ECE 431
Experiment #1
Three-Phase ac Measurements
PERFORMED: 26 January 2005
WRITTEN: 28 January 2005
Jason Wells
LEADER:
Jason Wells
RECORDER: Nathaniel Hakes
1
Introduction
The primary objectives of the experiment on three-phase ac measurement include becoming familiar
with the laboratory equipment as well as reviewing three-phase voltage, current, and complex power
relationships studied in previous courses. These objectives were met by investigating a wye-connected
resistive load, a delta-connected complex load, and an induction motor operating under no load conditions.
This experiment also introduced the one-wattmeter and two-wattmeter methods for measuring reactive and
real power, respectively.
2
2.1
Discussion and Results
One-Wattmeter and Two-Wattmeter Method
Although equipment exists than can directly analyze three-phase real and reactive power, it is often
expensive and delicate. As such, it is occasionally desirable to utilize relatively inexpensive single-phase
power meters to determine these quantities in the field. This experiment introduced two such methods
which are described in [1] on page 22. In the two-wattmeter method, the total three-phase real power of the
load is determined by
P3φ = P1 + P2
(1)
where P1, P2, and φ , the power factor angle, are given by
P1 = 3Vl I l cos(30 + φ )
(2)
P2 = 3Vl I l cos(−30 + φ )
(3)
φ = θV − θ I
(4)
Notice that P2 will be equal to zero if whenever the voltage, current, or cos(-30+ φ ) is equal to zero. This
will occur when the power factor angle, φ , is equal to either -60 degrees or +120 degrees. Additionally, P1
will equal P2 if the power factor angle is equal to zero or 180 degrees (i.e. a purely resistive load). In the
one-wattmeter method, the total three-phase reactive power is determined from the observed power by
Q3φ = 3 Pobs
2.2
(5)
Balanced Wye-Connected Resistive Load
With the one-wattmeter and two-wattmeter methods established, a wye-connected resistive load was
tested to observe basic three-phase relationships according to the procedure in [1]. With a wye-connected
load, the line-to-line, line, and phase relationships are described theoretically by
Vφ = Vln = Vll
Iφ = I l
2
3
(6)
(7)
Raw data observed in the laboratory can be found in Appendix A and is included in Table 1 along with
results of several calculations.
Total three-phase power and reactive power were calculated using
Equations (1) and (5) respectively.
Table 1. Experimental Data and Results from the Wye-Connected Resistive Load.
Phase A (A-B)
Phase B (B-C)
Phase C (C-A)
Averages
Line
Current
(A)
1.38
1.38
1.36
1.37
Phase
Current
(A)
1.38
1.38
1.36
1.37
LineLine
Voltage
(V)
240.6
241.4
240.2
240.7
Phase
Voltage
(V)
138.4
138.9
139.2
138.8
Phase
Shift
(deg)
0
0
0
0
Total 3
Phase
Reactive
Power
(Vars)
OneWattmeter
Pobs (W)
0
-
0
-
TwoWattmeter
(P1) (W)
289
-
TwoWattmeter
(P2) (W)
290
-
Total 3
Phase
Power
(W)
579
-
The power factor for a given load can be determined by
P
=
S
p. f . =
P
(8)
P + Q2
2
In the case of the purely resistive load, Q is equal to zero, and the resulting power factor is 1 (unity). Also
notice that the P1 and P2 are equal for this load as predicted in Section 2.1.
Using the averages in Table 1, Equation (6) can be verified as shown below.
= Vln = Vll
Vφ
3 = 240.7
3 = 138.97 V
(9)
Theoretical
Compared to the observed average phase voltage of 138.8, this is less than a 1 percent error when
calculated as
%error =
− Vφ
Vφ
theoretical
observed
Vφ
100% = 0.122%
(10)
theoretical
The line current and the phase current are equal by definition.
2.3
Balanced Delta-Connected Complex Load
Next, a balanced delta-connected complex load was examined in the laboratory.
With a delta-
connected load, the line-to-line, line, and phase relationships are described theoretically by
Vφ = Vll
Iφ =
Il
3
(11)
(12)
Raw data observed in the laboratory can be found in Appendix A and is included in Table 2 along with
results of several calculations.
Total three-phase power and reactive power were calculated using
Equations (1) and (5) respectively.
3
Table 2. Experimental Data and Results from the Delta-Connected Complex Load.
