# Harmonics Basics

```Straight Talk About PWM AC Drive Harmonic Problems and Solutions
Rockwell Automation Mequon, WI
Abstract:
Though much has been written about harmonics and
related issues with respect to AC drives, many drives
users still seek clear answers to some basic questions.
The purpose of this paper is to provide the interested
reader with some basic information regarding AC
drives and harmonics with a simplified explanation of
harmonics and power factor, showing how both can
affect a distribution system. It is the intention of the
author to dispel some of the myths as well as point out
legitimate concerns, show some viable solutions and
their pros and cons.
Drive basics:
Before we can have a meaningful discussion on
harmonics with respect to AC drives, first it is
necessary to have a good understanding of the basic
workings of a modern PWM AC drive, specifically how
it draws power from the utility line. Figure 1 below is a
schematic diagram of a typical “voltage source” AC
drive power structure.
A modern AC drive power structure consists of three
basic stages. It is ironic that while most DC drives run
on AC, most AC drives run on DC. This is because the
inverter section shown in yellow in figure 1 requires a
stable DC source to operate. Therefore, the first stage of
the drive must convert three-phase AC to DC. The first
stage is known as the converter section.
In an AC drive, the converter stage consists of a threephase, full wave diode bridge, though SCRs (Silicon
controlled rectifiers) are sometimes used in place of diodes.
If this stage were isolated from the rest of the power
structure, we would see a DC voltage with a 360 Hz ripple
at the DC bus connection when 3 phase power is applied to
the input (see figure 2).
A filter is required to smooth out the ripple on the DC bus in
order to run the IGBT inverter. Therefore, a second or
“filter” stage is required. Primarily, this consists of a large
capacitor bank shown in green. Often an inductor or “link
choke”, shown in orange, may be added. The choke, when
used, helps buffer the capacitor bank from the AC line and
serves to reduce harmonics. We will discuss why as we go
on.
The third stage, shown in yellow, is the inverter section.
This section uses high-speed transistors as switches to apply
a “Pulse Width Modulated” or PWM waveform to the
motor. Taking advantage of the fact that a motor is basically
a large inductor, and that current does not change very fast
in an inductor, the DC bus voltage can be applied in pulses
of varying width in order to achieve current in the motor
that approximates a sine wave.
of the sine wave. As load is applied to the DC bus, the
capacitor bank discharges and the DC voltage level drops. A
lower DC voltage level means that the peak of the applied
sine wave is higher than the capacitor voltage for a longer
duration. Thus the width of the pulse of current is
determined in part by the load on the DC bus. Refer to
figure 3b.
Figure 3b shows input line voltage Vac, Filtered DC bus
voltage Vo (in red) and the pulsating Input Current I. Note
that the Vo trace in black would be before the filter capacitor
Figure 2 – Unfiltered Three-Phase Rectified Voltage.
For the most part, it is the rectifier and the filter that
have an affect on the power line. Let’s use a single
phase model to show how the converter and filter work
to change AC into DC. Shown in figure 3a below is a
single phase representation of a diode rectifier circuit
with a filter capacitor and load resistor across the DC
bus.
Figure 3a – Single Phase Converter and Filter.
Figure 3b - Single Phase Converter Measurements.
Upon application of AC power the capacitor will charge
up to the peak of the applied line voltage through the
diode bridge. Each diode works electrically the way a
check valve works in a fluid. It allows current to flow in
one direction. For the four diodes in the single-phase
bridge, two are conducting at a time (one plus and one
minus) while the other two are blocking. When the
polarity of the AC input changes, the conducting and
blocking diode pairs also change.
The aforementioned characteristics hold true for the three
phase model with the difference being 6 diodes and 6 pulses
per cycle rather than two pulses per cycle as shown in the
single phase model. For an AC drive, the load is the Inverter
section. One can see by looking at figure 2 that if we have a
three phase diode bridge converter we get 6 of these voltage
pulses for one complete three phase line cycle. It is the
pulsating input current shown in figure 4 that gives us the
term “nonlinear load” since the current does not flow in
proportion to the applied voltage.
