flows until an excessive breakdown voltage VBR is reached, at which point a
high avalanche current destroys the diode. When the diode is forward biased with positive VAK voltage, the
diode at about 0.7 V becomes like an ON (closed) switch offering little resistance, and current flow is
190
http://www.electronicshub.org/types-of-diodes/ and https://en.wikipedia.org/wiki/Diode
text and main graphic: https://en.wikipedia.org/wiki/Diode
191
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determined mostly by the load resistance. Modern power diodes are constructed to handle currents into the
192
10 kA range, and when fabricated and/or used in series, can process voltages as high as 1 MV.
Examples of diode use in Lab 1 are presented further below.
Bipolar Junction Transistors BJT
These consist of 3 layers, N-P-N (common in power electronics, especially for high speed ON/OFF switching)
193
or P-N-P layers. The middle Base layer is thin, thus the transistor differs from back-to-back diodes.
Bipolar transistors use “both electron and hole charge carriers. In contrast, unipolar transistors, such as
field-effect transistors [FETs], only use one kind of charge carrier. For their operation, BJTs use two junctions
194
BJT transistors offer high switching speeds and
between two semiconductor types, n-type and p-type.”
high reliability. The main drawbacks are (1) high internal heating in the saturation region when IC is very
high, and (2) the transistor will remain closed (ON) only when maximum base current is present, causing high
195
losses in the base circuit.
Schematic Diagram and structure of
196
Note that the base layer is
NPN BJT.
shown as relatively thin.
The voltage between the collector and
emitter is VCE, between base and
collector is VCB, and between base and
emitter is VBE.
A twin letter subscript (e.g., VCC or VBB)
indicates a power supply voltage source.
Vcc is the collector supply; VBB is the
base supply; VEE is the emitter supply.
VCC is the voltage actually at the supply
source which, after passing through the
197
Conventional positive current IC enters
at the collector C, current IB enters at
the base B, and current IE exits at the
emitter E.
192
193
194
195
196
197
198
The characteristic curves depicting IC vs. VCE show 3 regions.
198
In the cutoff region, the base current is 0 and IC is nearly 0, so that
the transistor is effectively switched OFF (switch open).
In the saturation region, the transistor is effectively switched ON
(switch closed), VCE is nearly 0, and IC is determined primarily by
the supply voltage VCC , which typically passes through a load
resistor RL to reach the collector.
http://www.chtechnology.com/rectifiers.html and EEAI3 p. 319
EEAI3 p. 330
https://en.wikipedia.org/wiki/Bipolar_junction_transistor text and first image, by author:Inductiveload
EEAI3 p. 322
http://www.electronics-tutorials.ws/transistor/tran_2.html
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The following describes some interesting details about the region of operation useful in audio and video
amplifiers but not usually in power electronics. In the linear region (aka active region or mode), the transistor
acts as an amplifier , and IC = βIB. Power transistors cannot operate in this region long due to excessive
heating. The DC current gain or amplification β = IC/IB (also shown as hFE or βDC) is almost constant for
increasing IB, and the amplification is nearly linear. β can be in the hundreds. The term hFE derives from the
h-parameter model, 'F' is from forward current amplification, and 'E' refers to the transistor operating in a
199
“In amplifier design applications, the Q-point [quiescent point]
common emitter (CE) configuration.
corresponds to DC values for IC and that are about half their maximum possible values,,,. This is called
midpoint biasing and it represents the most efficient use of the amplifiers range for operation with AC signals.
The range that the input signal can assume is the maximum and no clipping of the signal can occur
200
The base voltage is biased to operate
(assuming that the signal range is less than the maximum available).”
halfway between its cut-off and saturation regions, thereby allowing the transistor amplifier to accurately
reproduce the positive and negative halves of the highest amplitude AC input signal superimposed upon this
201
positive DC biasing voltage.
H-Bridge circuit for DC to AC conversion
202
The following material from course Lab 1 and the textbook demonstrates use of the NPN BJT to produce DC
to AC conversion using a single phase H-Bridge circuit. “An H bridge is an electronic circuit that enables a
voltage to be applied across a load in either direction. These circuits are often used in robotics and other
203
According to lab TA John J. Sealy, this
applications to allow DC motors to run forwards and backwards.”
lab actually uses Insulated-gate bipolar transistors (IGBTs, see below).
H-Bridge circuit for DC to Single Phase AC
conversion: The triggering components, which
determine the switching period of the transistors, are
not shown but implied. Black arrows indicate current
flow passing through Q1 and Q2; Red arrows indicate
current flow passing through Q3 and Q4. The red
current direction through the load is the reverse of the
black current flow through the load, thus providing a
squarish type of AC which is not sinusoidal. The
input VS, triggering, and load voltages are graphed to
the right.
Yellow (Ch1) is input DC voltage (a bit noisy)
measuring 83V rms. Red square wave (Ch4) =
triggering base voltage, peaks are off scale in this
image but more than 4V peak, 3.4V rms, duty cycle
appears asymmetrical [but I lack specifics],
frequency is 315 Hz. Blue (Ch2) is output voltage of
80.6 V rms 316Hz AC.
An analogous DC to AC conversion can be done with conversion of a single DC source to 3-phase AC, using a
204
six-pulse converter having 6 transistors.
199
200
201
202
203
204
https://en.wikipedia.org/wiki/Bipolar_junction_transistor#h-parameter_model
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/lecture-notes/20_bjt_2.pdf
http://www.electronics-tutorials.ws/transistor/tran_2.html paraphrased and interpreted
EEAI3 p. 351, schematic diagram from Lab 1 amended by MCM
https://en.wikipedia.org/wiki/H_bridge
EEAI3 p. 352
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Pulse Width Modulation (PWM) for DC to AC conversion
This is another technique for converting DC to AC, in order to control the magnitude of the output voltage, the
205
The textbook EEAI3 did not
frequency of the output voltage, and the phase sequence of the output voltage.
provide a circuit example (other than the 3-phase DC/AC inverter on p. 353), and I have not studied this topic
206
PWM should not be confused with PCM or Pulse-code modulation, which is used to sample and encode
(digitize) an analog audio signal as digital audio for use with CDs, DVDs, digital telephony, and other audio
streams.
A carrier signal vcarrier of fixed rms voltage and fixed high frequency is used, along with 3 control signals of
adjustable frequency and voltage. (For single phase, only one control signal is needed.) The PWM circuit
determines the switching status of the 6 transistors in the 3-phase DC/AC inverter (4 transistors in single
phase). The control frequencies are shifted from each other by the requisite 120º for balanced 3-phase. In
one PWM 3-phase technique, the switching of transistors Q1 and Q4, which join emitter to collector at point a,
is determined as follows (where Δva = va-control - vcarrier):
If Δva > 0, Q1 is closed and Q4 is open
If Δva < 0, Q1 is open and Q4 is closed
The varying switching determines the duration of pulses (for example, pulses that alternate between voltage
va0 or 0, where va0 is measured between point a and the negative side of the DC source). The varying pulse
width is the basis for the name “width modulation”. The line-to-line voltage between a and b is given by vab =
va0 - vb0.
A graphic, adapted from an audio example, depicts the high frequency carrier (at top, a sawtooth pattern in
this case), the width-modulated pulses (at the bottom, for example, vab = va0 - vb0), and the smoothed output
207
AC waveform for one phase (in the middle, oscillating at the frequency of the control frequency):
Buck Boost DC to DC converter
Another example of power conversion that was examined in the course Lab 1 is the buck-boost converter,
which is used to perform DC to DC conversion (step-down or step-up voltages, accompanied by reversed
208
It makes use of both an NPN BJT as well as a conventional diode. (The text also describes the
polarity).
buck converter or chopper, for step-down, and the boost converter, for step-up.)
205
EEAI3 p. 356
https://en.wikipedia.org/wiki/Pulse-code_modulation
207
slightly by MCM
208
EEAI3 p. 349
206
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Buck Boost DC to DC converter
The transistor acts as a switch. When ON, energy
flows into and is stored in the inductor, and blocked
from the load resistor by the diode. When OFF, energy
flows out of the inductor into the load (in the reverse
polarity compared to the DC source, so current is
allowed by the diode). The capacitor smoothes the
fluctuations. The average value of the load voltage is
controlled by adjusting the duty ratio (duty cycle),
defined as (ton / ton + toff), thus the fraction of
commutation period τ for which the transistor is ON
209
(closed).
Yellow (Ch1) is input DC voltage (a bit noisy)
measuring -89V average. Red square wave (Ch4) =
triggering base voltage, peaks are at 4V peak, 3.6V
rms, duty cycle is asymmetrical [but I lack specifics],
frequency is 1084 Hz. Blue (Ch2) is output voltage
of +30V average DC value (though varying irregularly
at 213Hz). This is an example of both reversing
polarity and reducing the absolute value of the
magnitude of the varying DC voltage.
In the Buck Boost DC to DC converter example to the
right:
Yellow (Ch1) is input DC voltage (a bit noisy)
measuring -19.4V average. Red square wave (Ch4) =
triggering base voltage, peaks are at 4V peak, 2.5V
rms, duty cycle is asymmetrical and differs from above
[but again I lack specifics], frequency is same as above
at 1084 Hz. Blue (Ch2) is output voltage of +33.7V
average DC value (though varying irregularly). This is
an example of both reversing polarity and increasing
the absolute value of the magnitude of the varying DC
voltage.
Silicon Controlled Rectifiers SCR
This is a 4 semiconductor layer (PNPN) device consisting of P and N layers at the Anode A, then a Gate layer
G, and finally an N layer at the Cathode (K). According to the textbook EEAI3, the SCR is a member of the
210
larger family called thyristors (etymology: thura=gate + transistor).
209
210
https://en.wikipedia.org/wiki/Buck%E2%80%93boost_converter
https://en.wikipedia.org/wiki/Thyristor
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211
In the diagram above, the diode symbol with Anode and Cathode as usual is supplemented by a gate
electrode G. The 4 semiconductor layer PNPN structure is shown, with a physical diagram and an equivalent
schematic depicting two tightly coupled bipolar junction transistors (BJTs). The upper BJT is has PNP layers,
212
the lower has NPN.
The I–V graph above depicts responses for thyristors including SCRs as follows (where V is the Anode to
213
Cathode voltage and I is the Anode to Cathode current).
“In a conventional thyristor, once it has been switched ON [closed] by the gate terminal, the
device remains latched in the ON-state [closed] (i.e. does not need a continuous supply of gate
current to remain in the ON state), providing the anode current has exceeded the latching
211
212
213
https://en.wikipedia.org/wiki/Bipolar_junction_transistor
https://en.wikipedia.org/wiki/Thyristor text and image
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current (IL). As long as the anode remains positively biased, it cannot be switched OFF [open]
until the anode current falls below the holding current (IH).
A thyristor can be switched OFF [open] if the external circuit causes the anode to
become negatively biased (a method known as natural, or line, commutation)...
After the current in a thyristor has extinguished, a finite time delay must elapse before
the anode can again be positively biased and [yet] retain the thyristor in the OFF-[open] state.
This minimum delay is called the circuit commutated turn off time (tQ). Attempting to
positively bias the anode within this time causes the thyristor to be self-triggered by the
remaining charge carriers (holes and electrons) that have not yet recombined [, thus returning
the thyristor to the ON closed state].
For applications with frequencies higher than the domestic AC mains supply (e.g. 50 Hz
or 60 Hz), thyristors with lower [shorter] values of tQ are required... Today, fast thyristors are
more usually made by electron or proton irradiation of the silicon, or by ion implantation...”
The negative voltage VBR is the reverse breakdown voltage—when attained, the device is destroyed, as with a
diode. At the positive VBO, the breakover voltage, the diode is switched ON (closed), even if there is no gate
current. For progressively higher values of gate current, the SCR is latched ON at progressively lower but
positive voltages VAK. Once IH is attained, the device remains latched ON (closed), allowing a high current to
flow determined by the load even for fairly low voltages VAK.
Single phase full wave rectification (AC to DC converter)
In the instructional lab, our class demonstrated the successful function of a full wave rectifier circuit
employing 4 SCRs. The demos are implemented using LabVolt (now Festo Didactic) modules interfaced with a
desktop computer. This equipment was demonstrated to me by TA John J. Sealy.
A single SCR can be used as a half-wave rectifier, but this is wasteful of power.
Circuit diagrams are shown immediately below for a single phase full wave rectifier and for a 3-phase full
wave rectifier. These are examples of AC to DC converters, one of the major categories of power electronics. It
should be emphasized that the direct current or DC may be highly variable and not constant, as long as it
varies within one polarity, positive or negative. By varying the triggering (gating) angle α, the rms output
214
voltage across the load can be varied from zero to Vmax/√2, as shown in the formula:
Vrms−full width =
Vmax
√2
α
��1 − +
π
sin 2α
2π
�
Usage of these circuits include constant-current circuits, often used to
(1) charge batteries while protecting against excess charging current. (According to the text, these utilize a
varying triggering angle α, which depends on the battery voltage. The current flows to charge the battery
when αmin < α < 180º - αmin. When battery voltage is low, average charging current is reduced by an increase
215
[Thus the charging current is not actually constant!]
in αmin., and increase as the battery voltage rises.)
(2) drive motors at constant torque.
While these demo circuits are instructive, real-world rectification and battery charger circuits would typically
involve more complex control circuitry to achieve more uniform output voltage, safe charging current, etc.
214
215
EEAI3 p. 335
EEAI3 p. 336
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Single phase full wave rectification: Diagram, taken
216
from the course’s Lab 1 and the textbook, depicts
single phase full wave rectification using 2 SCRs and 2
diodes. The gating circuitry is implied but not shown.
Full wave 1-phase rectification, but with output
voltage smoothing resulting from adding a capacitor in
parallel and an inductor in series.
Red square wave (Ch4) = triggering voltage, gating
angle still α = 0º.
Blue (Ch2) is input voltage.
Yellow (Ch1) is output rectified DC voltage, now less
variable with 117 V rms, 60Hz due to smoothing.
Magenta is output current, 0.18 A rms at 60 Hz,
delayed apparently from LC effects.
216
EEAI3 p. 334 (in chapter 10)
Page 72 of 116
Full wave rectification with SCR bridge shown to left
and no LC smoothing.
Red square wave (Ch4) = triggering voltage, about
3.8V peak. Gating angle α = 0º
Blue (Ch2) is input voltage of 122V rms 60Hz AC.
Yellow (Ch1) is output rectified DC voltage, which is
quite variable, is 121V rms at 120Hz.
Magenta is output current, 0.1 A rms at 120 Hz.
Full wave rectification , and with little or no output
voltage smoothing.
Red square wave (Ch4) = triggering voltage, gating
angle at about 120º (past the peak input voltage).
Blue (Ch2) is input voltage. Yellow (Ch1) is output
rectified DC voltage, quite variable at 60V rms,
120Hz.
