Laboratory Manual For Electric Energy Engineering EE

```Laboratory Manual
For
Electric Energy Engineering
EE-360
Electrical Engineering Department
King Fahd University of Petroleum & Minerals
Dhahran, Saudi Arabia
Experiment
Title
No.
1
Three Phase Circuit
Page
No.
3
2
Three Phase Power Measurement
6
3
Magnetic Circuit
9
4
Equivalent Circuit of Transformer
12
5
Regulation and efficiency of a single phase
Transformer
16
6
Load Characteristic of shunt and compound
DC generator
19
7
Torque Speed Characteristic of DC shunt
and compound motors
22
8
Determination of Parameters of
Synchronous Generators
26
9
Torque Speed Characteristics of 3Φ
Induction Motors
29
10
Determination of Induction Motor Parameters
32
2
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#1
THREE PHASE CIRCUITS
Objectives:
•
•
•
To learn how to make wye (Y) and delta (∆) connections
To study the relationship between voltage and current in three phase
circuits.
To make power calculations.
Apparatus:
•
•
•
•
2 AC voltmeters
2 AC Ammeters
1 3Φ variable AC power supply
Theory :
In a Y connection , the line and the phase quantities are related by:
Vp=VL/√3
(1)
Ip=IL
(2)
Whereas the relationships for a delta connection are
Ip=IL/√3
(3)
Vp=VL
(4)
The real and reactive powers for a 3 Φ circuit (either Y or ∆ connection) are
given as
3
P=√3 VL IL cos θ
(5)
Q=√3 VL IL sin θ
(6)
Where θ is the power factor angle of the balanced load
Procedure:
A:
Y – Connection
a
A
A
V
V
3 Phae Ac
B
b
C
c
Fig. 1 :
The Y - Connection
2. Switch the load to unity power factor mode
3. Select the balanced load from each phase
4. With the load switch off turn the power supply on and adjust the line to
neutral voltage to 120 volt or VL = 208 volt
5. Measure the line and phase voltages and currents. Make the table similar to
table1 on a separate page and enter your readings in the first 4 columns
VL
Vp
IL
Ip
VL / Vp
IL
Ip
/ P
4
Q
Remarks
Take three readings, one at the rated value of the load current (8A), one at ½
rated load and one at ¼ rated.
6. Repeat step 5 for 0.8 and 0.8 leading power factor loads
B:
∆ Connection
1. Connect the three phase load as shown in fig. 2
A
A
a
3 Phae ac
N
V
N
b
N
B
A
C
c
Fig. 2 : The Delta- Connection
2. Turn the power supply on and adjust for 120V A.C (Note: Vp=VL for ∆)
3. Repeat step 5 of the Y connection for unity, 0.8 lagging and 0.8 leading
power factors and enter in a table similar to table 1, call it table 2.
Report
1. Complete tables 1 and 2.
2. Calculate the total real and reactive powers.
3. Draw phasor diagrams showing the line and phase voltages and currents for
both Y and ∆ connections. Draw only for rated load, unity power factor
condition.
4. Verify the relationships for the phase and the line voltages and currents and
state reasons for any errors.
5
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electrical Engineering Department
EE 360
Electric Energy Engineering -
Experiment # 2
THREE PHASE POWER MEASUREMENT
Objectives:
1. Measure power in balanced Y and ∆ systems.
2. Determine power factor of 3Φ systems.
Apparatus:
2 Wattmeters
1 Voltmeter
1 Ammeter
1 3Φ variable AC power supply (Variac)
Theory:
a
M
A
V1
A
Three
Phase
V
B
b
V1
c
C
M
Fig.1: Two Wattmeter Connection
If two wattmeters are connected to measure the power of any 3Φ load, it can be
shown that the wattmeters will read V1
6
P1 = VL IL cos ( 30 – θ )
P2 = VL IL cos ( 30 + θ )
(1)
(2)
Where θ the power factor angle of the load. From (1) and (2) we can show that
the total power
PT = P1 + P2 = 3 VL IL cosθ
(3)
tanθ = 3 ( P1 - P2 ) / ( P1 + P2 )
(4)
Procedure
1. Connect the circuit as shown in fig 1. Connect the
2. Before you switch on, have your connections cheeked by the instructor.
3. Set the supply voltage to 200 V from a variac
4. Select the load power factor to be unity
5. On a separate sheet of paper make a table with 11 columns as shown in
table.1.