When a load is applied to the DC bus, the capacitor will
begin to discharge. With the passing of the next input
line cycle, the capacitor only draws current through the
diodes and from the line when the line voltage is greater
than the DC bus voltage. This is the only time a given
diode is forward biased. This only occurs at or near the
peak of the applied sine wave resulting in a pulse of
current that occurs every input cycle around the +/-peak
In fact, with a nonlinear load, current may not flow at all for
a major part of the applied voltage cycle. In a three-phase
system, the widest conduction time possible would be 120
degrees (roughly +/-60 degrees from the peak). Once we go
outside this 120 degree conduction window, one of the other
two phases will have a higher peak voltage and current will
flow from that phase.
with a specific magnitude. For example, the 5th harmonic on
a system with a 60 Hz fundamental waveform would have a
frequency of 5 times 60 Hz, or 300 Hz. These higher order
waveforms are called “harmonics”. The collective sum of
the fundamental and each harmonic is called a Fourier
series. This series can be viewed as a spectrum analysis
where the fundamental frequency and each harmonic
component are displayed graphically in a bar chart format as
shown in figure 6.
Figure 4: Input Line to Neutral Voltage (in black)
and Input Current (in green) on phase A of a 3
phase AC drive.
Figure 6 – Harmonic Spectrum Analysis.
To arrive at a total current, each component is added as a 90
degree vector. That is to say the total current is the square
root of the sum of the square of each component.
Figure 5: 60Hz Input Line to Neutral Voltage (in
red) and Input Current (in blue) on phase A of a
Harmonics Explained:
Now that we understand how current is drawn from the
AC line by a drive, let’s try to define the term
“harmonics”. Looking at the waveforms in figure 5 we
can see that each waveform is close to a perfect sine
wave and the current is proportional to voltage
(although the current is lagging the voltage). This is a
linear load and contains no harmonics. A perfect sine
wave by definition has no harmonics but rather one
fundamental component at one frequency. The
waveforms in figure 5 are sine waves at one frequency,
60 Hz. We saw that nonlinear loads such as AC to DC
rectifiers produce distorted waveforms. Harmonics are
present in waveforms that are not perfect sine waves
due to distortion from nonlinear loads. Around the
1830’s a French mathematician named Fourier
discovered that a distorted waveform can be
represented as a series of sine waves each an integer
number multiple of the fundamental frequency and each
Leaving the mathematical representations aside we can say
something about the harmonic content by simply looking at
the wave shape. The more it looks like a sine wave, the
lower the harmonic content. If a waveform is a perfect
square wave, it will contain all of the odd number harmonics
out to infinity. Even number harmonics can be detected by a
lack of symmetry about the X-axis. If the top and bottom
half of the waveform to not look like mirror images of each
other, even harmonics are present. Typically a drive will not
cause even harmonics. The sources of most even harmonics
are arc furnaces, some florescent lights, welders and any
device that draws current in a seemingly random pattern.
Another noteworthy fact is that balanced three phase
rectifier type loads (such as an AC drive) do not produce a
third harmonic component. Nor do they produce any
harmonic component with 3 as a multiple (3rd, 9th, 15th, 21st
ect). These are known as triplen harmonics and are not
present in most AC drives. If we look close at figure 6 we
can see no even harmonics or triplens. The 11th harmonic
and higher is a point where the magnitude diminishes to a
very low level. What we are left with is the 5th and 7th order.
These are the “problem child” harmonics for AC drives. If
we can reduce these two harmonic components, we will
have gone a long way in meeting any harmonic specification
for AC drives.
As we can see from the six-pulse waveform in figure 7, we
do not have a sine wave or a square wave. It can be said that
the input current contains some harmonics.
low impedance is known as a “stiff” source. Figure 8 is a
“soft” source (such as a generator) with voltage flat topping.
The distorted line voltage might then introduce harmonic
currents in other linear loads such as motors. Harmonic
current in a motor does not contribute to torque at the shaft,
but does add heat and can raise the operating temperature of
a motor.
Figure 7 – Typical input current for an AC drive
Harmonic Problems:
Now that we know harmonic currents flow in an AC
drive with a 6 pulse front end, let’s address what, if any,
problems this may cause. Although noise coupling into
phone lines and other equipment is often sited, the main
issue is the added cost of the power distribution
infrastructure. Power is only transferred through a
distribution line when current is in phase with voltage.
This is the very reason for concerns about input “power
factor”. Displacement power factor in a motor running
across the line can be explained as the cosine of the
phase angle between the current and voltage as shown
in figure 5. Since a motor is an inductive load, current
making the power factor about 0.75 to 0.8 as opposed to
about 0.95 for many PWM AC drives. In the case of a
resistive load, the power factor would be 1 or “unity”.
In such a case all of the current flowing results in power
being transferred. Poor power factor (less than 1 or
“unity”) means reactive current that does not contribute
power is flowing.
Neither harmonic nor reactive current flowing through
a system produce power. The power infrastructure has
to carry these currents causing heat loss due to
increased I^2*R drop in the wire and higher flux in
transformer iron. Transformers and distribution lines in
some cases may need to be upsized to handle the
burden of this additional non power producing current.