Magenta is output current, 0.05 A rms at 120 Hz,
delayed due to large gating angle.
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3-phase source (phases are represented by Red,
Yellow, and Blue), full wave rectification via 6 SCRs,
output presented as single phase to single load. The
triggering circuitry for the SCRs is not shown.
Graph shows sample output to the load with firing
angle α = 30 degrees and no LC smoothing of the
waveform. “At any time two SCRs need to conduct,
one from the top half and another [from the] bottom
half... Two SCRs are triggered at the same time. For
example, when SCR S2 is to be triggered, SCR S1 is
also triggered. In the same way, when SCR S3 is to
217
There are
be triggered, SCR S2 is also triggered...”
218
6 switching events per cycle, with each event
having a conduction period of 60º.
Other devices mentioned as relevant to Power Electronics include:



Metal Oxide Semiconductor Field Effect Transistor (MOSFET): an efficient voltage-controlled device in
which the ON (closed) input resistance (VDS/ID) is a few milliohms) [D=Drain; S = Source; G = Gate]
Other Thyristors
o Silicon Diode for Alternating Current (SIDAC). This voltage-triggered device switches ON (closed) at
a fixed breakover voltage.
Hybrid Power Devices:
o Darlington Transistor: This combines two bipolar transistors to reduce base current in the
219
saturation region, when compared to a single BJT.
o Insulated Gate Bipolar Transistor (IGBT): combine and provide the benefits of a MOSFET and a
220
“The IGBT combines the simple gate-drive characteristics of MOSFETs with the highBJT.
221
current and low-saturation-voltage capability of bipolar transistors.”
217
http://www.technik-emden.de/~elmalab/projekte/ws9899/pe_html/ch05s2/ch05s2p1.htm text & both
images
218
EEAI3 p. 342
219
EEAI3 p. 327
220
EEAI3 p. 328
221
https://en.wikipedia.org/wiki/Insulated-gate_bipolar_transistor
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Transformers
This discussion is partly drawn from the textbook Chapter 11.
222
A transformer is “An electrical device without moving parts, which transfers energy of an alternating current
in the primary winding to that in one or more secondary windings, through electromagnetic induction.
Except in the case of the autotransformer there is no electrical connection between the two windings and,
223
It is also defined as, “a device employing the
except for the isolating transformer, the voltage is changed.”
principle of mutual induction to convert variations of current in a primary circuit into variations of voltage
224
A transformer may have more than two conductors or windings.
and current in a secondary circuit”.
Invention
Drawing on Michael Faraday’s work with inductance in
the 1820s and 1830s, including a device he created in
226
1831 which had all basic elements of a transformer,
“scientists discovered that, when two inductors were
placed side by side without touching, the magnetic field
from the first coil affects the secondary coil―this
227
discovery led to the invention of the first transformers.”
The transformer was invented by Antonio Pacinotti in
228
1860 according to the textbook, though I found little
electrical generator or dynamo of 1860.
Others are also credited with being involved in its
invention and development. The story is complex, and I
can offer only a few key early events.
“... Ottó Bláthy, Miksa Déri, Károly Zipernowsky of the
Austro-Hungarian Empire first designed [at the Ganz
Company] and used the [ZBD toroidal shaped]
transformer in both experimental, and commercial
systems. Later on Lucien Gaulard, Sebstian Ferranti,
and William Stanley perfected the design...
The property of induction was discovered in the
1830's but it wasn't until 1886 [or 1885] that William
225
Stanley, working for Westinghouse built the first reliable
Early ZBD toroidal iron core transformer from 1885
commercial transformer. His work was built upon some
rudimentary designs by the Ganz Company in Hungary (ZBD Transformer 1878), and Lucien Gaulard and
John Dixon Gibbs in England. Nikola Tesla did not invent the transformer... The Europeans mentioned
above did the first work in the field. George Westinghouse, Albert Schmid, Oliver Shallenberger and Stanley
229
made the transformer cheap to produce, and easy to adjust for final use.”
222
EEAI3 p. 363-394
http://thesciencedictionary.org/transformer/
224
http://www.merriam-webster.com/dictionary/transformer
225
http://www.edisontechcenter.org/Transformers.html , image retouched by MCM
226
http://ieeexplore.ieee.org/iel1/39/11919/00546444.pdf 1996 article. requires pmt or university proxy
227
http://www.cettechnology.com/history-of-transformers-and-inductors/
228
EEAI3 p. 363
229
http://www.edisontechcenter.org/Transformers.html , including ZBD transformer photo slightly enhanced
by MCM
223
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Another source states, “Those credited with the invention of the transformer include:
230
• Lucien Gaulard and John Gibbs, who first exhibited a device in London in 1881 and then
sold the idea to the American company Westinghouse. They also exhibited the invention in
Turin in 1884, where it was adopted for an electric lighting system.
• William Stanley of Westinghouse, who built the first model based on Gaulard and Gibbs' idea
in 1885.
• In 1884-85, three Ganz Factory engineers, Ottó Bláthy, Miksa Déri and Károly Zipernowsky,
developed a new power distribution system, based on the application of transformers.
• ...Nikola Tesla’s “... true achievement was to develop the device for practical AC power
distribution.”
Regarding the ZBD inventors: “On Bláthy's suggestion, transformers were constructed with a closed iron core;
their joint work resulted in one of the most important inventions in electro-technology at that time. This
system is still the basis of long-distance power transfer and high-voltage electric energy distribution. In 1885
231
The image above depicts
they took out a patent relating to alternating current closed iron core transformers.”
232
an early toroidal iron core ZBD transformer from 1885.
Types and Uses of Transformers
Definitions are given here with some overlap due to varying sources:
Power systems involve transformers that step up and step down voltage, and include the following:
233
Transmission transformer: “Power transformers are used in transmission network of higher voltages for
step-up and step down application (400 kV, 200 kV, 110 kV, 66 kV, 33kV) and are generally rated above
200MVA...” The high voltages reduce current and therefore I2R energy losses as heat.
234
Distribution transformer:
Installed in distribution substations located near load centers, these reduce
transmission line high voltage to 5 to 220 KV for local distribution ending at service transformers.
Service transformer: These are located close to customer’s loads, and reduce distribution voltage to split
phase 120/240V (in the US) for final delivery to the customer loads.
Power systems also use transformers for less raw power applications:
Circuit transformer: Small transformers used in power supplies and electronic circuits. These can also be
used for impedance matching, filters, and electrical isolation of different parts of a circuit.
Some of the specific transformer types, including non-power applications, include:
235
Autotransformer: Transformer in which part of the winding is common to both primary and secondary
circuits. “An autotransformer has only a single winding, which is tapped at some point along the winding.
AC or pulsed DC power is applied across a portion of the winding, and a higher (or lower) voltage is produced
across another portion of the same winding. Autotransformers are commonly used as spark coils in
automotive engines, and as high-voltage flyback transformers in television sets and computer monitors...
Variac was a trademark in the mid-20th century for a variable autotransformer intended to conveniently vary
the output voltage for a steady AC input voltage. A sliding contact determined what fraction of the winding
was connected across the output; a common configuration provided for 120 V as input and percentages of
230
231
232
233
234
235
http://www.fact-index.com/t/tr/transformer.html
http://www.omikk.bme.hu/archivum/angol/htm/blathy_o.htm
http://www.edisontechcenter.org/Transformers.html *
EEAI3 p. 363
https://en.wikipedia.org/wiki/Distribution_transformer
https://en.wikipedia.org/wiki/Transformer and
https://en.wikipedia.org/wiki/Transformer_types
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that voltage as high as about 110%. More compact semiconductor light dimmers have displaced them in
236
many applications, such as theatrical lighting.”
Autotransformer with fixed step-down
237
and step-up taps
238
voltages and currents
Three-Phase or Polyphase transformer: Transformer with more than
one phase (typically 3-phase). 3-phase may have Wye-Wye, Wye-Delta,
Delta-Wye, or Delta-Delta configurations. “The reasons for choosing a Y
or Δ configuration for transformer winding connections are the same as
for any other three-phase application: Y connections provide the
opportunity for multiple voltages, while Δ connections enjoy a higher
level of reliability (if one winding fails open, the other two can still
239
maintain full line voltages to the load).”
The diagram to right depicts a 3-phase transformer with a star (Wye)
connected set of windings and a delta connected set (i.e., Wye-Delta
configuration). Here the core consists of three limbs that are closed at
the top and bottom. Note that as a result of the properties of balanced
3 phase construction, including primary currents and resulting
magnetic fluxes, the core fluxes induced by the 3 primary windings sum
240
A Phase angle regulating
to 0 at the black dots I have added.
transformer is a specialized transformer used to control the flow of real power on three-phase electricity
transmission networks.
Grounding transformer: Transformer used for grounding three-phase circuits to create a neutral in a three
wire system, using a wye-delta transformer, or more commonly, a zigzag grounding winding.
Leakage transformer: Transformer that has loosely coupled windings. “A leakage transformer, also called a
stray-field transformer, has a significantly higher leakage inductance than other transformers, sometimes
increased by a magnetic bypass or shunt in its core between primary and secondary, which is sometimes
adjustable with a set screw. This provides a transformer with an inherent current limitation due to the loose
coupling between its primary and the secondary windings. The output and input currents are low enough to
241
“This is particularly
prevent thermal overload under all load conditions—even if the secondary is shorted.”
236
http://www.fact-index.com/t/tr/transformer.html and EEAI3 p. 372
238
http://www.electrical4u.com/what-is-auto-transformer/ Discusses pros and cons of these.
237
239
240
241
http://myelectrical.com/notes/entryid/199/power-transformers-an-introduction image modified by MCM
https://en.wikipedia.org/wiki/Transformer_types
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required in the case of welding transformers, where high currents may occur if the welding electrode gets
242
fused with the job. Thus these transformers have high leakage inductance.”
Resonant transformer: Transformer that uses resonance to generate a high secondary voltage. “A resonant
transformer is a transformer in which one or both windings has a capacitor across it and functions as a tuned
circuit. Used at radio frequencies, resonant transformers can function as high Q_factor bandpass filters. The
transformer windings have either air or ferrite cores and the bandwidth can be adjusted by varying the
coupling (mutual inductance). One common form is the IF (intermediate frequency) transformer, used in
243
used in electronic ballasts for fluorescent lamps, and high voltage power supplies...”
Audio transformer: Transformer used in audio equipment. “Signal and audio transformers are used to
couple stages of amplifiers and to match devices such as microphones and record players to the input of
amplifiers. Audio transformers allowed telephone circuits to carry on a two-way conversation over a single
pair of wires. A balun (balun transformer) converts a signal that is referenced to ground to a signal that has
balanced voltages to ground, such as between external cables and internal circuits.”
Chokes: These are not transformers but are of interest and are sometimes confused with transformers.
Audio or radio frequency chokes are wound coils which have impedance which rises with frequency, thus they
selectively impeded or block frequencies above a certain threshold value. A radio frequency choke provides
RF filtering. Chokes may be similar in design to transformers. Chokes (ferrite lumps or chokes) are often
placed along power cords to computer to filter out higher frequencies, reducing EMI and RFI propagation and
244
Lamp Chokes: A magnetic, coil, or choke ballast is another wound coil similar to a choke but used for
an entirely different function. Fluorescent lamps, mercury vapor lamps, sodium vapor lamps, iodine lamps,
neon sign lamps ... need a high voltage for starting and once started, the running [load] voltage assumes a
245
“Fluorescent
value much lower than the mains voltage. The ballast provides the high voltage for starting.”
lamps are negative differential resistance devices, so as more current flows through them, the electrical
resistance of the fluorescent lamp drops, allowing for even more current to flow. Connected directly to a
constant-voltage power supply, a fluorescent lamp would rapidly self-destruct due to the uncontrolled current
flow. To prevent this, fluorescent lamps must use an auxiliary device, a ballast, to regulate the current flow
246
However, the newer generation ballasts for fluorescent lighting are electronic, not
through the lamp.”
magnetic, and operate at high frequencies.)
Output transformer: Transformer used to match the output of a tube amplifier, such as
for an electric guitar, to its load, or to optimize the output regarding the quality of the
sound. Leo Fender inhibited the low frequency response of his guitar amplifier, reducing
the likelihood of speaker damage, by diminishing the actual size of the output
247
transformer.
Instrument transformer: Potential transformer or current transformer used to accurately
and safely represent voltage, current or phase position of high voltage or high power
circuits. “The most common usage of instrument transformers is to operate instruments
or metering from high voltage or high current circuits, safely isolating secondary control
circuitry from the high voltages or currents. The primary winding of the transformer is
connected to the high voltage or high current circuit, and the meter or relay is connected
248
The textbook includes a photo of a current transformer and
to the secondary circuit.”
249
250
diagram, and one for 110 kV operation is depicted to the right.
242
243
244
245
246
247
248
249
250
http://www.electrotechnik.net/2011/02/leakage-transformers.html
https://en.wikipedia.org/wiki/Transformer_types#Resonant_transformer
https://audiosystemsgroup.com/SAC0305Ferrites.pdf
https://en.wikipedia.org/wiki/Fluorescent_lamp
http://www.victoriaamp.com/understanding-your-output-transformer-part-one-by-mark-baier/
https://en.wikipedia.org/wiki/Instrument_transformer
EEAI3 p. 30
https://en.wikipedia.org/wiki/Current_transformer
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Pulse transformer: Specialized small-signal transformer used to transmit digital signaling while providing
251
electrical isolation, commonly used in Ethernet computer networks...
Transformer Construction and Theory
A representative diagram of a single
phase transformer is shown to the
252
right.
insulated wire and/or wire separated by
insulating varnish, etc., so there is
electrical isolation from the core
The primary winding carries AC current
Ip due to applied primary AC voltage Vp.
The oscillating current in the primary
winding induces an oscillating magnetic
flux φ in the core (ideal instantaneous
quantities, simplified):
Vp = +Np
dφ
dt
The instantaneous flux in the core is
given by
φ=
1
N1
∫ Vp dt
φ is the magnetic field or flux density, which is proportional to the number of turns in the primary Np. These
values assume that all flux generated in the windings is captured in the core (infinite permeability), that there
are no losses, and no net magnetomotive force.
For the depiction in the diagram above of current in the primary winding, where voltage is positive and rising
and conventional current flows toward the core at the top of the primary winding, the magnetic flux points up
in the direction of the green arrow on the primary side. This flux direction is given by applying Ampère's
253
Correspondingly, the
circuital law using the right hand rule for the case where a voltage induces a flux.
direction of current in the secondary as depicted reflects the application of Faraday’s law of Induction wherein
a flux induces a voltage:
VS = −NS
dφ
dt
Here the flux on the secondary side points downward, and the right hand rule would give the current flowing
toward the core at the top, but the minus sign indicates the current flows in the reverse direction, thus away
from the core at the top, as depicted. (There is some confusion about formula signage. However, Lenz’s law
states that “If an induced current flows, its direction is always such that it will oppose the change which
254
produced it.” )
Diagrams of transformers sometimes use dots to show points where the primary and secondary potentials are
255
in phase. (I have added these dots in the example above, based on a diagram in the textbook.