Pf
P1
P2
VAB
VCB
IA
PT
(Watt) (Watt) (Watt) (Volt) (Volt) (amp)
Pf
calc.
Pf
Error
(%)
PT
Calc.
Power
Error
calc.
Table.1: Results for Y connection
8 A, one for ½ rated and one for ¼ rated loads.
7. Repeat step 6 for 0.8 lagging as well as leading power factor conditions.
8. Connect the three phase load in ∆.
9. Set the supply voltage to 100 volts (VL= VP for ∆).
10. Repeat step 6 for unity, 0.8 lagging and 0.8 leading power factor conditions.
Enter the results in a table similar to table 1.call table 2.
7
Note: At a certain power factor, one of the wattmeters may try to read
backwards. Switch the supply off, reverse the voltage OR the current coil
connection. Mark the reading as negative.
Report
1. Using the wattmeter readings, compute the power factor from equation (4).
Enter it as pf (calculated) in tables.1 and 2. Calculate the percent error
between the calculated and the recorded power factors.
2. Use equations (1) and (2) to calculate the total power. Compare it to the
measured total power and enter the percent error in the tables.
3. Comment on the levels of error between the computed and measured values.
State any sources of error.
4. Draw a phasor diagram and show why equations (1) and (2) can be used to
calculate the total power.
8
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#3
MAGNETIC CIRCUITS
Objective:
1. To determine the B-H characteristics of an iron core
2. To find the relative permeability (µr)
3. To calculate the reluctance “R”
Apparatus:
1 Rectangular laminated core
1 coil
1 voltmeter
1 ammeter
1 variable AC supply
Theory:
I
A
N
V
Fig. 1 : A simple rectangular core
If a current of 1 A, flows from a supply of E volts through a coil of N turns, as
shown in fig 1, the magnetic field intensity can be written as
H = NL / LC
9
(1)
From faraday’s law of electromagnetic induction, the rms values of the induced
voltage across the coil (E) is
E = ωNΦ
= ωNAB
(2)
B=µH
(3)
From (1), (2) and (3) it is clear that E-I characteristic of the core is equivalent to
the B-H characteristic. Further, it can be shown that
E = ωN2A µ I
Lc
(4)
Where, the permeability can be written as:
µ = µr µo;
µo = 4 π x 10-7
(H/n)
The reluctance of the core can be expressed as:
R= NI / Φ
= Lc / (µA)
(5)
Procedure
1. Find the typical dimensions of the core. The instructor may help you to get
the accurate numbers.
2. Connect the circuit as in fig 1
3. On a separate sheet of paper make a table as shown below:
Table 1
E
I
K= E / I
µr
R
4. Set the input voltage of 10V. Record the current and enter them in table 1.
5. Repeat step 4 up to 150 volts in steps of 10 volts.
10
Report
1. Plot E Vs I on a graph paper.
2. Find K, and R for each reading and complete the table. Here,
K=E/I
µ r=
KLc
2 π fN2A µo
3. Plot µ and R as functions of I
4. Derive equations (4) and (5)
Core Dimensions:
Lc = 40 cms
N = 400 turns
A = 9 Sq. cms
11
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#4
EQUIVALENT CIRCUIT OF TRANSFORMER
Objectives:
1. To determine the equivalent circuit of a single phase transformer
2. To verify the voltage current relationship
Apparatus:
1 Single-phase transformer
1 Variable AC power supply
1 AC voltmeter
2 AC ammeters
1 Wattmeter
Theory
The approximate equivalent circuit of a transformer is given in Fig. 1.
Req
Xeq
Xm
Rc
Fig 1. Equivalent Ciruict of transformer
Where, Rc =1/g and xm =1/b. These quantities are obtained from the open circuit
power, voltage and current measurements. These are
12
and,
Y = g - jb = Io / Vo
(1)
g = Po / Vo2
(2)
b = √ |Y|2 – g2
(3)
The equivalent resistances and reactances (Req, Xeq) are obtained from the
current, voltage and power measurements in the primary winding when the
secondary is shorted. These are written as
Req = Psc / I2sc
|Zeq| = Vsc / Isc
Xeq = √|Zeq|2 - Req2
(4)
(5)
(6)
Procedure
1. Note the current, voltage and volt-ampere ratings of both windings of the
transformer. Note the turns ratio
2. Connect the circuit as shown in Fig2. with the high voltage side open
circuited
3. Adjust the supply voltage until the voltage on the primary side is the rated
value.