Harmonic current distortion can also introduce voltage
distortion. Since a typical 6 pulse nonlinear load draws
current only near the peak of the sine wave, I^2*R
power lines only occurs at the peak. A combination of
high source impedance and harmonic currents can
cause a “flat topping” effect on the line voltage. A
source with high impedance is known as a “soft” source
because voltage is easily distorted, while a source with
Figure 8 – Voltage (in red) flat topping on a “soft”
source.
While all of these potential issues are real the reality is they
are normally not as serious as some would like us to believe.
The IEEE-519 document has set limits on the level of
“allowable harmonics” and specified these limits at “the
point of common coupling” or PCC. The PCC is the point
where the customer meets the utility, and is usually the
point between the utility transformer and the customer’s
facility transformer as seen in figure 9. IEEE-519 defines
limits at the PCC because the power company pays for the
infrastructure up to the PCC. The user bares the cost of the
distribution system within their own facility and any over
sizing that may be required.
Harmonic distortion measurements are normally given in
“total harmonic distortion” or THD. THD defines the
harmonic distortion in terms of the fundamental current
h=¥
THD % =
å (M
h
)2
h=2
M
´ 100 %
fundamenta l
Where Mh is the magnitude of either the voltage or current
harmonic component and Mfundamental is the magnitude of
either the fundamental voltage or current. It is important to
note that THD uses the instantaneous fundamental current
as the denominator. Therefore, if a consumer’s plant is
THD calculated may be very high. However, the current
distortion relative to the utility supply may actually be less
than when they are running at peak load.
Thus IEEE-519 uses a term called TDD (total demand
distortion) to express current distortion in terms of the
maximum fundamental current that the consumer draws:
h=¥
TDD % =
å (I
h
h=2
)2
´ 100 %
Iload is the maximum fundamental current that the
consumer draws and it could be measured over a specified
time period, or estimated. Keep in mind that TDD is only
used to measure current distortion, not voltage distortion.
Because TDD uses the maximum fundamental current
consumed as the denominator, TDD will most likely less
that THD.
The limits IEEE 519 places on current distortion also
depend on the ratio of Isc/Iload where Isc is the short
circuit current. Isc for a supply transformer can usually be
obtained from the utility. Isc can also be calculated
knowing the supply transformer impedance using the
following formula:
Isc »
KVA
Zxfrm, pu ´ V sec ondary ´ 3
The ratio of Isc/Iload determines the “stiffness” of the
supply. Therefore, the “stiffer” the supply, the higher the
ratio Isc/Iload will be, and the more current TDD allowed.
loads being loaded to the same level. In other words, if we
looked at input current to three identical 100 horsepower
drives in the same facility running at equal power levels, we
would most likely see three distinct harmonic spectrum
patterns from each drive. Each could have a current THD
level of say 20%. Looking up stream before the three branch
circuits for each drive we would see a total current for each
together. However the THD in current at the same point
upstream might only be 7%. Be cautious of anyone who
tries to interpret “point of common coupling” as anyplace
other than the utility interface. They may be trying to sell
equipment that might not be needed.
Furthermore, the displacement power factor that one might
see with a drive might be 0.95% as opposed to 0.75% power
factor for the same motor across the line. This frees up
ampacity in the system. Some of this may be used up by the
increase in harmonics but in most cases the over all effect is
a net benefit by using a drive. In most cases sizing the
transformer and power feed lines as if the motor were
running across the line is more than adequate to handle any
harmonic currents from an AC drive.
Solutions:
One of the simplest solutions in reducing harmonics is to
add a reactor at the line input side or in the DC link. This
reactor or inductor will not allow current to change fast. It
forces the capacitor bank to charge at a slower rate drawing
current over a longer period of time. The addition of this
component can reduce typical distortion levels from more
than 80% to less than 20% THD depending on source
impedance. Figure 10 shows an AC drive without a dc link
reactor or line reactor and figures 4 and 7 show AC drives
with dc link reactors. Most drive manufactures include these
reactors in larger drives. Making sure all large drives (10
horsepower and above) have a reactor can go a long way
toward reducing harmonics in a given facility.
Figure 9 – Example of the PCC.
In most cases it is much easier to meet IEEE-519 limits
at the utility interface than to try and meet it at every
point in the facility. This is especially true where many
sources of harmonics exist within a facility. Unlike
point source water pollution in a stream or river system,
when all of the point sources of current harmonics in a
given facility are added up, many of them cancel each
other out. Natural phase shifting and variations in
source impedance produce different distortion
characteristics even on two or more identical nonlinear
Figure 10: Input Line to Neutral Voltage (in red) and
Input Current (in green) on phase A of a 3 phase AC
drive without a DC Link choke or line reactor.