“Positively
increasing instantaneous current entering the primary winding's dot end induces positive polarity voltage at
256
the secondary winding's dot end.”
251
252
253
254
255
256
http://www.encyclopedia-magnetica.com/doku.php/pulse_transformer
https://en.wikipedia.org/wiki/Transformer
https://en.wikipedia.org/wiki/Right-hand_rule#Direction_associated_with_a_rotation
https://en.wikipedia.org/wiki/Lenz's_law
EEAI3 p. 369
https://en.wikipedia.org/wiki/Transformer
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Core Construction: The modern transformer core is made of high permeability silicon steel, which reduces
the magnetizing current required and helps confine the flux to the core (minimizing leakage) in order to
257
There are many important aspects of core design, and I mention only
maximize coupling of the windings.
some of the considerations.
Permeability μ is a measure of the ability of a material to support the formation of a magnetic field within
itself. It is the degree of magnetization (symbol usually M) induced in a material in response to an applied
magnetic field (aka, auxiliary magnetic field, symbol usually H). Magnetic permeability is typically
represented by the Greek letter μ. Thus, B = μH. The reciprocal of magnetic permeability is magnetic
reluctivity (symbol usually � = 1/μ)... In SI units, permeability is measured in henries per meter (H·m−1) or
N·A−2. The permeability constant (μ0), also known as the permeability of free space, is exactly 4π × 10−7 H·m−1.
the relative permeability is μr = μ/μ0. A closely related property of materials is magnetic susceptibility, which
is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response
258
to an applied magnetic field, and is given by Хm = μr - 1.
In choosing the material for the core, the main problems are
[magnetic] hysteresis loss and eddy current loss. For hysteresis
259
(see graph , in which M is represented by mh and H is shown as
h), the smaller the area enclosed in the hysteresis loop, the lower
the hysteresis loss. A small quantity of silicon alloyed with low
carbon content steel produces core material which has low
hysteresis losses and high permeability. To further reduce the core
losses, another technique known as cold rolling is employed. This
technique reorients the grains in ferromagnetic steel in the
direction of rolling. Steel with silicon alloying and cold rolling is
commonly known as Cold Rolled Grain Oriented Silicon Steel
(CRGOS). This material is now universally used for manufacturing
260
(Cold-rolled non-grain-oriented steel, often
transformer core.
abbreviated CRNGO, is also used because of lower cost.) Core
steels in general are much more expensive than mild steel.
CRGOS is also called electrical steel. “Electrical steel is an iron alloy which may have from zero to 6.5%
silicon (Si:5Fe). Commercial alloys usually have silicon content up to 3.2% (higher concentrations usually
provoke brittleness during cold rolling). Manganese and aluminum can be added up to 0.5%... Silicon
significantly increases the electrical resistivity of the steel, which decreases the induced eddy currents and
narrows the hysteresis loop of the material, thus lowering the core loss. However, the grain structure hardens
and embrittles the metal, which adversely affects the workability of the material, especially when rolling it.
When alloying, the concentration levels of carbon, sulfur, oxygen and nitrogen must be kept low, as these
elements indicate the presence of carbides, sulfides, oxides and nitrides. These compounds, even in particles
as small as one micrometer in diameter, increase hysteresis losses while also decreasing magnetic
permeability. The presence of carbon has a more detrimental effect than sulfur or oxygen. Carbon also
causes magnetic aging when it slowly leaves the solid solution and precipitates as carbides, thus resulting in
an increase in power loss over time. For these reasons, the carbon level is kept to 0.005% or lower. The
261
carbon level can be reduced by annealing the steel in a decarburizing atmosphere, such as hydrogen.”
Although CRGOS has low specific iron loss, it has some disadvantages: it is susceptible to increased loss due
to flux flow in directions other than grain orientation, and it also susceptible to impaired performance due to
impact of bending and cutting of the CRGOS sheet.
The core itself is like a secondary coil of one turn, and electrical eddy currents are induced in it which reduce
efficiency and generate heat. In order to minimize these effects, the core is made of laminated plates
separated by insulating varnish or low conducting oxidized layers to reduce electrical conduction. These
257
258
259
260
261
https://en.wikipedia.org/wiki/Transformer
https://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29 edited and paraphrased
https://en.wikipedia.org/wiki/Magnetic_hysteresis
http://www.electrical4u.com/core-of-transformer-and-design-of-transformer-core/ paraphrased & edited
https://en.wikipedia.org/wiki/Electrical_steel
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laminations confine eddy currents to highly elliptical paths that enclose little flux and thus result in low eddy
currents—the thinner the better, but costs rise with thinner plates. Cores made of powdered iron or non262
Other
conducting magnetic ferrites are sometimes used in higher frequency non-power applications.
expensive materials to reduce core eddy current losses, for instance in distribution transformers, include
263
It is possible to have a transformer with only an air
amorphous (non-crystalline) metal such as Metglas®.
core, sometimes used in RF applications.
Cores are often rectangular and either of core type or shell type in design (in the latter, the core partly
surrounds the windings). A simple construction approach is to have E cross section laminations which are
stacked and wound, and then capped with I-shaped laminations. (This is the so-called E-I transformer core.)
Perhaps the ideal shape of the steel core is a toroid with a circular cross section (like a donut), but this makes
the laminations vary in width and difficult to construct, and the toroid is more difficult to wind. Oil cooling
The limbs of the core laminations are typically layered in interleaved manner, which yields increased magnetic
flux loss at the joints but lower manufacturing cost. A better arrangement with lower cross grain loss due to
264
When
a smoother path for the flux is to have the core limb joints mitered at 45°, but costs are higher.
transformer cores are assembled by joining up 2 or more sections after windings are applied (e.g., two Cshaped or E-shaped sections), any air gaps between the apposed sections greatly increase flux losses.
The oscillating magnetic flux induces a voltage (electromotive force EMF) in the secondary winding, given by
Vs = −𝑁2
dφ
dt
“Power-frequency transformers may have taps at intermediate points on the winding, usually on the higher
voltage winding side, for voltage adjustment... Automatic on-load tap changers are used in electric power
transmission or distribution, on equipment such as arc furnace transformers, or for automatic voltage
regulators for sensitive loads. Audio-frequency transformers, used for the distribution of audio to public
265
address loudspeakers, have taps to allow adjustment of impedance to each speaker...”
A useful relation comparing voltages and number of windings is
V
V
VT = NP = NS or
P
S
VP
VS
=
N𝑃
NS
or VS
N
= VP NS
P
where VT is the voltage per turns in either winding. Therefore, if NS > NP, the transformer is a step-up voltage
transformer whereas if NS < NP , the transformer is step-down voltage transformer.
Assuming no losses, the output power is equal to the input power, the current ratios are given by
𝐼𝑃
𝐼𝑆
𝑉
= 𝑉𝑆 =
𝑃
𝑁𝑆
𝑁1
The magnetomotive forces ℑ of the primary and secondary windings, expressed in ampere-turns, are equal and
given by
ℑ = 𝐼1 𝑁1 = 𝐼2 𝑁2
Thus, the current is smaller in the winding with a higher number of turns, and the wire in such a winding
can be correspondingly smaller in caliber (having a higher wire gauge number).
Calculations of magnitudes are simplified by the concept of Reflected Load Impedance. Briefly, the load
across the secondary Zload = E2/I2. This load may be considered as “seen” from the primary by the following
equation:
262
263
264
265
https://en.wikipedia.org/wiki/Transformer
https://en.wikipedia.org/wiki/Amorphous_metal_transformer and
http://metglas.com/products/magnetic_materials/2714a.asp
http://www.electrical4u.com/core-of-transformer-and-design-of-transformer-core/
https://en.wikipedia.org/wiki/Transformer
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′
N
2
2
also called the load impedance referred to the primary winding.
Transformer Ratings
A typical set of transformer ratings would be “10 kVA, 8kV/240V”. Magnitudes thus are implied or may be
derived as follows:
Rated apparent power S = 10 kVA
Voltage Ratio VP/VS = 8000/240 = 33.3
Rated current of the primary IP = S/VP = 10000/8000 = 1.25 A
Rated current of the secondary IS = S/VS = 10000/240 = 41.7 A
At full load, when current and voltage are operating at (maximal allowable) rated values, load
impedance is
Zload = V2/I2 = 240/41.7 = 5.76 Ω
Magnitude of the reflected impedance of full load is given by
N
2
′
= Zload �N1 � = 5.76(33.33)2 = 6400 Ω = 6.4 kΩ
2
A representative rating for a 3-phase Delta-Wye transformer might be: “60 kVA, 8kV(Δ)/416V(Y)”
Rated apparent combined power of the 3 phases S = 60 kVA
Rated apparent power of each phase = 60/3 = 20 kVA
Primary windings are connected in Delta
Rated line-to-line voltage VL-L of primary circuit = 8 kV.
The voltage across any primary winding = 8 kV.
Secondary windings are connected in Wye
Rated line-to-line [VL-L] voltage of secondary circuit = 416 V.
The voltage across any secondary winding [VL-N] = 416/√3 = 240 V.
The line-to-line voltage ratio [Vprimary L-L/Vsecondary L-L] of the transformer is 8000/416 = 19.23
The voltage per turn is constant in any winding of the transformer, and given as
VT =
Vphase of primary
N1
etc.
Multiple Windings and Other Considerations
Transformers may have multiple windings. For transformers with multiple windings, the relationships again
apply:
V
V
V
VT = N1 = N2 = N3 etc.
1
2
3
The computation of currents is more involved.
266
EEAI3 p. 370
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For calculations with actual non-ideal transformers, it is necessary to consider non-zero parallel and series
resistances and inductances in the primary and secondary circuits, B-H hysteresis effects, etc. (Details
mostly omitted).
Equivalent circuits for representing non-ideal transformers include the following 3 examples:
267
(1)
(2)
(3)
Transformer Efficiency η is given by one of several equivalent ratios:
η=
Output power
Input power
Output power
= Output power+losses etc.
267
Images are from these resp. sources:
(1) http://blog.oureducation.in/equivalent-circuits-of-transformer/
(2) http://www.electrical4u.com/equivalent-circuit-of-transformer-referred-to-primary-and-secondary/
(3) https://commons.wikimedia.org/wiki/File:Transformer_equivalent_circuit.svg
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Voltage Regulation is another useful transformer index.
Voltage Regulation =
Magnetostriction related transformer hum: “Magnetic flux in a ferromagnetic material, such as the transformer
core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect
known as magnetostriction, the frictional energy of which produces an audible noise known as mains hum or
transformer hum. This transformer hum is especially objectionable in transformers supplied at power
268
frequencies and in high-frequency flyback transformers associated with PAL system CRTs.”
268
https://en.wikipedia.org/wiki/Transformer edited MCM
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Electric Machines (Motors and Generators)
This discussion is partly drawn from the textbook Chapter 12.
269
Motors
Asynchronous Induction Motors vs. Synchronous Motors
90% of the energy consumed by motors is consumed by induction motors, which have rotor rotation that is
close to but ultimately asynchronous with respect to airgap flux rotation speed. However, the terminology can
get confusing. Asynchronous induction motors are the primary focus of the textbook and this webpage
pertaining to electrical energy systems. It is important however to clearly distinguish these from synchronous
motors (see below).
Stators and Rotating Magnetic Fields
A 3-phase motor stator is itself stationary (as the name implies) but it produces a rotating air-gap field via its
field windings which acts on the rotor inducing it to turn.
270
In the diagram that follows, the 3-phase motor has 3 pairs of windings (green, red, and blue), one pair for
each separate phase, and separated by 120˚. The 3 sine waves shown are the air-gap fluxes produced by
each of the paired windings. For instance, the magnetic field produced by the blue winding oscillates in a
plane between these top and bottom blue windings, going from maximal amplitude pointing to the top
winding, passing through zero magnitude, and continuing to maximal amplitude pointing to the bottom
winding. These add together in vector form to yield the resultant (phasor sum) magnetic air-gap flux vector
depicted as the rotating black arrow:
271
An animated GIF here shows how the 3 separate windings produce magnetic vector components that sum
to yield a rotating net magnetic field vector (RMF).
For 3-phase stators, the magnitude of the rotating total flux vector is constant and equal to 1.5 φmax, where
φmax is the peak flux magnitude generated by a single winding. The textbook shows an example of a clockwise
269
EEAI3 p. 395-480
https://en.wikipedia.org/wiki/Rotating_magnetic_field
271
https://en.wikipedia.org/wiki/Synchronous_motor#Starting_methods
Unfortunately, Word document cannot show captured animated GIFs
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rotating total magnetic field vector, i.e., it maintains a constant magnitude but a continuously rotating
272
direction.
The direction of magnetic flux for any winding is determined by the right hand rule, with conventional current
flow direction represented by direction the curving fingers point, and magnetic field represented by the
thumb.
Airgap Flux Rotation Speed
The total airgap flux vector completes a revolution with each AC cycle, or τ = 1/f = 1/60 second, at least for a
“two-pole” arrangement. A single phase stator with only one pair of windings has 2 poles. Typically f is 60 Hz
in the US (50 Hz in many other countries). In general, the synchronous speed ns is the rotational speed of the
airgap flux that is determined by the frequency of the supply voltage, and is given by
ns = 2f/p (in rev/s) = 120f/p (in rpm)
where p is the number of stator poles (p is twice the number
of pole pair windings pp).
A two-pole machine is one in which each phase has two
opposing windings (i.e., “poles”, in which one winding
creates a N pole when the opposite creates a S pole, etc.)
Here, the synchronous speed ns is given by
ns = 2f/p (in rev/s) = 60 rev/s = 3600 rpm
273
The diagram to the right illustrates a 2-pole 3-phase
machine stator, having 6 windings (poles). For this 2-pole
motor, the synchronous speed ns is also given by
ns = 2f/p (in rev/s) = 60 rev/s = 3600 rpm
A four-pole 3-phase machine has 2x3 = 6 pairs of windings,
or 12 windings (poles). For this 4-pole motor, the
synchronous speed ns is given by
ns = 2f/p (in rev/s) = 30 rev/s = 1800 rpm
A 10-pole machine operated at 60 Hz has a synchronous speed given by
ns = 2f/p = 12 rev/s = 720 rpm.
Induced Voltage, Current, Torque, and Slip of Rotor of Asynchronous AC Induction Motors
The rotating airgap flux is the driving force of the motor’s rotor rotation. The rotating magnetic field B induces
274
This leads to a rotor current i which interacts with
a voltage e in the rotor conductors per Faraday’s Law.
