ELEC 331
FUNDAMENTALS OF ELECTRICAL POWER
ENGINEERING
LABORATORY MANUAL
EXPERIMENT 1
POWER MEASUREMENT IN THREE-PHASE
CIRCUITS
I.
OBJECTIVES
There are three objectives to this experiment:
-
To study the relationship between voltages and currents in three-phase circuits with
delta and wye connections;
-
To measure power in three-phase circuits using the two-wattmeter method;
-
To become familiar with the principle of power factor correction.
II. INTRODUCTION
A three-phase circuit is usually connected in either delta or wye configuration. Power in a
three-phase circuit is usually measured using two wattmeters – the dual wattmeter
method. At power factors less than 0.5, one of the instruments has a negative reading. When
a reading is negative, it is necessary to reverse the voltage or current connection in order
1
to obtain an upscale deflection (with the Lab-Volt dual three-phase wattmeter, the reversal
is done with a toggle switch). Remember that all voltage and current quantities are line-toline and line quantities unless otherwise specified. Note that in Fig. 1-4 the voltage and
current isolators E1 and I1 are combined to form a single wattmeter in a two wattmeter
system. Similarly, E2 and I2 form the second wattmeter
When the source and load are both balanced, expressions for the dual wattmeter readings
are:
P1  Vab I a cos(angle between Vab and I a )
or
 VL I L cos(30   )
P2  Vcb I c cos(angle between Vcb and I c )
or
 VL I L cos(30   )
where  is the load angle and total power is the sum of P1 and P2.
When the power factor is less than unity, a current that is greater than the minimum is
required to transmit a given active power, resulting higher transmission losses and loading
of transformers. There are means to minimize these losses. For inductive loads, for
example, the most common solution is to install capacitor banks in parallel with the loads.
Strategies that improve the power factor of electrical circuits are classed as power factor
correction (PFC) techniques
Three-phase ac circuits, transformers, ac machines and their per-phase equivalent circuits
can be described by phasor diagrams. Figure 1-1 shows a wye-connected 3-phase source
that is connected to a wye-connected load. In this case, the voltage sources and the load
elements are assumed to be equal, hence the system is said to be balanced. The phase loadangle, , is the same for each load.
2
E3
To
Osc.
i
I3
To
Osc.
Figure 1-2 shows the phasor diagram that corresponds to the 3-phase
1 2 3 system given in Fig.
250Vac
1-1. The per-phase equivalent circuit is also shown as it would appear on an oscilloscope
display. Note that the voltage Van is taken as the reference for the single-phase equivalent
A circuit.
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0-208V
Three-Phase Wye Connected Source
Ia
Three-Phase Wye
Connected Load
a
0-208V
+
Van
Load a
Vab
0o
Van
V
Za
n
n
o
-240
Vcn
Load b
+
+
c
To DAQ
Vbn

In
-120o
b
Vbc
Zc
+
Ib


Zb
Vca
Load c
L
Ic
Osc.
Figure 1-1. A 3-phase wye connected source and load.
D

o
150
120o
Vcn
Vca
Ic

Ib
-90o
Ia
30o
 Van
Ia

Vbn
Vab
Van
Vpk
Ipk
Vbc
-120o
16.7ms
t (ms)

8.33ms
(b) Oscilloscope representation of 1-phase
equivalent wye connected circuit (with
lagging PF).
(a) Phasor diagram of 3-phase wye system.
Figure 1-2. Phasor diagram of 3-phase system and the voltage and current waveforms of
a single phase (lagging PF, 60 Hz).
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Ia
Ia
a
a
+
Van
Vab
Vca
Zbn
b