4. Record the current, voltage and power in this condition. Take another reading
at 110 % of the rated value.
5. Next, connect the transformer for the short circuit test as given in Fig 3. The
variable supply will be on the high voltage side.
13
L
Variable AC
Source
Digital
Wattmeter
220V side
Open Circuit
110 / 220 V
N
Fig. 2 : The Open Circuit Test connection
6. Gradually increase the supply voltage from zero until the rated current flows
in the shorted secondary winding
7. Record the current, voltage and power. Repeat step 6 for 110 % of rated
current and record the values.
A
L
Variable AC
Source
Digital
Wattmeter
110V side
short Circuit
220 / 110 V
N
Fig. 3 : The Short Circuit Test connection
8. Connect the circuit as shown in Fig. 4 for a load test
9. Adjust the supply voltage and the resistive load such that rated current flows
through the load at rated voltage
Measure the voltages and currents on both sides of the transformer
14
A
L
Variable AC
Source
Digital
Wattmeter
V
220 / 110 V
N
Fig. 4 : The Load Test connection
Report
1. Calculate Rc, Xm, Req and Xeq from the open circuit and short circuit tests.
2. Draw the approximate equivalent circuit diagrams and label the parameter
values. Note that some of the values have to be transferred to the other side of
the winding by multiplying with approximate constant.
3. For the unity power factor loading condition of Fig 4, calculate the primary
current and voltage using the equivalent circuit you obtained. Start with the
measured values of current and voltage on the load side.
4. Compare the calculated quantities with measured ones and compute the
percent error
5. State the possible sources of errors, if any.
15
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#5
REGULATION AND EFFICIENCY OF A SINGLE PHASE
TRANSFORMER
Objectives:
1. To determine the regulation of a transformer
2. To determine the efficiency of a transformer
Apparatus:
1 Single-phase transformer
1 Variable AC power supply
2 Voltmeters
2 Ammeters
2 Wattcmeters
Theory
The voltage regulation of transformer at rated load is defined as:
VR = (Vno load - Vrated) / Vrated
(1)
If the approximate equivalent circuit of a transformer is used then for a lagging
V1= Vno load = Vrated <0o + I (cos θ – j sin θ) (Req + j Xeq)
= Vrated <0o + (Req cos θ + I Xeq sin θ) + j (- I Req sin θ + I Xeq cos θ)
Neglecting the imaginary part on the right hand side,
16
(2)
VR = I (Req cos θ + Xeq sin θ)
Vrated
(3)
The efficiency of the transformer can be written as
η = Power output / Power input
(4)
Or
η =
Power Output___
Power output + Loses
The losses are,
Core loss = No load power input – No load copper loss
Copper loss = I22 Req
Procedure :
L
Variable AC
Source
Digital
Wattmeter
Digital
Wattmeter
220 / 110 V
N
Fig. 1 : A Transformer with Load
1. Record the ratings of the transformer
2. Note down the parameters of the approximate equivalent circuit from the
previous experiment. If you are using a different transformer, perform the
open circuit and short circuit test again.
3. Connect the circuit as shown in Fig.1.
4. Make a table on the separate page as table.1.
5. Select unity power factor load.
6. Adjust the input voltage so that the load voltage is the rated value for a
certain load current. Record Pi, Po, V2 and I2. Switch the load off and record
V2. This is V2 (no load)
7. Repeat step 6 for various loads until you have reached the rated current. Take
17
8. Select 0.8-power factor lag. Repeat step 6 for rated current
9. Repeat step 8 for 0.8 p.f . leading.
Table 1
P.f
V2
I2
Pi
Po
V2
(No
η=
P2/Pi
VR
Η
(cal)
VR
from
eq3
Report
1. Calculate efficiency and voltage regulation fro your test results. Enter them in
columns 7 and 8 in table 1
2. Plot efficiency as function of load current for the unity power factor load
3. For rated, ½ and ¼ rated load, Calculate the efficiency from the equivalent
circuit. Enter them in table 1. Compare with measured values
4. Calculate the voltage regulation for rated load at unity, 0.8 lagging and 0.8
leading power factors using equation 3. Enter them in the table. Compare
5. State reasons of any discrepancy between the measured and the calculated
values
18
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#6
Load Characteristics of Shunt and Compound DC Generators
Objectives:
1. To study the load voltage vs. current characteristics of shunt connected DC
generator.