275
B to cause a force and thus a torque T on the rotor per the Lorentz equation (Laplace Force):
The top equation and diagram depicts the Lorentz force on a positively charged particle. The diagram shows
how the right hand rule applies: the velocity vector v of a positive charge (index finger) crossed (anticommutatively) with the magnetic field vector B (along middle finger) yields the Lorentz force vector F (along
thumb).
The bottom equation is the Lorentz force adapted to a positive charge current I flowing in a wire of length L in
a magnetic field B. The lower diagram depicts again how the right hand rule applies: the velocity vector v has
become the positively charged current vector I (direction of palm of hand); the magnetic field vector B (along
272
273
274
275
EEAI3 p. 396-398
http://www.southernsoaringclub.org.za/a-BM-motors-3.html
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html
EEAI3 p. 403
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fingers curling in from palm) yields the Lorentz force vector F (along thumb), which becomes a torque in N-m
276
on the rotor.
However, the rotor’s rotation typically lags somewhat behind the airgap flux rotations (due to friction and
load), so that the actual rotor and shaft rotation is somewhat less than ns. Such motors may be termed
asynchronous ac induction motors.
The quantity slip defines the extent by which the rotor’s rotation rate n differs from the airgap flux’s rotation
rate ns:
S = (ns - n) / ns
or in terms of angular velocity,
S = (ωs - ω) / ωs
where ω = (2π/60) n [units of ω are rad/s, n is in rpm]. At startup when ω = 0, S = 1. Slip is close to 0 when
the load is minimal and the rotor is rotating at almost the synchronous speed. A typical value of S is less
277
than 0.1 or 10%, often 1% to 4% slip.
Types of Induction Motors
A wide variety of induction motors exists, and I can only touch on some of the key aspects. Most of the large
motors used in industry are three-phase induction motors. “Single-phase motors are used almost exclusively
to operate home appliances such as air conditioners, refrigerators, well pumps, and fans. They are generally
designed to operate on 120 V or 240 V. They range in size from fractional horsepower to several horsepower,
278
(The reference source just cited also discusses multispeed motors and
depending on the application.”
several types of synchronous motors—Holtz motors and Warren motors—as well as universal motors, which
are series wound motors that can operate on DC or AC).
276
x-Right_hand_rule_cross_product.svg.png and
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html
277
EEAI3 p. 402
278
http://www.industrial-electronics.com/electric_prin_2e_19.html
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Motor nameplate specifications
Motor nameplate specifications are summarized here,
NEMA specifications):
279
and may include some of the following (emphasis on
• Manufacturer’s Type
• Rated Volts (at which the motor is designed to operate optimally)
• Full Load Amps FLA (when full-load torque and HP are reached)
• Rated Frequency (operating Hz)
• Number of Phases (1 or 3)
• Full Load RPM “RPM” (when voltage and frequency are at rated values)
• Synchronous Speed (of the rotating airgap magnetic field, not the same as the actual rotor rotation speed)
• Insulation Class (the 20,000 hr. life temperature, ranging from 105 ºC to 180 ºC, expressed as A, B, F, or
H)
• Maximum Ambient Temperature AMB
• Altitude (max. height above sea level at which motor will remain within its design temperature—
motors are less efficiently cooled when air is thin)
• Time Rating (length of time the motor can operate at its rated load and max. ambient temp—standard
motors are rated for continuous use, specialized motors such as a pre-lube motor allow shorter duration use)
• Horsepower HP (rated shaft horsepower at rated speed) and closely related Torque, for which
HP = speed [RPM] × Torque [lb-ft] / 5250); or
HP = speed [RPM] × Torque [lb-in] / 63025);
• Locked Rotor kVA Code (starting inrush current expressed as code letters ABCDEFGHJKLMNPR
based on kVA/HP ratios ranging in value from 0 to 15.99, where the value increases from A to R)
• Power Factor PF (ratio of active power W to apparent power VA, expressed as a %)
• Service Factor SF (factor of overloading the motor can handle for short periods when operating
within correct voltage tolerances—
e.g., a 10 HP motor with SF 1.15 can operate at 11.5 HP for short periods)
• Full Load Nominal Efficiency (average power output / power input for this motor model,
given as a %, ideal is 100%)
• Frame Size (standard motor dimensions, expressed as a size number and letter designation)
• NEMA Design Letter for Induction Motors (A, B, C, or D)
• Enclosure Types ENCL (include ODP, TEFC, TENV, TEAO, TEWD, EXPL, HAZ including various classes)
• Thermal Protection (temp. sensing and protection techniques, including:
None
Auto = Auto shutoff w auto reset
Man = Auto shutoff with manual reset
Impedance
Thermostat T-St which open and close contacts)
• Other aspects:
Bearings
Shaft Type
Mounting
Power Factor Correction (i.e., capacitor size)
Special Markings and Certifications (UL, CSA, ASD)
Rotor Design
The rotor may consist of windings that are shorted internally and permanently as part of the rotor structure
(termed a squirrel cage rotor), or externally through a system of slip rings and brushes. In a 3-phase slip ring
rotor, each phase has an isolated slip ring and circuit (the slip ring is in continuous contact with its brush),
and the 3 circuits are connected in Wye configuration. (DC motors, not otherwise discussed here, often make
280
use of split ring commutators and brushes that periodically reverse the current direction in the rotor circuit. )
Squirrel cage rotors lack the flexibility of varying speed and torque, in contrast to wound rotors with
accessible rotor circuits.
279
280
http://www.pdhonline.org/courses/e156/e156content.pdf
hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html
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281
For squirrel cage internally shorted rotors (illustrated here ), “The motor rotor shape is a cylinder mounted
on a shaft. Internally it contains longitudinal conductive bars (usually made of aluminum or copper) set into
grooves and connected at both ends by shorting rings.. The name is derived from the similarity between this
rings-and-bars winding and a squirrel cage. The solid core of the rotor is built with [insulated] stacks of
electrical steel laminations [in which the conductive bars are embedded]... The rotor has a smaller number of
slots than the stator and must be a non-integer multiple of stator slots so as to prevent magnetic interlocking
of rotor and stator teeth at the starting instant... The field windings in the stator of an induction motor set up
a rotating magnetic field through the rotor. The relative motion between this field and the rotor induces
electric current in the conductive bars. In turn these currents lengthwise in the conductors react with the
magnetic field of the motor to produce force acting at a tangent orthogonal to the rotor, resulting in torque to
turn the shaft. In effect the rotor is carried around with the magnetic field but at a slightly slower rate of
rotation. The difference in speed is called slip and increases with load... The conductors are often skewed
slightly along the length of the rotor to reduce noise and smooth out torque fluctuations that might result at
some speeds due to interactions with the pole pieces of the stator. The number of bars on the squirrel cage
determines to what extent the induced currents are fed back to the stator coils and hence the current through
282
them...”
Startup and Rotor Rotation Direction
The presence of and direction of rotation of a 3-phase induction motor is determined and assured by the
rotating airgap flux. For single phase induction motors, special efforts must be taken to assure that the rotor
rotation will begin on startup in the correct direction and with adequate torque. Various techniques include
the following:
Circuit diagram of capacitor-start induction motor
281
282
283
284
283
Diagram of auxiliary stator windings with capacitor284
Centrifugal switch turns off
start induction motor.
aux winding once the motor attains a certain speed.
https://en.wikipedia.org/wiki/Squirrel-cage_rotor
http://www.industrial-electronics.com/elecy4_22.html diagram
http://www.learnengineering.org/2013/08/single-phase-induction-motor.html
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diagram
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285
The direction of rotation is
the pole—thus, this motor rotor will rotate in the
clockwise direction.
286
Single phase 4-pole shaded-pole induction motor.
The shading coil opposes a change of flux as current
increases or decreases
(1) Resistance-start split-phase induction-run motor. “The resistance-start induction-run motor is so
named because the out-of-phase condition between start and run winding current is caused by the start
winding being more resistive than the run winding... The start winding ... does have some inductive
reactance, preventing the current from being in phase with the applied voltage. Therefore, a phase angle
287
difference of 35° to 40° is produced between these two currents, resulting in a rather poor starting torque.”
(2) Auxiliary stator windings with capacitor, which operates initially as a 2-phase motor.
This approach may take the form of a permanent-split capacitor PSC motor (capacitor-start capacitorrun), which is somewhat inefficient but works adequately in smaller motors up to about 1/4 hp. The split
refers to the division of current between the run winding and the start winding.
A capacitor-start induction motor (capacitor-start induction-run motor.) is more efficient if a larger
capacitor is used to start a single phase induction motor via the auxiliary winding, and this winding is
switched out by a centrifugal switch once the motor is running at perhaps 75% of rated speed. The auxiliary
winding may consist of many more turns of heavier wire than used in a resistance split-phase motor to
mitigate excessive temperature rise. The result is that more starting torque is available for heavy loads like
288,289
“When a capacitor of the proper size is connected in series
conveyers and air conditioning compressors.
with the start winding, it causes the start winding current to lead the applied voltage. This leading current
produces a 90° phase shift between run winding current and start winding current. Maximum starting
290
torque is developed at this point.”
The switching off of the starting winding can also be accomplished by a relay when a centrifugal switch is
unsuitable: “When [motors] are hermetically sealed, a centrifugal switch cannot be used to disconnect the
start winding. A device that can be mounted externally is needed to disconnect the start windings from the
circuit. Starting relays perform this function. There are three basic types of starting relays used with the
291
resistance-start and capacitor-start motors: 1. Hot-wire relay; 2. Current relay; 3. Solid state starting relay.”
285
http://www.industrial-electronics.com/electric_prin_2e_19.html diagram
287
http://www.industrial-electronics.com/electric_prin_2e_19.html
288
289
including image of capacitor-start induction motor.
290
http://www.industrial-electronics.com/electric_prin_2e_19.html
291
http://www.industrial-electronics.com/electric_prin_2e_19.html
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(3) Shaded pole motor: These provide low starting torque, low cost, low efficiency, no capacitors, and no
start switch. They are used on small direct drive fans, etc. This is “basically a small squirrel-cage motor in
which the auxiliary winding is composed of a copper ring or bar surrounding a portion of each pole... This
auxiliary single-turn winding is called a shading coil. Currents induced in this coil by the magnetic field
create a second electrical phase by delaying the phase of magnetic flux change for that pole (a shaded pole)
enough to provide a 2-phase rotating magnetic field. The direction of rotation is from the unshaded side to
the shaded (ring) side of the pole... Since the phase angle between the shaded and unshaded sections is
small, shaded pole motors produce only a small starting torque relative to torque at full speed... The
common, asymmetrical form of these motors ... has only one winding, with no capacitor or starting
windings/starting switch, making them economical and reliable... Because their starting torque is low, they
are best suited to driving fans or other loads that are easily started. They may have multiple taps near one
electrical end of the winding, which provides variable speed and power via selection of one tap at a time, as in
ceiling fans. Moreover, they are compatible with TRIAC-based variable-speed controls, which often are used
with fans. They are built in power sizes up to about 1⁄4 horsepower (190 W) output. Above 1⁄3 horsepower
292
“[Due to
(250 W), they are not common, and for larger motors, other designs offer better characteristics.”
293
the shaded pole,] The magnetic field would be seen to rotate across the face of the pole piece.”
Torque vs. Speed Relationship for Induction Motors
294
In the diagram above, the Torque, Current, and Rotor Speed are graphed. The rotor speed % is the % of the
synchronous speed ns. An asynchronous induction motor always rotates at a speed less than 100% of ns.
STARTING CHARACTERISTIC: “Induction motors, at rest, appear just like a short circuited
transformer and if connected to the full supply voltage, draw a very high current known as the
‘Locked Rotor Current’ or LRC. They also produce torque which is known as the ‘Locked
292
293
294
http://www.industrial-electronics.com/electric_prin_2e_19.html
Also discussed in EEAI3 p. 410-1
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Rotor Torque’ or LRT. The Locked Rotor Torque (LRT) and the Locked Rotor Current (LRC) are
a function of the terminal voltage of the motor and the motor design. The LRC of a motor can
range from 500% of Full-Load Current (FLC) to as high as 1400% of FLC. Typically, good
motors fall in the range of 550% to 750% of FLC. The starting torque of an induction motor
starting with a fixed voltage will drop a little to the minimum torque, known as the pull-up
torque, as the motor accelerates and then rises to a maximum torque, known as the
breakdown torque or pull-out torque [a region to be avoided for sustained operation], at
almost full speed and then drop to zero at the synchronous speed [ns]. The curve of the start
torque against the rotor speed is dependent on the terminal voltage and the rotor design. The
LRT of an induction motor can vary from as low as 60% of [Full Load Torque] FLT to as high
as 350% of FLT. The pull-up torque can be as low as 40% of FLT and the breakdown torque
can be as high as 350% of FLT. Typically, LRTs for medium to large motors are in the order of
120% of FLT to 280% of FLT. The [Power Factor] PF of the motor at start is typically 0.1-0.25
[indicating the current drawn by the motor is primarily the magnetizing current and is almost
purely inductive], rising to a maximum as the motor accelerates and then falling again as the
motor approaches full speed.
RUNNING CHARACTERISTIC: Once the motor is up to speed, it operates at a low slip, at a
speed determined by the number of the stator poles. [It is operating at nearly constant speed
in the nearly steady-state region where developed torque = rated load torque FLT, a region that
I have marked in color.] Typically, the full-load slip for the squirrel cage induction motor is less
than 5%. The actual full-load slip of a particular motor is dependent on the motor design. The
typical base speed of the four pole induction motor varies between 1420 and 1480 RPM at 50
Hz, while the synchronous speed is 1500 RPM at 50 Hz. The current drawn by the induction
motor has two components: reactive component (magnetizing current) and active
component (working current). The magnetizing current is independent of the load but is
dependent on the design of the stator and the stator voltage. The actual magnetizing current of
the induction motor can vary, from as low as 20% of FLC for the large two pole machine, to as
high as 60% for the small eight pole machine. The working current of the motor is directly
proportional to the load... A typical medium sized four pole machine has a magnetizing current
of about 33% of FLC. A low magnetizing current indicates a low iron loss, while a high
magnetizing current indicates an increase in iron loss and a resultant reduction in the
operating efficiency. Typically, the operating efficiency of the induction motor is highest at 3/4
load and varies from less than 60% for small low-speed motors to greater than 92% for large
high-speed motors. The operating PF and efficiencies are generally quoted on the motor data
sheets...”