n
Vab
Zab
Vca
Zcn
+
Vbc Ib
Vab

Zan

I
 ab
+
Ib
Vbc

Zca
Zbc
b
Ic
Ica
+
Vbc +
Ic

Vca
+
c
Ibc
c
Figure 1-3. The wye and delta connected loads.
Wye to Delta Transformation.
The transformation of a load from the wye configuration (Y) to the delta connection (Δ)
can be done on the basis of equal per-phase power capacity. Assume that the line-line
voltages (Vab, Vbc, Vca) in Fig. 1-3 are the same for each circuit. Starting with the wye
circuit the power in each phase is
𝑃∅𝑌 = 𝑉∅𝑌 ∙
𝑉∅𝑌
𝑍∅𝑌
By equating the power-per-phase in each circuit, PϕY = Pϕ Δ , the equivalent impedance of
the delta circuit can be found from
𝑍∅∆ =
𝑉∅∆
∙ 𝑉∅∆
𝑃∅𝛥
By comparing the values of the impedances, ZϕY and ZϕΔ, the transformation ratio can be
found.
Neutral Current in an Unbalanced Load.
The three-phase circuits used in this laboratory are assumed to be balanced. However, in
reality, three-phase sources and loads are often unbalanced (unequal).
In the wye
connected systems this imbalance can be measured by observing the neutral current, In.
(Fig. 1-1, Fig. 1-4). The value of the In is given by
𝐼𝑛 = 𝐼∅𝑎 + 𝐼∅𝑏 + 𝐼∅𝑐
Where for a balanced system,
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𝐼∅𝑎 = 𝐼 cos(−𝜃) + 𝑗 sin(−𝜃)
𝐼∅𝑏 = 𝐼 cos(−𝜃 − 120°) + 𝑗 sin(−𝜃 − 120°)
𝐼∅𝑐 = 𝐼 cos(−𝜃 − 240°) + 𝑗 sin(−𝜃 − 240°)
Note that when the load impedance is resistive the phase angle is zero and an open circuit
carries no current (I = 0).
Refer to: 1) Chapman, Stephen J., Electric Machinery Fundamentals, 4th ed., New York,
McGraw Hill, Appendix A. (Examples A-1 and A-2, pgs. 695 – 698).
III.
1.
PRE-LAB CALCULATIONS
Calculate the power factor (cos), load angle (), wattmeter readings P1 and P2, total
power from P1 and P2 readings (P1+P2) and total power using the direct method (Pphase
= 1.73 VI cos) for the followings loads and operating conditions, with loads wyeconnected to a 208 V, three-phase line-to-line power supply. Sketch a 3-phase phasor
diagram showing the current phasors for parts a,b and c. Indicate whether the currents
are leading or lagging. Sketch the 3-phase phasor diagram indicating the angles
between Vab and Ia, Vcb and Ic for part d.
(a) Each resistive load element rated at 120 V, 0.4A;
(b) Each capacitor load element rated at 120 V, 0.4A;
(c) Each inductor load element rated at 120 V, 0.4A;
(d) Each load element rated at 120 V, 0.4 A with 0.5 power factor lagging.
2.
For the resistive load, compute the value of the resistance required in a delta
connection, for the same power dissipation. Sketch the per-phase (single phase) phasor
diagram.
3.
For the 0.5 power factor load defined in 1(d), compute the values of R and L assuming
R and L are in series. Sketch the per-phase (single phase) phasor diagram.
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Warning:
High voltages are present in this experiment!
DO NOT make any connection while the power is on.
IV. PROCEDURE
The data to be collected for each step in this experiment is taken from the meters shown in
each diagram. In Fig. 1-4, for example, the rectangular boxes with upper-case letters refer
to voltmeters and ammeters located on the Lab-Volt Data Acquisition and Control Interface
(LVDAC). Text boxes with lowercase letters refer to voltage and current isolators located
on the Lab-Volt test-bench. These isolators are usually connected to the oscilloscope.
Circular text icons refer to analog voltmeters and ammeters located on the test-bench. The
label, DMM, refers to a digital multimeter. Normally all data can be recorded and
transferred to the PC using the data table in the Lab-Volt software. From the Lab-Volt
table the test results should be transferred immediately to an Excel spreadsheet for
calculation and plotting of the results. If communication with the LVDAC is interrupted
the Lab-Volt data table on the PC may freeze and the results can be lost. All the details of
the bench operation are in the document, Undergraduate Lab Equipment and
Procedures found on the Moodle course website and as Introduction to Lab Test
Equipment on the technicians personal webpage: users.encs.concordia.ca/~joe/ . This