2. Study the load characteristics of a compound generator.
Apparatus:
1 DC motor-generator set
1 Tachometer
1 DC Voltmeter
2 DC Ammeters
1 Power Supply
Theory:
The terminal voltage of a shunt generator is written as:
Vt = Ea – Ia Ra
(1)
Where Ia = If + IL
If is the shunt current and
For a short shunt compound generator, the terminal equation is modified to
Vt = Ea – Ia Ra - IL Rsc
(2)
Where Rsc is the resistance of the series winding.
19
Procedure:
1. Record the rated currents and voltages of the DC generator and the motor.
Record the rated speed of the motor and generator.
2. Make the connection as shown in fig.1.
+
R
+
LINE
If
-
rheostat
rheostat
+
+
+
M
-
DC
SUPPLY
A
Ia
+
G
-
Ea
SHUNT
Vt
V
-
SHUNT
+
-
A
-
Fig.1: Connection Diagram For Shunt Generator
3. Set the generator shunt field rheostat to its maximum value.
4. Set the motor shunt field to its minimum value.
5. Adjust the motor speed to almost rated value. You can go slightly higher than
the rated one. The motor speed can be adjusted by changing the resistance in
the motor field winding or with series resistance RLine.
6. Adjust the generator voltage to its rated value by controlling the field
rheostat. Keep the load disconnected during the voltage buildup.
Maintain the motor speed to same value.
8. Record the speed of the motor. Enter the load voltage, load current and field
current as in table.1 for different loading conditions. Take at least 10 sets of
Table.1
20
VL
IL
If
9. Repeat the procedure for the compound generator given in fig.2.
+
A
+
R
LINE
SERIES
Ia
+
M
-
DC
SUPPLY
+
G
-
IL
If
+
Ea
V
-
SHUNT
+
-
A
-
Fig.2: Connection Diagram for Compound Generator
REPORT:
1. Plot the load voltage and field current of the shunt generator against the load
current.
2. Repeat the above for the compound machine.
3. Find the voltage regulation at rated load from your experimental results for
both shunt and compound machines.
4. Comment which generator is better in terms of load characteristics and why?
21
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electrical Engineering Department
EE 306
Electric Energy Engineering - Experiment#7
Torque Speed Characteristics of DC Shunt and Compound Motors
Objectives:
1. To study the variation of speed of shunt motor when load is changed.
2. To study speed vs. load characteristics of a compound motor.
Apparatus:
1 DC motor- generator set
1 Tachometer
1 DC Voltmeter
2 DC Ammeters
1 Power supply
1 Resistance
Theory:
For DC shunt and long shunt compound motors, current and flux are related by:
Vt = Ea + Ia Ra
(1)
Ea = Ka ω m Φ
(2)
Which gives
ωm =
Vt − I a Ra
KaΦ
(3)
Using the equation
Ia = Tdev / (KaΦ)
(4)
We can write
22
ωm =
Ra
1
Vt −
Tdev
KaΦ
( K a Φ) 2
(5)
Equation (5) shows the relation between torque, speed, terminal voltage and flux
of the motor.
Procedure:
1. Record the rated voltage, current and speed of the motor and the generator.
The generator is used to load the motor.
2. Connect the circuit as shown in fig.1
A
A
+
DC
SUPPLY
Ia
+
M
-
+
G
-
Ea
+
DC FIELD
SUPPLY
-
V
-
Fig.1: The Shunt Motor Generator Connection
3. Adjust the generator field resistance to maximum and motor field to
minimum.
4. Start the motor and bring the speed to slightly more than rated.
5. Apply the generator field and buildup the voltage to its rated value.
switching in the load rack. Adjust the generator terminal voltage to the rated
value every time by varying the field rheostat and/or the field supply voltage.