Equivalent Circuit for Induction Motors and Power Analysis
As with transformers, analysis of reactance and currents etc. can be aided by the use of equivalent circuit
approximations, which refer the rotor circuit to the stator circuit using the turns ratio. This is detailed in the
295
textbook (p. 406-7), and a representative sample from another source is shown here:
295
http://www.eecs.ucf.edu/~tomwu/course/eel4205/notes/21%2520IM%2520Equivalent%2520Circuits.pdf
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According to the textbook, this analysis allows determination of a load resistance or developed power
resistance Rd, which is the electrical representation of the mechanical load. In the power analysis, the input
power Pin is divided into Stator copper loss Pcu1 (wire resistance), Stator core loss Pc (eddy currents, etc.) and
Airgap power Pg. Airgap power Pg is divided into Rotor copper loss Pcu2 and Developed power Pd. Developed
power Pd is divided into Rotational losses Protation and Output power Pout, the latter being the final goal.
The motor efficiency η = Pout / Pin
Synchronous Motors
Most synchronous electric machines are dual action electromechanical converters: when converting rotational
motion to electricity they are called generators, and when converting electricity into rotational motion they are
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“Generator action will be observed if the [rotor] field poles are ‘driven ahead of the resultant
called motors.
air-gap flux by the forward motion of the prime mover’ [such as a water turbine]. Motor action will be
observed if the [rotor] field poles are ‘dragged behind the resultant air-gap flux by the retarding torque of a
297
The rotor may consist of a rare earth permanent magnet (such as samarium-cobalt), giving such a motor a
high power to volume ratio, or it may be excited by an external separate DC source. The magnetic field of the
rotor aligns itself with the rotating magnetic field of the stator and the rotor thus spins at the synchronous
speed.
The following quotes pertain to synchronous motors.
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“A synchronous electric motor is an AC motor in which, at steady state, the rotation of the shaft is
synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral
number of AC cycles. Synchronous motors... have a rotor with permanent magnets or electromagnets that
turns in step with the stator field at the same rate... The synchronous motor does not rely on current
induction to produce the rotor's magnetic field. Small synchronous motors are used in timing applications
such as in synchronous clocks, timers in appliances, tape recorders and precision servomechanisms in which
the motor must operate at a precise speed; speed accuracy is that of the power line frequency, which is
carefully controlled in large interconnected grid systems... Synchronous motors are available in subfractional self-excited sizes [up to] to high-horsepower industrial sizes. In the fractional horsepower range,
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297
298
EEAI3 p. 395
https://en.wikipedia.org/wiki/Synchronous_motor
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most synchronous motors are used where precise constant speed is required. These machines are commonly
299
used in analog electric clocks, timers and other devices where correct time is required.”
“... Synchronous motors are very rarely used below 40kW output because of the higher cost compared to
induction motors. In addition to the higher initial cost synchronous motors need a DC excitation source and
starting and control devices are usually more expensive... Where applications involve high kW output and low
speed synchronous motors are economical compared to induction motors. The various classes of service for
which synchronous motors are employed may be classified as: Power factor correction; Voltage regulation;
300
Constant speed constant load drives. Applications include the following:
• Synchronous motors are used in generating stations and in substations connected to the
busbars to improve the power factor... These machines when over excited delivers the reactive
power to grid and helps to improve the power factor of the system. The reactive power
delivered by the synchronous motors can be adjusted by varying the field excitation of the
motor...
• Because of the higher efficiency compared to induction motors they can be employed for loads
which require constant speeds. Some of the typical applications of high speed synchronous
motors are such drives as fans, blowers, dc generators, line shafts, centrifugal pumps,
compressors, reciprocating pumps, rubber and paper mills
• Synchronous motors are used to regulate the voltage at the end of transmission lines
• In textile and paper industries synchronous motors are employed to attain wide range of
speeds with variable frequency drive system”
A commercial description from WEG.net of industrial synchronous motors includes the following:
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“Why Using Synchronous Motors?
The application of synchronous motors in industry most often results in considerable economic
are:
Power Factor Correction:
Synchronous motors can help to reduce electric energy costs and to improve the efficiency of
the power system by supplying reactive energy to the grid they are connected...
Constant Speed:
Synchronous motors are capable of maintaining constant speed operation under overload
conditions and/or during voltage variations, observing the limits of maximum torque (pull-out).
High Torque Capacity:
Synchronous motors are designed with high overload capability, maintaining constant speed
even in applications with great load variations.
High Efficiency:
Synchronous motors are designed to provide high efficiency under a large range of operational
conditions providing significant savings with energy costs along its lifetime.
Greater Stability in the Operation with Frequency Inverters:
Synchronous motors can operate in a wide speed range, while maintaining stability regardless
of load variation (e.g.: rolling mill, plastic extruder, among others).”
299
300
301
https://en.wikipedia.org/wiki/Synchronous_motor
http://electricalquestionsguide.blogspot.com/2012/09/applications-synchronous-motors.html
http://www.weg.net/files/products/WEG-specification-of-electric-motors-50039409-manual-english.pdf
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Other Motors
I have omitted much discussion of DC motors as well as Linear Induction Motors and Stepper Motors. The
latter are used to precisely position the rotor in steps, as with hard disk drives, printers, plotters, scanners,
fax machines, medical equipment laser guidance systems, robots, and actuators.
Synchronous Generators
Time does not permit adequate coverage of this interesting topic. The stator is similar to that of the induction
motor, and typically consists of 3-phase windings in multiple pole configurations. The rotor is excited by an
external DC source through a slip ring system. The rotor is spun by the prime mover (water turbine, steam
turbine, wind turbine, etc.)
By way of example, the 32 main generators at the Three Gorges dam each weigh about 6,000 tonnes and are
designed to produce more than 700 MW of power each. The designed head [pressure] of the generator is 80.6
meters (264 ft). Three Gorges uses Francis turbines. Turbine diameter is 9.7/10.4 m (VGS design/Alstom's
design) and rotation speed is 75 revolutions per minute. Rated power is 778 MVA, with a maximum of 840
MVA and a power factor of 0.9. The generator produces electrical power at 20 kV. The stator, the biggest of
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its kind, is 3.1/3.0 m in height. Average efficiency is over 94%, and reaches 96.5%.
Recall that a 10-pole machine operated at 60 Hz has a synchronous speed given by
ns = 2f/p = 2 * 60 Hz/ 10 poles = 12 rev/s
Assuming 50 Hz power generation, the Three Gorges rotation rate of 75 RPM predicts the following number of
poles (in the rotor, as it turns out!):
p = 2f/ns = 2 * 50 Hz/ (75/60 [rev/s]) = 80 poles
302
303
303
https://en.wikipedia.org/wiki/Three_Gorges_Dam and
http://www.chinatourmap.com/three_gorges_dam/power_generation.html
http://www.slideshare.net/endutesfa/three-gorges-project Slide 46 of 81
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Electrical Safety
This is an important topic, and some of what I present below may have mistakes. Please consult primary
sources before making any important decisions regarding electrical safety. This discussion is partly drawn
from the textbook Chapter 9. I have omitted the topic of biological and health effects of low frequency
304
magnetic fields.
Human Electrical Shock Physiology
The capacity of humans to withstand electrical shock was studied by Charles F. Dalziel in the 1950’s and
1960’s. He found that human responses correlate more closely with current rather than voltage. The
305
following table draws on his published results for average responses (but individuals may vary!):
Here, the let-go current (the threshold level above which the victim
cannot let go of the conductor), is shown as “pain, with loss of
voluntary muscle control”. The stage specifying difficulty breathing
is also called respiratory tetanus, because respiratory muscles are in
spasm and breathing is impaired or impossible. Cardiac fibrillation,
for which the research was conducted in non-humans, occurs at
100 mA in 0.5% of men and at 67 mA in 0.5% of women (according
to the textbook). In general, Dalziel found that women are more
sensitive than men to electrical current, and that AC is more
hazardous than DC. Secondary shock current describes currents
that are possibly painful, but do not cause permanent tissue injury
or death. Primary shock current can exceed let-go threshold, cause
heating and burns (including of nerves), respiratory tetanus, or
ventricular fibrillation.
The OSHA gives a similar table (to right), based on another
researcher’s work: “This table shows the general relationship
between the amount of [probably AC] current received and the
reaction when current flows from the hand to the foot for just 1
306
second.”
The severity of electrical shock depends on the following:
307
304
EEAI3 p. 310
http://www.ibiblio.org/kuphaldt/socratic/output/shock.pdf,
image annotated MCM based on Charles F. Dalziel, “Deleterious Effects of Electric Shock”, 1961 available at
http://www.electriciancalculators.com/dalziel/dalziel_study.pdf. Also, EEAI3 p. 274-5
306
W.B. Kouwenhoven, “Human Safety and Electric Shock,” Electrical Safety Practices, Monograph, 112,
Instrument Society of America, p. 93. November 1968, cited in
https://www.osha.gov/Publications/osha3075.pdf OSHA, 2002.
307
EEAI3 p. 275
305
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






The amount of current (amps) flowing through the body. Current is determined partly by voltage and
partly by the resistance in the current path.
Voltage: Higher voltage may be more likely to throw the victim away from the hazard, due to violent
muscle contraction, but there is no guarantee, and otherwise higher current will result from higher
voltage.
Body Resistance: is higher in bones, fat, and tendons, lower in nerves, blood vessels, and muscles.
Total resistance hand to hand varies widely, from 13,500 Ω for driest skin conditions to 820 Ω for the
wettest conditions (e.g., sweaty palms). The textbook EEAI3 suggests rule of thumb resistances of
500 Ω for each hand + arm, 500 Ω for each leg, and 100 Ω for the torso,
with a useful average of 1000 Ω between two hands or two feet.
The current's path through the body. For instance, in dogs a path from one forelimb to one hindlimb
is more likely to cause ventricular fibrillation than one passing between the two forelimbs (i.e., ECG
308
leads II or III vs. lead I, apparently because the former passes more current through the heart).
The length of time (duration) the body remains part of the circuit. Dalziel estimated the time to
ventricular fibrillation is t = (K/I)2, where K is 116 for < 70kg body weight and 154 for > 70 kg. (See
also graph below regarding duration and VF.)
The current's frequency. The let-go current follows a U-shaped pattern, being lowest in the 50 to 100
309
Hz range, and much higher for DC and for AC of 1000 Hz and above.
Ground resistance and other factors affecting resistance. E.g., standing on an insulating substance is
much safer than standing in water (see below).
The graph to the right depicts in greater detail the risk of
ventricular fibrillation for AC current passing from left hand
to both feet, from exposure in specified mA and duration
310
ranges.
The graph below, from the excellent article on Electrical
Safety by Walter H. Olson, shows the effect of frequency per
311
Charles Dalziel.
308
L. A. Geddes, et al, “Threshold 60-Hz Current Required for Ventricular Fibrillation in Subjects of Various
Body Weights”, IEEE Transactions On Biomedical Engineering, November 1973. Dr. Geddes was a much
respected mentor for me at Baylor College of Medicine in 1965-1966.
309
EEAI3 p. 278
310
Weineng Wang, Zhiqiang Wang, Xiao Peng, “Effects of the Earth Current Frequency and Distortion on
Residual Current Devices”, Scientific Journal of Control Engineering, Dec 2013, Vol 3 Issue 6 pp 417-422,
article in Chinese thus unreadable by me, cited in https://en.wikipedia.org/wiki/Electric_shock
311
https://eva.fing.edu.uy/pluginfile.php/68296/mod_resource/content/1/c14.pdf
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Ground Resistance, Ground Potential, Ground Potential Rise, Touch and Step Potentials
These are important considerations in evaluating shock risk.
Voltages are measured between 2 points. The center of the Earth is taken to have potential or voltage of 0V.
This is the point of reference by which other voltages may be compared. “The real Earth ... is electrically
neutral. This means that it has the same number of electrons and protons, so their charges cancel out
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Our
overall. Scientifically, we describe this by saying that the Earth has an Electric Potential of zero.”
textbook EEAI3 specifically defines this condition as existing at the center of the Earth. This allows for the
possibility that there may be a potential (a so-called Ground Potential GP) between a point on or near the
Earth’s surface (such as on water pipes, building or substation foundations, transmission tower footings,
etc.), and the center of the Earth. This GP is relevant when high voltage towers leak current to the ground, or
lightning strikes nearby. In these cases, the local ground potential may differ from 0V and create a hazard.
We may determine the effective resistance, the Ground Resistance GR, between the ground point of interest
and Earth’s center. This resistance determines how much current flows between the ground object having
nonzero voltage potential and the zero voltage at the Earth center.
Mathematical computation of GR is easiest for a buried conducting hemisphere located at the Earth’s surface.
For current I flowing through this hemisphere of radius r0, current density J for a point on or outside its
313
surface at a distance r from its center (r ≥ r0) is given by:
I
J = 2πr2
We may compute the voltage (GP) between points on concentric virtual hemispheric equipotential surfaces
found on or outside the buried hemispheric conductor. If these points are on concentric virtual hemispheres
of radius ra and rb, where r0 < ra < rb, the voltage between the virtual hemispheres (and thus any two points,
one on each) is
ρI
1
1
Vab = 2π �r − r �
312
313
a
b
https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/earth/earth.htm
EEAI3 p. 281
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where ρ is the electrical resistivity of soil in the region (assumed to be uniform), measured in Ω-m. Values of
ρ can vary widely, due to varying soil types, moisture content, salt or chemical content, and temperature [for
314
instance, frozen conditions raise resistivity]. Values of ρ range from 10 Ω-m for wet organic soil to 10,000 Ω315
Some of the factors affecting resistivity are demonstrated in this diagram adapted from
m for bedrock.
316
IEEE:
An extensive commercial webpage describes current methodologies (like the Wenner 4-point [four-pin] Soil
317
Resistivity Test) for measuring soil resistivity.
The textbook EEAI3 illustrates a simpler three-point test.
Hemisphere: The Ground Resistance Rg between a point on the buried hemisphere (at r0) and the center of
the Earth is estimated by
ρ
1
ρ
ln �
Rg =
� −r
2π r
Rg =
2πl
Rg =
4r
0
1
center of earth
ρ
� = 2πr
0
Rod: For a conducting grounding rod buried to depth l and having radius r, the IEEE quoting Thug gives the
318
Ground Resistance Rg estimated by two different approximations, the first also given in the textbook:
2l+r
r
�
or
Rg =
ρ
2πl
4l
ln � r − 1�
Circular Plate: A circular plate of radius r at the surface has approximate GR:
ρ
Ground resistance is relevant when a person or other living thing is standing near a source of ground
potential. If each foot has a Ground Resistance Rf, which varies by soil and shoe sole conditions, etc., the
combined (parallel) Ground Resistance for both feet is 0.5 Rf.
Touch potential
319
If a transmission tower has a leakage or fault current I (diagram below ) passing down to ground (perhaps
from a dirty, salt-laden, wet, or otherwise faulty insulator), a point on the structure of the tower where a man
touches it will have a Ground Potential Rise GPR, i.e., the voltage above 0V, given by
GPR = Itg Rg
314
315
https://en.wikipedia.org/wiki/Soil_resistivity
Determining The Soil Resistivity To Design a Good Substation Grounding System:
http://electrical-engineering-portal.com/determining-the-soil-resistivity-to-design-a-good-substation-grounding-system
and T.
IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a
Grounding System”, IEEE Std 81-2012
317
http://www.esgroundingsolutions.com/what-is-soil-resistivity-testing/
318
IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a
Grounding System”, IEEE Std 81-2012; also EEAI3 p. 283.
319
http://www.esgroundingsolutions.com/what-is-step-and-touch-potential/
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where Itg is the tower to ground fault current, and Rg is the Ground Resistance at that point on the tower. The
man touching the tower is exposed to this Touch Potential, and a part of the Itg current becomes diverted
through his body and both feet into the ground. The current through the man is modeled in the textbook (p.
288) based on his presenting a resistance (Rman + 0.5 Rf ),
which is in parallel to the Ground Resistance Rg of the
tower.
For example, if the fault current down the tower is 10A
into moist soil with ρ = 100 Ω-m (grounded at a
hypothetical hemisphere having r=0.5 m), the man’s
resistance Rman is 1000 Ω, and each foot has sole
area = 0.02 m2, then
Rg = 32 Ω
point (GPR) = IRg = 320V
mA
Rf = 3ρ = 300 Ω (each foot)
Vman = ImanRman = 270 V
V at touch
Iman = 270.7
This level of current will kill the man in less than a
second of contact.
Step potential
This is another hazard of being near a source (leaking transmission tower, lightning bolt, etc.) passing a large
current into and along the ground. If a current is passing horizontally, the soil surface is not equipotential.
Instead, there is a gradient of surface voltage (potential), highest near the source and tapering off with
horizontal distance (as well as with vertical or oblique underground distance).
See diagram at right, from a website that also provides the
following. “Hazardous Step Potentials or step voltage can
occur a significant distance away from any given site. The
more current that is pumped into the ground, the greater
the hazard. Soil resistivity and layering plays a major role
in how hazardous a fault occurring on a specific site may
be. High soil resistivities tend to increase Step Potentials.
A high resistivity top layer and low resistivity bottom layer
tends to result in the highest step voltages close to the
ground electrode: the low resistivity bottom layer draws
more current out of the electrode through the high
resistivity layer, resulting in large voltage drops near the
electrode. Further from the ground electrode, the worst
case scenario occurs when the soil has conductive top
layers and resistive bottom layers: in this case, the fault
current remains in the conductive top layer for much
320
greater distances away from the electrode.”
With step potentials, there is a difference in potential arising from a ground current passing below the feet.
The feet are at different voltages, unless they happen to be at exactly the same distance from the source, the
soil and foot resistances are identical, etc.)
The textbook EEAI3 gives an example as follows:
The fault current down the tower is 1000A into moist soil (ρ = 100 Ω-m) and is grounded at a hemisphere (for
which r is not stated). The man’s leg to body resistance Rman is 1000 Ω. Each foot a and b has Ground
Resistance Rf. A voltage difference Vab exists between the feet due to the current, higher for foot placed at a
which is closer to the hemisphere than foot placed at b. The stride length (distance between feet on the
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http://www.esgroundingsolutions.com/what-is-step-and-touch-potential/
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321
The solution applies Thévenin's theorem to compute an equivalent Thévenin resistance Rth and Thévenin
voltage Vth. Here, Vth is simply the voltage Vab when the feet are off the ground (no human load across a and
b). Rth is simply the sum of the two Rf for the open circuit, or 2Rf.
ρI
1
1
Vth = Vab = 2π �r − r � =
a
b
Rf = 3ρ = 300 Ω (each foot)
Iman = R
Vth
th +Rman
V
th
= 2R +R
f
100×100 1
man
2π
1
�5 − 5.6� = 341V
341
= 600+1000 = 213.13 mA (hazardous, quite possibly lethal)
The step voltage is Vstep = Iman × Rman = 213.13V
If a 1 m grounding rod is used rather than a hemisphere, Iman = 308.75 mA, even worse. In either case, The
victim may fall over from the initial shock, then have lethal current passing through heart etc. .
In summary, it can be dangerous to stand or walk near a high current leak passing along the ground.
Home Electrical Safety
The following focuses on US and North American residential standards, and mostly ignores 3-phase.
Home Electrical Service
Home electrical service enters the home like this:
Distribution Transformer
providing L-N-L single phase
120/240V service (aka split
phase) (above). Diagram
323
(below)
322
Single Phase: The distribution transformer secondary (on the left above)
provides one of the 3 possible phases to the home, specifically a hot black line
and a hot red line (synonym: service wires, phases, legs). This level of service
is called single phase or split phase. With single phase (split phase), there is
240 V rms between the lines (the line to line L-L voltage).
Single phase also provides a white (or gray) neutral conductor (synonym:
grounded conductor, neutral point) arising from the transformer secondary as
a center tap. There is 120V rms between either phase and the neutral
conductor, the Line-to-Neutral or L-N voltage. (The neutral conductor arises
from the center of the wye connection in a 3-phase power system.)
321
322
323
https://en.wikipedia.org/wiki/Th%C3%A9venin's_theorem (I have not mastered this technique)
http://www.thecircuitdetective.com/bkgrd.htm
http://electrical-engineering-portal.com/power-distribution-configurations-with-three-three-phase-hot-power-lines (diagram)
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(For 3-Phase power, there are “three ac voltages separated from each other by 120 electrical degrees, or by a
third of a cycle. These systems deliver power over three hot wires where the voltage across any two hot wires
324
measures 208 V [rms].” )
After the meter, the lines power feeds into the breaker panel (synonyms: load center, distribution board,
junction box, service panel, or circuit panel) wherein are found the circuit breakers (aka miniature circuit
breakers MCBs). “The United States electrical codes require that the neutral be connected to earth at the
‘service panel’ only and at no other point within the building wiring system... The neutral is neither switched
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nor fused.”
Ideally and typically, there should be a main breaker, which is a 2-pole breaker, typically 200A, that can shut
off all power being fed to the busbars (bus bars) that in turn feed the branch circuit breakers. These can be
manually tripped or automatically trip when current exceeds 200A in either phase.
I have not made a careful study of the rather complex technology of circuit breakers. Home circuit breakers
typically have air gap circuit interruption (use air alone to extinguish the arc) and trip after a nominal current
has been exceeded for a specified time delay. 240 circuits use 2-pole circuit breakers to trip both phases
simultaneously if either exceeds its trip amperage. (Three phase circuits must use three-pole common trip
breakers.) I read that circuit breakers should be turned off and on to make sure they are not stuck and that
326
they are in good operating condition. There are provisos however, see this article .
327
The figure that follows is excerpted from a specification sheet for a GE 40A miniature circuit breaker (MCB).
It is a log-log plot. On the horizontal axis is plotted Amperes, and on the vertical axis is plotted t (time to
clear in seconds). The green band represents the range of currents and time delays for which the circuit
breaker clears (opens). It is apparent that as overload current increases (in this case, currents exceeding 40
A), the time delay before the MCB trips (clears) becomes shorter. When the current barely exceeds 40A, it
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http://www.belden.com/blog/datacenters/3-Phase-Power-Wye-It-Matters.cfm;
voltages are line-to-neutral voltages multiplied by √3 = 120√3 = 120•1.732 = 207.8V rms. A standard 4-wire
3-phase wye system with line-to-neutral voltages of 120 volts and V1N chosen as the reference phasor at zero
degrees has line-to-line voltages of: V12 = 208∠30°
V23 = 208∠-90°
V31 = 208∠150°
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https://en.wikipedia.org/wiki/Electrical_wiring_in_North_America
326
http://www.examiner.com/article/basic-home-electricity-part-1-how-to-maintain-circuit-breakers-gfcisand-afcis
327
Sheet DES-063. Molded Case Circuit Breakers Q Line Type THQB/THHQB - Model C. Graph “Depicts the
Long-time Delay and Instantaneous Time-current Curves. Fetch this sheet from
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takes many seconds to trip (apparently as many as
1000 s). For currents in the 150 A range, the MCB trips
in about 2 to 10 seconds. For higher currents exceeding
200 A, the MCB clears in 0.01 to 1 second. For extreme
currents > 1000 A, the graph shows clearing in less than
0.02 seconds. However, at some excess short circuit
current, the MCB may not be able to properly function
and might be destroyed—this is not shown in the graph.
It is also apparent that this MCB clears at a lower current
for lower temperatures (~35A at 25° F) whereas it clears
at a higher current for higher temperatures (~42A at 50°
F), though this is a modest difference.
The diagram to the left illustrates
how 240V and 120V circuits flow
to and from loads, and often
sub-branches (yellow). 120V
current flows from red or black to
neutral, whereas 240V current
flows from one hot to the other.
“By Code, a dedicated circuit is
used for each of most large
appliances like the electric range,
electric water heater, air
conditioner, or electric dryer;
these as well as electric heaters
will have two (joined) breakers in
order to use 240 volts rather than
the 120 volts used by most other
items. A dedicated circuit of 120
volts is usually provided for each
dishwasher, disposal, gas or oil
furnace, and clothes washer. Most other 120-volt
circuits tend to serve a number (from 2 to 20) of
lights and plug-in outlets. There are usually two
circuits for the outlets in the kitchen/dining area,
and these use a heavier wire capable of 20 amps of
flow...”
“Besides black, red, and white wires, the cables in
homes wired since the 1960's also contain a bare or
green ‘ground(ing)’ wire. [diagram to left] Like the
neutral, it is ultimately connected to the
transformer’s grounded terminal, but this wire is not
connected so as to be part of the normal path of flow
around the circuit. Instead, it is there to connect to
the metal parts of lights and appliances, so that a
path is provided ‘to ground’ if a hot wire should
contact such parts; otherwise you or I could be the
best available path... When a ground wire does carry
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current, it is taking care of an otherwise dangerous situation; in fact, it usually carries so much flow
suddenly, that it causes the breaker of the circuit to trip...”
“Even when a circuit is switched off, we call hot wires hot to remind ourselves of their future potential to
shock and to distinguish them from neutrals and grounds. Only hot wires should be switched, never neutrals
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or grounds.”
Finally, to clear up one of the great mysteries of home life, I have included this explanation of 3-way light
switches:
Note that the diagram shows the light off. To switch the light on, either switch may be flipped (causing the
internal arrow to shift from top pointing to bottom pointing or conversely), completing a hot line connection to
329
the bulb.
Power Receptacles (Outlets, Sockets, and Female Connectors) and Plugs (Male Connectors)
330
Standard sizing and specifications of wiring devices (plugs, receptacles, plates, etc.) are given by NEMA.
These specifications include single gang wallplates, duplex plates, devices, plugs (blades, prongs), receptacles
(sockets), etc.
A typical diagram for a single female NEMA 5-15R receptacle is
shown to the right (with corresponding mirror-image male plug
at lower left). [Here, 5 signifies 125V grounded 3-wire HotNeutral-Ground, 15R signifies 15 amp
receptacle, as opposed to 15P for plug]. The
taller (wider) blade socket is connected to
the neutral white wire. The shorter blade
socket is for the hot “line” black wire, and
the socket marked G is for the green ground
connection. The ground blade of the plug is
longer to establish a ground connection
before the hot connection is made.
“NEMA connectors are power plugs and receptacles used for AC
mains electricity in North America and other countries that use
the standards set by the US National Electrical Manufacturers
Association. NEMA wiring devices are made in current ratings
from 15 to 60 amperes, with voltage ratings from 125 to 600
volts. Different combinations of contact blade widths, shapes,
orientation, and dimensions create non-interchangeable
328
http://www.thecircuitdetective.com/bkgrd.htm This website is an excellent source of household electrical
information
329
http://www.thecircuitdetective.com/3and4wyinfo.htm
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(registration required)
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connectors that are unique for each combination of voltage, electric current carrying capacity, and grounding
system... NEMA 1 (two-prong, no DC safety ground) and NEMA 5 (three-prong, with safety ground pin)
connectors are used for commonplace domestic electrical equipment; the others are for heavy duty or special
purposes. NEMA 5–15R is the standard 15 amp capacity electric receptacle (outlet) found in the United
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States. Similar and interchangeable connectors are used in Canada and Mexico.”
Locking Receptacles: These permit curved blades to be rotated to lock into place by twisting (rotating) the
plug. For example, L5-30 [locking] receptacles are common at marinas for secure boat connections. These
consist of Hot-Neutral-Ground connections. More complex locking connectors include NEMA L14-50R, which
has Hot-Hot-Neutral-Ground connections for either 125 or 240 V and up to 50A.
Polarized plugs vs. Unpolarized plugs: For polarized plugs having only 2 blades, the wider blade is for the
neutral wire connection, whereas the narrower blade is for the line “hot” wire. “Polarized NEMA 1-15 plugs
will not fit into unpolarized sockets, which possess only narrow slots. Polarized NEMA 1-15 plugs will fit
NEMA 5-15 grounded sockets, which have a wider slot for the neutral blade. Some devices that do not
distinguish between neutral and line, such as internally isolated AC adapters [and double insulated small
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appliances], are still produced with unpolarized narrow blades.”
240V Plugs and Sockets: These typically have a ground connector (for the green ground wire) and 2 hot/live
identically sized connectors. Some of these have more than 3 connectors, for instance: “All NEMA 14 devices
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offer two hots, a neutral and a ground, allowing for both 120 V and 240 V.”
Higher Voltage and 3-Phase Industrial Connectors: Though not encountered in most homes, these are
common in industry, hospitals, etc. For example, NEMA L23-50R is a locking receptacle for 50A 3-Phase
connections in a range of voltages up to 600V, offering for the Wye 3-Phase configuration 3 hot connections
(X, Y, and Z) plus Neutral and Ground.
Color Coded Industrial Receptacles: “...Although colors are not standardized by NEMA, some industries
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utilize colors for certain applications, following de facto standards:
 A receptacle with a green dot is a so-called "hospital grade" device.
 A receptacle (any color) with an orange triangle, or an all-orange receptacle, is an isolated ground (IG)
device, where the grounding pin of the receptacle is connected to ground independently of the frame of
the receptacle and wiring outlet box.
 A blue receptacle may indicate built-in surge suppressors.
 A red receptacle may indicate a special-service outlet such as one connected to an emergency standby
power source.
 At least one manufacturer makes a yellow receptacle, which identifies it as corrosion-resistant”
Preventing Shock Hazards in the Home
Earth Grounding versus Neutral Connections
Here are some observations from Wikipedia:
“As the neutral point of an electrical supply system is often connected to earth ground, ground
and neutral are closely related. Under certain conditions, a conductor used to connect to a
system neutral is also used for grounding (earthing) of equipment and structures. Current
carried on a grounding conductor can result in objectionable or dangerous voltages appearing
on equipment enclosures, so the installation of grounding conductors and neutral conductors
is carefully defined in electrical regulations...