Line
Current
(A)
4.96
4.96
4.95
4.96
Phase A (A-B)
Phase B (B-C)
Phase C (C-A)
Averages
Phase
Current
(A)
2.86
2.87
2.86
2.86
LineLine
Voltage
(V)
240.4
241.2
240.8
240.8
Phase
Voltage
(V)
240.4
241.2
240.8
240.8
Phase
Shift
(deg)
-48.7
-48.5
-48.7
-48.6
OneWattmeter
Pobs (W)
-817
-
Total 3
Phase
Reactive
Power
(Vars)
-1415
-
TwoWattmeter
(P1) (W)
1120
-
TwoWattmeter
(P2) (W)
240
-
Total 3
Phase
Power
(W)
1360
-
The power factor for a given load can be determined by
p. f . =
P
1360
=
= .6390 leading
2
2
S
1360 + ( −1415 )
(13)
Since the load is capacitive and reactive power is negative, the power factor is leading. The theoretical
power factor can be predicted based on the nominal values of R and C in our complex load as shown below
where Z is the complex impedance of the load at line frequency.
1
)) = cos(−48.52) = 0.6624 leading (14)
1
+ j ( 2π 60 ) 24uF
125
p. f .theoretical = cos(angle( Z )) = cos(angle(
Comparing this to the power factor as calculated by Equation (13), this is less than a 5% error.
%error =
p. f .theoretical − p. f .(13)
p. f .theoretical
100% = 3.53%
(15)
Using the averages in Table 2, Equation (12) can be verified as shown below.
Iφ
= Il
3 = 4.96
3 = 2.864 A
(16)
Theoretical
Compared to the observed average phase current of 2.86 A, this is less than a 1 percent error when
calculated as
%error =
− Iφ
Iφ
theoretical
observed
Iφ
100% = 0.14%
(17)
theoretical
The line voltage and the phase voltage are equal by definition. Also notice that the P1 is greater than P2 for
this load.
2.4
Induction Motor
Finally, an induction motor was tested under no load conditions. Again, data was taken regarding its
voltage, current, and power magnitudes and is presented for convenience in Table 3. Total three-phase
power and reactive power were calculated using Equations (1) and (5) respectively. Power factor in the
table was calculated using Equation (8) and is lagging since this is an inductive load. Notice that P1 is less
than P2 for the induction motor at no load.
4
Table 3. Experimental Data and Results from the Induction Motor at No Load.
Line
Current
(A)
3.66
3.68
3.64
3.66
Phase A (A-B)
Phase B (B-C)
Phase C (C-A)
Averages
Line-Line
Voltage (V)
241.2
241.8
240.9
241.3
Phase
Voltage
(V)
241.2
241.8
240.9
241.3
Total 3
Phase
Reactive
Power
(Vars)
1402
-
OneWattmeter
Pobs (W)
809
-
TwoWattmete
r
(P1) (W)
-347
-
TwoWattmeter
(P2) (W)
522
-
Total 3
Phase
Power
(W)
175
-
Power
Factor
0.1239
To verify the results of the one-wattmeter method, the total three-phase reactive power observed by this
method can be compared against reactive power obtained from voltmeter, ammeter, and power observed in
the two-wattmeter method. This alternative reactive power calculation is shown below.
Q3φ = S32φ − P33φ =
(
3Vll I l
)
2
− ( P1 + P2 ) =
2
(
)
3(241.3)(3.66) − (175 ) = 1519 Vars
2
2
(18)
Compared to the one-wattmeter method, this has a percent error of 7.7 %.
%error =
Q3φ − Q3φ
calc
observed
Q3φ
100% = 7.7%
(19)
calc
3
Conclusions
The goals of this laboratory were to become familiar with the laboratory equipment and to review basic
three-phase power relationships. In the balanced wye and delta connections, the data indicates that the
relationships described in Equations (6-7) and (11-12) are indeed accurate yielding percent errors of less
than 1%. Additionally, the data verified that the power factor of a load could be reasonably predicted given
the nominal values of the load components. The approximately 3.5% error in this prediction likely comes
from the fact that capacitors have typical tolerances of 5 to 10% on their nominal capacitance. There was a
significant percentage error between the three-phase reactive power calculated by the one-wattmeter
method compared to using V, I, and power from the two-wattmeter method. This error was likely caused
by misreading the analog wattmeter display.
Ultimately, the data was consistent with theoretical
predictions and familiarity with the equipment was obtained.
References
[1] P.W. Sauer, P.T. Krein, P.L. Chapman, ECE 431 Electric Machinery Course Guide and Laboratory
Information, University of Illinois at Urbana-Champaign, 2005.
Appendix
(Raw data)
5