7. Record the motor speed n (rpm) and the motor armature current Ia for every
8. Make connection as given in fig.2 for the compound motor.
23
A
A
+
DC
SUPPLY
SERIES
FIELD
+
M
-
+
DC FIELD
SUPPLY
-
+
G
-
V
-
Fig.2: The Compound Motor Generator Connection
9. Repeat steps 3 thru 7 for the compound motor.
Report:
1. Plot the speed vs. motor armature current for the DC shunt motor.
2. Repeat 1 for the compound motor.
3. Calculate the speed regulation from no load to full load of the DC shunt
motor.
4. Repeat 3 for the compound motor.
Compare the torque-speed characteristics of the two motors and note your
observation.
24
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#8
Determination of Parameters of Synchronous Generators
Objectives:
1. To determine the synchronous impedance of an alternator.
2. To determine its voltage regulation.
Apparatus
1 3Φ alternator
1 DC motor
1 AC Voltmeter
1 DC Ammeter
1 DC voltmeter
1 DC power supplies
1 Tachometer
Theory:
For a certain excitation the synchronous impedance per phase of a synchronous
machine can be calculated as
Zs = Ea / Ia
(1)
Where Ea is the open circuit voltage per phase and Ia is the short circuit current.
The synchronous reactance then can be calculated as
(2)
X s = Z s2 − Ra2
Ra is considered as 1.5 times the armature DC resistance Rdc .Xs is the saturated
reactance when Ea is taken from the open circuit characteristics and
Ia is the corresponding short circuit current for the same excitation.
For a certain load current Ia, the internal voltage per phase can be written as
25
Ea = Vt + Ia ( Rs + jXs )
(3)
Where Vt is the terminal voltage per phase. Note, Ia is a complex number
The voltage regulation of the generator at the rated load is given as:
VR = (VNL-VFL)/VFL X 100%
(4)
Where, VNL = Ea
and
VFL = Vt (rated)
Procedure:
1. Note the rated values of current, voltage and speed of the synchronous
generator as well as the motor that will drive the generator.
2. Connect the motor generator set as shown in fig.1 for the open circuit test.
A
+
+
DC FIELD
SUPPLY
-
FIELD
DC
SUPPLY
E
A
-
C
DC MOTOR
B
SYN. ALTERNATOR
Fig.1: The Open Circuit Test
3. Adjust the alternator field rheostat to the maximum value and that for the
motor to the minimum value.
4. Adjust the motor speed to the synchronous speed of the alternator. You can
control the speed by the resistors in the line or in the motor field circuit.
5. Vary the field current in steps by varying the rheostat in the field circuit
and/or the supply voltage. Record the line-to-line voltage (E) and the filed
current If. Make sure that the speed remains constant through the whole test.
6. Take the readings upto 110 % of the rated voltage of the alternator.
7. Stop the motor and connect as in fig .2 for the short circuit test of the
alternator
26
IA
A
A
A
+
DC FIELD
SUPPLY
-
FIELD
DC MOTOR
C
B
DC MOTOR
SYN. ALTERNATOR
Fig.2 The Short Circuit Test
8. With the generator exciter off, bring DC motor upto synchronous speed.
Close the 3Φ switch and gradually increase the excitation. Record the field
current If and the armature current Ia. Take readings upto 120 % of the rated
generator current.
9. Switch the alternator exciter off. Stop the motor and make connection as
given in fig.3 for measurement of DC resistance of the armature.
B
A
+
+
DC
POWER
SUPPLY
V
-
-
C
A
Fig.3: DC Resistance measurement Of The Alternator
10. Adjust the DC power supply so that the current flowing through the alternator
winding does not exceed the rated value. The DC resistance is given as
Rdc = Vdc / 2Id c
The armature resistance Ra can be considered to be 1.5 times Rdc
Note: the armature DC resistance can also be measured by an accurate
millimeter, or by some resistance measurement bridge.
27
Report:
1. Using the OCC and SCC test results, plot EA and IA against If on the same
graph paper.
2. From the plotted graphs, determine Zs and Xs using equations (1) and (2).
Calculate only the saturated value.