In North America, the cases of some kitchen stoves (ranges, ovens), cook tops, clothes dryers
and other specifically listed appliances were grounded through their neutral wires as a
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332
333
334
https://en.wikipedia.org/wiki/NEMA_connector incl. diagrams and paraphrased text
https://en.wikipedia.org/wiki/NEMA_connector
ibid.
ibid.
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measure to conserve copper from copper cables during World War II. This practice was
removed from the NEC [National Electrical Code] in the 1996 edition, but existing installations
(called "old work") may still allow the cases of such listed appliances to be connected to the
neutral conductor for grounding...
Combined neutral and ground conductors are commonly used in electricity supply companies'
wiring and occasionally for fixed wiring in buildings and for some specialist applications where
there is little alternative, such as railways and trams. Since normal circuit currents in the
neutral conductor can lead to objectionable or dangerous differences between local earth
potential and the neutral, and to protect against neutral breakages, special precautions such
as frequent rodding down to earth (multiple ground rod connections), use of cables where the
combined neutral and earth completely surrounds the phase conductor(s), and thicker than
335
normal equipotential bonding must be considered to ensure the system is safe.”
Causes and Techniques for Reducing Shock Hazards
Ground connections are illustrated in diagrams below. DC voltages are typically depicted, but the principles
336
generally apply to AC with minimal reinterpretation. Quotes, paraphrases, and diagrams are from here
unless otherwise noted.)
Hazardous Hot Live Wire, Con: Touching a live wire lets
a standing grounded person be an alternate path to
ground, and he is shocked. The bird on the wire is not in
contact with the ground, thus is not shocked.
Circuit grounding ensures that at least one point in the
circuit will be safe to touch (at the bottom of the load
here, but not at the top, as shown to the right).
335
336
Neutral Grounding, Pro: By grounding one side
of the load, the person is not shocked when
touching that side. “Because the bottom side of
the circuit is firmly connected to ground through
the grounding point on the lower-left of the
circuit, the lower conductor of the circuit is made
electrically common with earth ground. Since
there can be no voltage between electrically
common points, there will be no voltage applied
across the person contacting the lower wire, and
they will not receive a shock. For the same
reason, the wire connecting the circuit to the
grounding rod/plates is usually left bare (no
insulation), so that any metal object it brushes
up against will similarly be electrically common
with the earth.”
https://en.wikipedia.org/wiki/Ground_and_neutral
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Neutral Grounding Alone, Con: If a circuit is
completely ungrounded, a person touching just a
single wire might seem safe. However, if part of
the circuit becomes grounded through accident,
such as a tree branch touching a hot power line,
the person touching the same high voltage side
becomes a path to ground that returns through
the tree to the hot, and he is shocked.
If the neutral wire contacts the case (floating
chassis), there is no shock hazard. (Here, DC is
shown, but the principle applies to AC as well.)
Floating Chassis, Con: Inside the home, if an internal
hot wire touches the metal external case of an
ungrounded toaster (a so-called floating chassis), a
person could be shocked by providing an alternate path
to ground.
Reversed Polarity, Con: Designers try to assure that the
hot wire inside the toaster will never contact the case.
However, if the plug or receptacle is not polarized, and
hot and neutral connections to the toaster are reversed,
and there is an accidental internal hot wire connection to
the case, the person might touch the hot case and be
shocked. This is one of the major argument for
polarization of plugs and receptacles.
Double Insulation, Pro: Some engineers address
the safety issue simply by making the outside
case of the appliance nonconductive. Such
appliances are called double-insulated, since the
insulating case serves as a second layer of
insulation above and beyond that of the
conductors themselves. If a wire inside the
appliance accidently comes in contact with the
case, there is no danger presented to the user of
the appliance.
It is important never to cut the third prong off a power
plug when trying to fit it into a two-prong receptacle [or to
use a 2-prong plug adapter]. If this is done, there will be
no grounding of the appliance case to keep the user(s)
safe...
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The third prong on the power cord provides a
direct electrical connection from the appliance
case to earth ground, making the two points
electrically common with each other. If they’re
electrically common, then there cannot be any
voltage drop between them [not entirely, see
below]...If the hot conductor accidently touches
the metal appliance case, it will create a direct
short-circuit back to the voltage source through
the ground wire, tripping any overcurrent
protection devices.
Chassis Grounding Alone, Pro and Con: Other
engineers tackle the problem of safety by maintaining a
conductive case, but using a third conductor to firmly
connect that case to ground. [This is the green or bare
metal ground conductor added in the 1960s.]
Ground Fault Circuit Interrupter GFCI, Pro: When a
toaster has a faulty hot connection to the metal case, a
person may be shocked by providing an alternate path to
ground. In this case, the hot and neutral currents are no
longer exactly equal, being greater on the hot side
Bonding to Neutral Alone, Con: If instead of grounding
a chassis, one bonds (connects) the chassis to neutral, a
fault is more likely to trip the circuit breaker. The
textbook finds this a fairly good approach, but it has the
drawback that heavily loaded equipment causes a
significant voltage on the chassis even in the absence of a
fault. The textbook p. 299 gives an example in which the
chassis voltage proves “high” at 9V.
According to the textbook EEAI3 p. 295-7,
however, there is still some current through the
man in this case, and it is still possibly
hazardous, especially if the grounding is faulty.
In addition, the circuit breaker does not usually
trip, so the problem persists.
However, by interposing a Ground Fault Current
Interruptor, or GFCI, the difference in current
comparing hot and neutral is readily detected,
and the GFCI shuts off current to the faulty
toaster very rapidly. These are often used in wet
areas such as bathrooms and kitchens. (See
textbook p. 306, and diagram further below.)
EGC Grounded Chassis Plus Bonding of
Ground to Neutral, Pro: This is one of the better
solutions, and was adopted in the US and most of
the world. (textbook p. 299-300). The neutral is
grounded at the service panel. In addition, an
Equipment Grounding Conductor EGC is
grounded locally near the service panel (copper
rod, etc.) and provides a ground connection to all
cases and chassis that might otherwise be hot
from a fault.
Using this approach, the chassis voltage under
heavy load is about 3 V rather than 9 V for the
example to the left, which is an improvement and
apparently not considered harmful. See textbook
pl 302. (A GFCI might still be nice however.)
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337
The Ideal Residential Electrical Service, Pro: According to the textbook, the US and most other
countries failed to adopt the safest possible residential electrical service configuration. In this system, the
power company provides 3 separate wires to each house: hot, neutral, and ground (EGC). Neutral is
connected to the EGC only close to the transformer, so the development of a voltage on a chassis due to heavy
loading does not arise (i.e., the situation discussed above as Bonding to Neutral Alone). The EGC is grounded
also near the transformer, but not otherwise. An internal fault sends high current along a path to ground of
very low resistance, thus easy to clear with a circuit breaker. The electric utility companies however regard
the third wire to be unnecessary, or at least not providing sufficient benefit to justify the extra cost.
Broken Shared Neutral Wire (Loss of Neutral Integrity), Con: The textbook p. 306-7 describes an unusual
and surprising cause of a shock hazard. It occurs when two (or more) homes share the same hot and neutral
lines from a shared distribution transformer. The hot lines are intact, but the neutral from House 1 is
broken, past the point where the neutral branch to House 2 is given off. Current which would normally
return from House 1 on its Neutral 1 is interrupted, so instead its current passes from neutral 1 to ground,
and returns to the transformer via the ground connection for neutral at the transformer. However, even if the
hot is not energized at House 2 (its power is off), if a person at House 2 touches a grounded metal case or
chassis, he provides an alternate return path for the ground current leakage: the current partially passes
from ground through his body to the chassis, then via the EGC to the bonded neutral for house 2, with final
return on the intact part of the neutral to the transformer. In summary, a fault affecting House 1 wiring can
lead to a potentially lethal shock hazard for a person touching a grounded chassis in House 2. How truly
bizarre!
More About How a Ground Fault Circuit Interrupter GFCI works
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The working of a GFCI circuit breaker is sketched in this NEMA diagram above.
The current on the
ungrounded hot “load power” line should be exactly equal to the current returning on the load neutral wire.
In the sensing coil, the two currents coil in opposite winding directions. This normal condition results in no
net magnetic flux generated in the sensing coil. If there instead is a fault current, the load neutral and load
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338
EEAI3 p. 309-10
https://www.nema.org/Products/Documents/NEMA-GFCI-2012-Field-Representative-Presentation.pdf
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power currents passing through the sensing coil are not exactly equal, the sensing coil detects this imbalance
(as little as 4 to 6 mA greater current in the hot “load power” line). This causes the trip solenoid to open the
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Pushing the
trip mechanism, shutting off the hot “load power” line and apparently also the neutral line.
Test button introduces a small current diversion (with current limited by the test resistor), creating an
imbalance sensed at the sensing coil, opening the trip mechanism. The Reset button restores the closed
status of the trip mechanism.
Note: “All GFCI outlets have one little-known flaw: their circuitry eventually wears out, usually after about 10
years... The reset button alone won't tell you if a pre-2006 GFCI outlet is still working properly—you'll need
to check it with a special tester... All GFCIs manufactured after mid-2006 are designed to tell you when they
fail. The vast majority indicate failure by shutting off power permanently. So someday your GFCI (and any
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other outlets connected to it) will simply stop delivering power and you'll have to replace it.”
GFCE devices should be tested at regular intervals to be sure they are still working.
Power Quality
We skipped this important but advanced subject in our class, discussed in Chapters 13,
some highpoints.
341
and I offer only
Problems can arise when two or more loads arranged in parallel share the same voltage source. This
arrangement lowers the total impedance Z across the multiple loads, and this leads to reduction of the load
voltage.
Variations of the load voltage take on several possible forms:


Fluctuations: small changes between 90% and 110% of the rated value. If slow and infrequently
recurring (over hours, with frequency ≪ 60 Hz), it may not be noticeable by people or equipment
Flickers: These are fast and sometimes cyclic change in V that are often readily detected visually and
can be annoying. They can also cause computer freezeups, jitter of TV images, faulty signals and
malfunctions in electronics, and loss of stored information, etc.. The rapidity of change makes it more
apparent. The textbook states that incandescent lights are more susceptible to visible flicker (19%
reduction in light intensity in the book example for a 10% reduction in voltage) compared to ballasted
fluorescent lighting (10% 342
reduction in light intensity in the same example). This is attributable to
differences in gain factor, a measure of how much the light intensity changes when the voltage
fluctuates. Flicker can be reduced by installing a series capacitor on the distribution feeder. (In the
textbook example, the magnitude of load voltage reduction when a 2nd load is switched on is reduced
from 12.5% to only 0.1%.)
Humans detect flicker with greatest sensitivity (and become annoyed maximally) at a flicker
recurrence rate of about 8-10 Hz, whereas flicker is visually undetectable beyond a critical flicker
frequency CFF of as low as 35 Hz for many humans, but up to 80 Hz or more for the most sensitive
folks. Flicker may still be harmful to equipment even if not visually apparent. Flicker is more
apparent when it is of high amplitude, when it is recurrent, when mean light intensity is greater, and
also when the light wavelength (spectral composition) falls in the range where human perceptibility
of
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light is maximal (a relationship expressed by its luminous flux). Other factors also enter in.
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http://www.elec-toolbox.com/Safety/safety.htm#GFCIs
http://www.familyhandyman.com/electrical/wiring-outlets/testing-gfci-outlets/view-all
341
EEAI3 p. 418-513
342
flicker is less with electronically ballasted fluorescents [which output rapid AC of over 20 kHz], but that
incandescent bulbs flicker less than old-fashioned magnetically ballasted fluorescents. This topic seems to
generate active debate.
343
http://webvision.med.utah.edu/book/part-viii-gabac-receptors/temporal-resolution/ and
340
http://home.ieis.tue.nl/rcuijper/reports/Perz%2520M_Master%2520Thesis_Flicker%2520Perception%2520in%2520the%2520Periphery.pdf and
https://en.wikipedia.org/wiki/Flicker_fusion_threshold and
https://en.wikipedia.org/wiki/Luminous_flux
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




Sags: Voltage drops below 90% of rated for up to a few seconds. These are common power quality
problems. They occur normally when heavy electric loads switch on, such as elevators, pumps, A/C
compressors and heating blowers, refrigerators, vacuum cleaners, etc. When motors and transformers
are first energized, the inrush current can be high (as much as 25 times the full-load steady state rated
current), and these commonly cause voltage sags. (It may be necessary to add an inrush current
limited circuit to prevent the high current from tripping circuit breakers or causing other damage.)
Sags of course can also arise from faults, such as a tree falling across a line, which acts like an
impedance added in parallel, thus reducing the load voltage. The impact of the fault is greater when
the Voltage sag VS can be expressed by:
VS (Voltage Sag) = (Vload ─ Vss)/Vss
and may take on negative or positive values. The textbook gives an example where switching in a
motor causes a VS = ─24% due to the inrush current. This is reduced by adding in a capacitor in 344
parallel to the load (motor)—specifically, adding a 6 Ω capacitor reactance changes the VS to +3%.
Swells: Voltage rises above 110% of rated for up to a few seconds.
Undervoltage (Brownout): Voltage below 90% for at least several minutes.
Overvoltage: Voltage above 110% for at least several minutes.
Interruptions: decrease in voltage below 10% of rated for any period.
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An example of the inrush current in one of the 3 phases of a motor is illustrated (below).
Here, the voltage
is in blue, the superimposed current in red. The time scale at the bottom shows that the current begins to
flow in the first division on the left, just before 09:49:01.0, at which time the current rapidly builds up to a
Irms peak of about 850 A (by 09:49:01.0, value estimated from a separate graph not shown). The current then
tapers off to the equilibrium value which has been nearly attained at the right side of the graph, around 180 A
rms at about 09:49:04.0 (i.e., 3 seconds after the start, also shown on a separate graph). During the peak of
the inrush current, the voltage shows a sag, from ~220 V rms to ~ 206 V, or about 14 V rms, then rises to a
The transient inrush current peak decays to the steady state with an exponential decay factor or factors.
Motor inrush currents are high in high-efficiency motors.
344
EEAI3 p. 492.
http://ecmweb.com/site-files/ecmweb.com/files/archive/ecmweb.com/mag/612ecmPQfig2.jpg , image
slightly modified by MCM and stretched horizontally.
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Harmonic Distortion
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Periodic waveforms that are not purely sinusoidal can be represented by a Fourier Series (details omitted).
These include a series of terms involving sin(kωt) and current components Ik, where k has values 0,1.2....The
Individual harmonic distortion IHD for a component with index k and angular frequency kωt is the fraction
Ik/I1. Here, I1 is the current in pure sinusoidal form for the fundamental frequency. The Total harmonic
distortion THD is IH/I1 , where IH
2
= �Idc
+ I22 + I32 + ⋯ Thus the THD is a measure of the total distortion of
the waveform arising from DC and harmonics compared to a purely sinusoidal fundamental signal I1 having
frequency f=2πω = 1/T (in Hz or s-1). Here, T= waveform period =1/f = 1/2πω (in s). THD is ≥ 0 and can
exceed 100%.