In most cases, beyond the addition of a reactor,
harmonic mitigation techniques are not needed. If they
are, many options exist including: 12 or 18 pulse
converters, Passive filters, Active filters and Active
front ends.
The 12 and 18 pulse solutions rely on two or three
separate three-phase systems each feeding a diode or
SCR bridge. The DC output is then combined to feed
the capacitor in the DC bus. Each of the three phase
input sections is phase shifted from the other by
60degrees/n where n is the number of three phase feeds.
Thus an eighteen pulse system requiring three separate
3 phase feeds would have a phase shift of (60degrees/3)
20 degrees. This type of system is effective if all of the
three phase feeders have balanced voltage. It also
requires one rectifier section for each 3 phase feed and
a special transformer to produce the multiple secondary
phase shifted outputs.
has the typical 6 pulse waveform shown previously in figure
7. The primary current in the 12 pulse transformer looks a
bit different. The 12 pulse primary current shown in figure
11b is the algebraic sum of the two secondary outputs. Since
a 30 degree phase shift exists, the peaks do not line up. The
result is an input current that looks a bit more sinusoidal and
therefore has a lower harmonic content. Figure 11c shows
the 18 pulse solution. Notice the improvement in the current
shape over the 12 pulse input.
Figure 11c Primary current for an 18-pulse system.
A passive filter, as seen in figure 12, offer some help in
reducing harmonics by allowing current to flow primarily at
the fundamental. They use energy storage devices such as
inductors and capacitors to draw current from the line at low
frequency (60 Hz) and deliver it to the drive in the required
bursts or pulses (harmonics).
Figure 11a – 12 Pulse converter (parallel output
type).
Figure 12 Passive Filter on AC Drive.
Active filters can be very effective but are also somewhat
expensive. They work by using an active switch
arrangement that looks very much like the inverter side of a
drive. Using current sensors this device adds the sine wave
complement of the current it measures to the line, making
the current up stream from the drive look sinusoidal.
Figure 11b – Primary current for a 12-pulse system.
Figure 11a shows a typical 12 pulse front end
configuration. Notice the transformer has two, 30
degree phase shifted secondary outputs . Each
secondary windings feeding it’s diode bridge and each
An active front end, as shown in figure 13, allows an AC
drive to take current from the line in what is very close to a
pure sine wave. Therefore, THD is very low. The active
front end also has other important benefits. It is bidirectional and can be used to feed multiple drives. Simply
put this means that it can draw current from the line and
deliver current to the line should the drive or drives need to
handle regenerative energy from an overhauling or
decelerating motor.
degrees phase shifted. This means that the power factor is –
1 rather than 1. It is still unity power factor with the minus
system is regenerating.
Conclusion:
Figure 13, Active Front End Converter.
While it is true that in some cases AC drives can cause
harmonic related problems, it is important to recognize these
instances are not the norm. Often what drives add to the
system in harmonics they make up for with improved input
power factor actually freeing up KVA in the power
distribution system. This is especially true when a link
choke is included in the drive. Though many elaborate
harmonic mitigation solutions exist, it is often an
unnecessary expense. IEEE-519 needs only to be satisfied at
the Point Of Common Coupling and not within a given
facility. When attacking harmonics, passive filters and
multi-pulsed solutions are among the lowest cost. Active
filters cost a bit more and do a better job. An active front
end may be the most expensive in terms of up front cost.
Long term though, money saved by not requiring dynamic
braking equipment, and energy savings in regeneration of
power may make this the most economical solution if
regeneration or “braking” are required.
Acknowledgements:
Thanks to Nick Guskov and Howard Murphy for assistance
with the graphics and other content of this paper.
Figure 14a – Active front end motoring.
References:
IEEE Recommended Practices for Harmonic Control in
Electric Power Systems, IEEE Std.519-1992.
Roger C. Dugan, Mark F.MaGranaghan, H. Wayne Beaty,
Electrical Power Systems Quality. McGraw-Hill inc. 1996
Figure 14b – Active front end regenerating.
Figure 14a shows input line to neutral voltage and input
current for an active front end converter in the motoring
condition. Notice current and voltage are in phase and
both current and voltage wave shapes look relatively
sinusoidal. The result is excellent power factor with low
harmonic content. Figure 14b shows the same
waveforms with the drive in a regenerative condition.
The only difference is that current and voltage are 180
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