3. Calculate, analytically, the voltage regulation of the generator for the
One. Rated load, unity power factor
Two. Rated load, 0.8 lagging p.f
Three.
Use equations (3) and (4).
28
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering - Experiment#9
Torque Speed Characteristics of 3Φ Induction Motors
Objectives:
1. To determine the torque speed characteristics.
2. To determine slip-torque characteristics.
3. To observe variation of efficiency.
APPARATUS:
1 3Φ induction motor
1 Prony brake
2 Wattmeters
1 3Φ variable power supply
1 Tachometer
1 Single pole switch
1 Digital Torquemeter
Theory:
The slip of an induction motor is defined as
s=
ns − nr
ns
where
ns is the synchronous speed
nr is the rotor speed
The efficiency of the motor is calculated from the ratio of the output mechanical
power to input electrical power as
η=
Pout
x 100%
P
29
Procedure:
1. Record the rated values of the induction motor. Note the synchronous speed.
2. Couple the induction motor to the prony brake as shown in fig.1, adjust the
prony brake belt so that it is not very tight.
3. Connect the two wattmeters to read the total power.
4. Start the motor and perform a load to 5 Nm in steps of 0.5 Nm.
a
P1
M
A
3Φ ac
A
T
V1
ROTOR
B
b
C
A
c
INDUCTION MOTOR
Prony Brake
Fig.1: Connection of 3Φ Induction Motor
5. Prepare a table similar to table.1 on a separate sheet of paper. Record the
motor speed n (rpm) and load T(Nm) and the wattmeter readings P1 and P2
(watts).
Report
1. Calculate the total input power, the slip and the output power for each
Pout = 2 ( π / 60) Tn
Slip s = ( ns – n ) / ns
watts
ns = 1800 rpm ( syn. Speed ).
2.
3.
4.
5.
Plot torque vs speed and torque vs slip.
Calculate efficiency of the motor and enter it in table.1.
Plot efficiency vs torque.
Find maximum torque and slip conditions.
30
Table.1
Torque-T
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Speed
P1
P2
Ptotal
(P1+P2)
31
Slip
Pout (watts)
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 306
Electric Energy Engineering-Experiment#10
DETERMINATION OF INDUCTION MOTOR PARAMETERS
Objective
The goal of this experiment is to determine the electrical parameters of a 3-ϕ
induction motor (primary and secondary resistance and reactance and the
magnetization branch values).
APPARATUS
1) 1 Three-Phase Induction Motor.
2) 1 Prony Brake.
3) 2 Digital Wattmeters.
4) 1 Three-Phase Variable AC Power Supply.
5) 1 DC Power Supply.
6) 1 DC Ammeter.
7) 1 DC Voltmeter.
8) 2 Three Phase Switches.
Introduction
Induction motor is an AC machine in which an alternating current is supplied to
the stator armature windings directly and to the rotor windings by induction.
Because it operates at balanced conditions, only a single phase is necessary. So,
the per-phase equivalent circuit of the induction motor in which the rotor
parameters are referred to the stator side is shown in Figure 1. It can be seen
from Figure 1 that the core loss represented by RC is neglected since its effect is
lumped with the rotational losses. The following equations can be derived:
V1 = E1 + (R1 + jX 1 )I 1 ................................................... (1)
⎛R
⎞
E1 = ⎜ 2 + jX 2 ⎟ I 2 ...................................................... (2)
⎝ s
⎠
To determine the parameters of the equivalent circuit of the three-phase
induction motor, it is subjected to three tests.
32
j X1
R1
I1
j X2
I2
+
+
j Xm
V1
R2 / s
E1
_
_
Figure 1: Per-phase equivalent circuit of a three-phase induction motor referred to the stator
Proceedure
A.
DC Test
Connect the circuit as shown in Figure 2 (while the motor is at standstill), apply
the dc voltage Vdc until the current Idc flowing in the induction motor is the rated
value. The stator resistance per phase can be calculated as R1 = Vdc / (2 Idc)..
I dc
A
V
Vdc
A
R1
R1
B
R1
C
Figure 2: DC test for the determination of the stator resistance
B.