An example of a problem arising from THD in a three phase system: the three phases (shown as 1, 2, and 3
in the diagram) will theoretically cancel each other out at the neutral wire. However, if the 3 phases contain
3rd order harmonics, the currents will not fully add to zero. As seen in the figure, the 3rd harmonics from the
3 phases will lead to an oscillating current in the neutral wire (“3rd harmonic wave”), which can be dangerous
347
since the neutral is expected and designed to carry minimal current...
Large and/or non-linear loads such as arc furnaces (aluminum smelters), adjustable speed drives (i.e.,
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variable frequency drives VFDs), and power electronic (such as SCR converters) can produce significant
349
The THD of computer power supplies, monitors,
harmonic distortions in the bus voltage and power grid.
AC/DC converters, electronic ballasts, X-ray and MRI equipment, and Uninterruptible Power Supply UPS
350
The textbook offers
power can be very large, again apparently because they represent non-linear loads.
Fluorescent Lamp THD=15-25%
Personal Computers THD=70-120%
Computer Monitors THD = 60-120%.
Although individual computers and monitors draw low currents, they often are present in large numbers on
dedicated feeders, causing the feeder to be “highly polluted with harmonics”. A better strategy is to
intersperse these nonlinear devices with simpler loads such as heaters and lights. The textbook gives an
example in which a polluted feeder feeding many computers having THD=65% is “treated” by adding a heating
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load, resulting in a reduction of THD to 17%.
In summary, harmonic distortion THD can cause many serious problems:

resonances that can produce very high voltages that are potentially dangerous or damaging to
equipment
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https://en.wikipedia.org/wiki/Fourier_series and
https://en.wikipedia.org/wiki/Harmonics_%28electrical_power%29
347
Image (by author Dkangell) copied and text paraphrased from
https://en.wikipedia.org/wiki/Harmonics_%28electrical_power%29#/media/File:3rd_orderHarmonics.png
348
https://en.wikipedia.org/wiki/Variable-frequency_drive
349
EEAI3 p. 501
350
http://www.eweb.org/powerquality/harmonic and other sources
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EEAI3 p. 502
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






increased losses in transmission lines, transformers, and generators; possibility of resonance damage
to insulators and lines from high voltage
damage to capacitor banks (from overvoltage)
overvoltage or added drag forces (drag torque) in synchronous motors. (The textbook p. 509 gives an
example of a 3-phase motor for which the normal rotation sequence of the magnetic field of the
fundamental is a-b-c, but for which the 5th harmonic exerts an out-of-sequence a-c-b drag torque
opposing the fundamental.) This can lead to sluggish rotation.
reduction of the overall power factor pf. Only voltages and currents of the same frequency produce
real power. Conventional low-cost devices used to measure power output and power factors are
inaccurate in the presence of severe harmonics. More accurate but much more expensive meters can
be justified by the power company wanting to maximize billable kWh.
increased EM interference of communication networks
premature aging of insulators
picture jitters; freezing and rebooting of computers and other sensitive equipment such as cell phones,
due to magnetically-induced voltages, etc.
This is clearly a complex and important subject.
Power Grid and Blackouts
We minimally discussed these topics, presented in Chapter 14,
points.
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and I will take time only to offer a few
Power companies choose generally to build generating capacity to meet the average regional power needs.
They find that it is not economically feasible to build capacity to handle the highest possible demand
encountered. Instead, the grid is interconnected, and companies buy power to meet high excess demand, and
sell power when generation exceeds local demand.
A blackout may result from a deficiency or a surplus in power relative to power demand exists, if not
corrected in seconds—a power balance must be maintained. Some bulky systems (e.g., hydroelectric
turbines) have relatively long lag times in responding to requests to change output.
When demand is reduced, must slow generators by reducing water input (can take 7 to 10 s), and in thermal
plants, can allow steam to escape and reduce combustion, etc. Can also increase exports and/or decrease
imports.
When demand is increased, can increase water input to turbines, recruit already spinning reserves if available
(these are rotating generators on standby that are not yet generating). Can also decrease exports or increase
imports.
Greater interconnectedness provides more opportunities to import needed power, but also increases
complexity and makes it possible for blackouts to spread to wider areas. If power generation is insufficient for
local demand, we may reduce exports, increase generation rate where possible, reduce loads by disconnecting
some where feasible (rolling blackouts), and import more power.
Topology of the grid is important, in terms of how various power stations are interconnected for maximizing
stability while minimizing cost of transmission lines and control equipment. Detailed analysis requires
solving nonlinear equations of great complexity.
Electrical demand in an urban region like Seattle tends to exhibit two peaks of demand, one around 9 AM and
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Demand above the generating capacity prompts importing of power from
the other around 6 PM.
neighboring utilities, whereas demand below generating capacity prompts exporting of power to neighboring
utilities (or reduction of production). The Northwest imports power from the East at noon ET and exports to
the East at 9 AM ET. In summer, the NW exports electricity southward for air conditioning, whereas it
imports it during the winter heating months.
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353
EEAI3 p. 515-539
An empiric formula said to be for the Seattle-area demand is given on EEAI3 p. 524.
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North American Interconnections and Reliability Councils
In North America, there is a web of interconnecting utilities allied under the umbrella non-profit organization,
354
North American Electric Reliability Corporation NERC, formed to “promote the reliability and adequacy of
bulk power transmission in the electric utility systems of North America.” It oversees:
The Eastern Interconnection (covers most of eastern North America, extending from the foot of the Rocky
Mountains to the Atlantic seaboard, excluding most of Texas):
Florida Reliability Coordinating Council (FRCC)
Midwest Reliability Organization (MRO)
Northeast Power Coordinating Council (NPCC)
ReliabilityFirst (RF ). This is the successor to three reliability organizations: the Mid-Atlantic Area
Council (MAAC), the East Central Area Coordination Agreement (ECAR), and the Mid-American
Interconnected Network (MAIN)

SERC Reliability Corporation (SERC)

Southwest Power Pool, Inc. (SPP)
The Western Interconnection covers most of western North America, from the Rocky Mountains to the Pacific
coast. It is tied to the Eastern Interconnection at six points, and also has ties to non-NERC systems in
northern Canada and Northwestern Mexico. Its reliability council is:




 Western Electricity Coordinating Council (WECC)
There are also:
The Texas Interconnection
 Texas Reliability Entity (TRE)
The Quebec Interconnection
The Alaska Interconnection, for which the reliability council is

Maps of much of the US grid are shown in the section, “Electrical Transmission”. Controls on these various
systems are loose and diverse. Recent 2014 Zonal Topology Diagrams of the WECC for summer and winter
355
are given here.
Causes of Blackouts
Blackouts are more likely to occur in times of heavy loading, when plants are generating near their limits and
unused reserve capacities (including spinning reserves are minimal. Blackouts can occur due to






Faults in transmission lines causing excessive currents
Lightning (causing insulator failure), earthquake (damaging
substations), strong winds (felling trees),
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heavy frost and ice storms (breaking heavily laden lines)
Failure of major devices, such as generators and transformers. For instance, a synchronous generator
can quickly go out of synchronism when mechanical input power and output demand are not in
balance.
Improper function of protection and control devices
Human errors
The textbook lists major US blackouts:

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355
356
1965: On the evening of November 9, the Northeast blackout of 1965 affected portions of seven
northeastern states in the United States and the province of Ontario in Canada. It affected 30M
https://en.wikipedia.org/wiki/North_American_Electric_Reliability_Corporation
https://www.wecc.biz/Reliability/2014PSA_draft.pdf
https://en.wikipedia.org/wiki/Ice_storm
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people and took 24 hours to restore the system. It began with tripping of an improperly set relay
protecting a line.
1977: On July 13–14, the New York City blackout of 1977 resulted in looting and rioting. It affected
8M people and lasted 25 hours. It began with lightning.
2003: On August 14, the Northeast blackout of 2003, a wide-area power failure in the northeastern
USA and central Canada, affected over 55 million people. This lasted several days. It began with a
coal-generation plant going off-line, tripping of an overloaded line, etc.
Severe global blackouts, affecting more than 100M people, include:
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2012: July 30 and 31, 2012 India blackouts, the first affected 300M people, the second affected 620M
people (the largest in history), the two lasted 2 days. Began with tripped breakers during a time of
above normal power demand
2001: January 2, 2001, India, affected 230 M people
2014 November 1, 2014, Bangladesh blackout, affected 150M
2015 January 26, 2015, Pakistan blackout, affected 140M.
2005: August 18, 2005, Java-Bali blackout, affected 100 M.
Future Power Systems
We did not take time for this subject, discussed in Chapter 15.
•
Smart Grid
o
o
o
o
o
o
o
o
o
o
o
o
357
358
359
360
361
362
363
364
357
Some of the topics of interest include:
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, including some of the following components
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Improved accessibility and bidirectional flow (e.g., from customer PV)
360
Improved system flexibility of network topology, Combined Heat and Power (CHP) Systems
Increased system capacity
Improved reliability, reduced blackouts and forced outages
Renewables (large scale and customer owned) integrated with weather prediction and operated
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with greater central communication and control
Improved Methods of Storing energy (Energy Storage Systems ESS, such as Superconducting
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Magnetic Energy Storage SMES, Batteries, Hydrogen H2 combined with Fuel Cells)
Intelligent Monitoring with advanced meters and sensors, rapid data-intensive analysis and rapid
secure communications, Geosynchronous and Low Earth orbit satellites, Phasor Measurement
Units PMU aka Synchrophasors (used to synchronize phase among remotely connected buses based
on a single clock). The real and reactive power flowing from bus 1 to a widely separated second
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bus 2, where the power angle = δ and the inductive reactance of the line = x, are given by
P2 =
V1 V2
x
sin δ
and
Q=
V2
x
(V2 − V1 cosδ)
provided these measurements are made with precisely synchronized time using PMUs.
Smart House with home Energy Management System EMS, Smart Appliances (which can be
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remotely controlled to reduce load when needed), Home Power Generation.
Self-Diagnosis, Fault detection, Self-Healing Grid, Rapid restoration, Substation and distribution
automation
Sustainability
EEAI3 p. 541-557
http://energy.gov/oe/services/technology-development/smart-grid and
https://en.wikipedia.org/wiki/Smart_grid
http://www.nist.gov/smartgrid/beginnersguide.cfm
http://energy.gov/oe/technology-development/smart-grid/distributed-energy/combined-heat-and-power-chp-systems
https://www.smartgrid.gov/the_smart_grid/smart_grid.html
http://www.sciencedirect.com/science/article/pii/S1875389212021645
EEAI3 p. 545
https://www.smartgrid.gov/the_smart_grid/smart_home.html
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Improved power system security and reduced vulnerability.
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Plug-In Electric Vehicles PEV and Plug-In Hybrid Electric Vehicles PHEV (with charging rates responsive to
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grid conditions to prevent blackouts)
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Alternative Renewable Energy Resources: Wind, solar, hydrokinetic, geothermal, biomass, H2, etc.
•
Less Polluting Power Plants: using coal gasification syngas, carbon sequestration
•
Distributed Generation Systems: including Natural Gas and/or Fuel Cell based home electricity
generation
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Improved Power Electronics
•
Enhanced Reliability of Power Systems
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Intelligent Operation, Maintenance , and Training
o
o
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Robots
Virtual Monitoring, Virtual reality techniques
Space-Based Power Plants?
https://www.smartgrid.gov/the_smart_grid/plugin_electric_vehicles.html
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Glossary and Mini-Topics
Topics and terms are included here for added emphasis or for when they are not fully treated in the body of
this summary.
Dynamo vs. Alternator
The word dynamo became associated exclusively with the commutated direct current electric generator,
while an AC electrical generator using either slip rings or rotor magnets would become known as an
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alternator.
Volt-Ampere VA, Watts, and UPS Selection:
“A volt-ampere (VA) is the unit used for the apparent power in an electrical circuit, equal to the product of
root-mean-square (RMS) voltage and RMS current... Apparent power is the magnitude of the vector sum
(S) of real (P) and reactive (jQ) AC power vectors... Some devices, including uninterruptible power supplies
(UPSs), have ratings both for maximum volt-amperes and maximum watts. The VA rating is limited by the
maximum permissible current, and the watt rating by the power-handling capacity of the device. When a
UPS powers equipment which presents a reactive load with a low power factor, neither limit may safely be
exceeded. For example, a (large) UPS system rated to deliver 400,000 volt-amperes at 220 volts can deliver
a current of 1818 amperes... In direct current (DC) circuits, this product is equal to the real power (active
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power) in watts. ”
Neil Rasmussen/APC: “The power drawn by computing equipment is expressed in Watts or Volt-Amps
(VA). The power in Watts is the real power drawn by the equipment. Volt-Amps is called the "apparent
power" and is the product of the voltage applied to the equipment times the current drawn by the
equipment. Both Watt and VA ratings have a use and purpose. The Watt rating determines the actual
power purchased from the utility company and the heat loading generated by the equipment. The VA
rating is used for sizing wiring and circuit breakers.
The VA and Watt ratings for some types of electrical loads, like incandescent light bulbs, are identical.
However, for computer equipment the Watt and VA ratings can differ significantly, with the VA rating
always being equal to or larger than the Watt rating. The ratio of the Watt to VA rating is called the "Power
Factor" and is expressed either as a number (i.e. 0.7) or a percentage (i.e. 70%).
UPS have both Watt ratings and VA ratings. Neither the Watt nor the VA rating of a UPS may be
exceeded. In most cases, UPS manufacturers only publish the VA rating of the UPS. However, it is a
standard in the industry that the Watt rating is approximately 60% of the VA rating, this being the typical
power factor of common loads. Therefore, it is safe to assume that the Watt rating of the UPS is 60% of the
published VA rating.
Using APC sizing guidelines or an APC Configuration can help avoid these problems, as the load power
values are verified. Equipment nameplate ratings are often in VA, which makes it difficult to know the
Watt ratings. If using equipment nameplate ratings for sizing, a user might configure a system which
appears to be correctly sized based on VA ratings but actually exceeds the UPS Watt rating.
By sizing the VA rating of a load to be no greater than 60% of the VA rating of the UPS, it is impossible
to exceed the Watt rating of the UPS. Therefore, unless you have high certainty of the Watt ratings of the
loads, the safest approach is to keep the sum of the load nameplate ratings [in watts or V-A] below 60% of
the UPS VA rating. Note that this conservative sizing approach will typically give rise to an oversized UPS
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and a larger [backup] run time than expected... ”
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https://en.wikipedia.org/wiki/Dynamo
https://en.wikipedia.org/wiki/Volt-ampere