Rated balanced voltage at rated frequency is applied to the stator, and the motor
is allowed to run on no-load. When the machine runs on no-load, the slip is close
to zero, and the circuit to the right of the shunt branch in Figure l is taken to be
an open circuit. Thus the equivalent circuit to the no-load test conditions is given
in Figure 3. Because of the relatively low value of rotor frequency, the rotor core
loss is practically negligible at no-load. From Figure 3, it follows that
Protational = Pnl − 3I nl2 R1 ................................................... (3)
P
Rnl = nl2 = R1 + lumped losses .................................... (4)
3 I nl
Vnl
Z nl =
= Rnl2 + X nl2 ............................................ (5)
3 I nl
X nl = Z nl2 − Rnl2 = X 1 + X m ......................................... (6)
33
No load power factor = cos ϕ 0 =
Inl
Pnl
3 Vnl I nl
..................... (7)
j X1
R1
+
j Xm
Vnl /sqrt(3)
_
Figure 3: Approximate equivalent circuit for no load test
Perform the following:
1.
2.
3.
4.
5.
Connect the circuit as shown in Figure 4. Apply the rated voltage.
Measure the rated voltage Vo = Vnl.
Measure the line current (Ia = Ib = Ic = Inl).
Measure the wattmeters powers W1 and W2, so Pnl = W1 + W2.
Calculate Rnl, Xnl, Znl, and φ0 from equations (4)−(7).
W1
a
Ia
b
A
V0
3 Phase Supply Rated
Voltage
Ib
c
B
C
Ic
W3
2
Figure 4: Schematic diagram for the no load test
C.
Blocked-Rotor Test
In this test, the rotor of the induction motor is blocked so that the slip is equal to
unity, and a reduced voltage value is applied to the machine stator terminals so
that the rated current flows through the stator windings. The iron losses are
assumed to be negligible in this test. Also, the shunt branch is neglected for this
test since the excitation current is small. The equivalent circuit corresponding to
the blocked rotor test condition is given in Figure 5. From Figure 5, it then
follows that
Rbl =
Pbl
= R1 + R2 .................................................... (8)
3 I bl2
34
Z bl =
Vbl
3 I bl
= Rbl2 + X bl2 ............................................ (9)
X bl = Z bl2 − Rbl2 = X 1 + X 2 .......................................... (10)
The following assumption can be taken:
X1 = X 2 =
1
X bl ......................................................... (11)
2
Finally, the magnetization reactance can be found:
X m = X nl − X 1 ............................................................ (12)
j X1
R1
Ibl
j X2
+
Vbl /sqrt(3)
R2
_
Figure 5: Approximate equivalent circuit for blocked rotor test
Perform the following:
1. Connect the circuit as in Figure 6. Keep the applied voltage to zero at
starting.
2. Increase the applied voltage until the rated current flows in the stator
winding.
3. Measure the applied voltage VS = Vbl.
4. Measure the line current (Ia = Ib = Ic = Ibl).
5. Measure the wattmeters powers W1 and W2, so Pbl = W1 + W2.
6. Apply equations 8−12 to calculate the parameters X1, X2 , Xm , R2 .
W1
a
Ia
b
A
V
VS
0
3 Phase
Supply
Ib
c
B
W32
Ic
Figure 6: Schematic diagram for the blocked-rotor test
35
C
Brake
Report
1. Record the ratings of the induction motor and determine the number of its
poles.
2. Find the parameters of the equivalent circuit of the three-phase induction
motor.
3. Draw the equivalent circuit of the induction motor and put the values of the
parameters that you found in the previous question along with their symbols.
4. Determine the no load power angle.
5. Determine the combined rotational losses of the motor.
36
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Electric Engineering Department
EE 360 LAB – EXP # 1 & 4
1. Y CONNECTION
Pf
0.8
lag
480W+420W+120W
480W+420W
480W+120W
480W
480W+420W+420W
+all inductance (22.9)
mH
480W+420W+420W
+all capacitors (22.9)
mH
0.8
P1
(W)
P2
(W)
PT
(W)
VAB
(V)
VCB
(V)
IA
(A)
P.f
Cal.
2. DELTA (∆) CONNECTION
For the above combinations of loading in ∆ connection reduce the applied
voltage (60 V) to limit the line current (same as in Y connected load).
37
P.f
```