manual should be consulted throughout the semester. The procedures in the document will
be included in the lab exam.
1. Turn on the LVDAC, the oscilloscope, and the computer. On the PC open the LVDAC
software and open the MS Excel software. Connect the circuit as shown in Fig. 1-4
with the resistive load unit in a wye configuration. Have your instructor check the
circuit. The numbers 4,5,6 in Fig 1-4 correspond to the Lab-Volt voltage source
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connections. Refer to the appendices or the Lab Equipment and Procedures document
for instructions on how to set up the oscilloscope, PC and data acquisition software. If
necessary, use E1 and E2 to verify the phase rotation of the voltage source. (To satisfy
the 2-wattmeter method, the polarity of E2 must be the reversed as shown in Fig. 1-4,
Vcb not Vbc). Set the resistance of each section to 300 . Turn on the power supply and
observe the ammeter to make sure there is no short circuit. Slowly adjust the line
voltage to 208 Vac as indicated by the voltmeter. Measure and record the all the
measurements shown in Fig. 1-4 including the neutral current. The required data is
indicated in the data-table found at the end of this document.
Ia
To DAQ
a
+
4
connections,
4, 6 are reversed
in diagram.
A
I1
+
0-208V
To DAQ
b
0-208V
c
i
W1
250Vac
1
I3
2 3
W2
6 5
4
Vab
Ib
To DAQ
Vbc
+
Vca
Ic
0 – 300 Ω
Neutral
To DAQ
e
To
Osc.
n
Vcn
Ic
+
b
I2
E3
L
O
A
D
Van
Vbn
To DAQ
E2
+
Ia
Ib
+
6
a
I3
V
E1
5
To
Osc.
To DAQ
2.5Aac Note: W2
DMM
A
M
+
c
I4
Figure 1-4 The Lab-Volt experimental circuit.
2. Measure and record the phase angle between the phase voltage (V), and the phase
current (I), using the oscilloscope (model Fluke; refer to Appendix for setting the
Oscilloscope). For the LeCroy oscilloscope refer to the Lab Equipment and Procedures
document. Note that the phase angle can also be seen using the LVDAC phasoranalyzer on the PC.
3.
Measure and record the meters shown in Fig. 1-4 using the Lab-Volt DAC and the
data table as in step 1. Include the line voltages and currents, the phase-voltages and
currents, the wattmeter readings and the powers, P, S and Q indicated on the PC
(LVDAM). Return the voltage to zero and turn off the power supply.
4. Open the resistance of one section, phase C. Use an Ohmmeter to adjust the variable
ballast resistance to 300 . Turn on the power supply and observe the ammeter to
7
make sure there is no short circuit. Slowly adjust the line voltage to 208 Vac as
indicated by the voltmeter E1. Reduce the ballast resistor to 0 . Measure the neutral
current on the DMM to record the imbalance. If the ammeter I4 is in the circuit record
the value of the current in the Lab-Volt table. Turn the voltage down to zero and turn
off the power supply.
5. Set the load on all 3 phases to 200  (parallel the 300  and 600  resistors). Turn on
the power supply and observe the ammeter to make sure there is no short circuit.
Slowly adjust the line voltage to 120 Vac as indicated by the voltmeter E1. Record all
measurements as before (see data table).
6.
Return the voltage to zero and turn off the power supply.
7. Replace the resistive load of Fig. 1-4 with the capacitor load. Set the capacitance of
each section to 4.4 F and the line voltage to 208 Vac. Repeat the measurements of
Steps 2 and 3. Return the voltage to zero and turn off the power supply.
8. Replace the resistive load of Fig. 1-4 with the inductor load. Set inductance of each
section to 0.46 H (3.2 H || 1.6 H || 0.8 H) and the line voltage to 208 Vac. Repeat the
measurements of Steps 2 and 3.
Return the voltage to zero and turn off the power
supply..
9.
Replace the resistive load of Fig. 1-4 with the resistive-inductive load composed of R
= 300  and L = 0.46 H (3.2 H || 1.6 H || 0.8 H) connected in series, and the line
voltage to 208 Vac. Repeat Steps 2 and 3. Print the waveforms that are observed on
the oscilloscope. All the phase angles can also be seen using the LVDAM phasoranalyzer on the PC. Print these diagrams in phase related groups (E1 and I1, E2 and
I2, E3 and I3). Return the voltage to zero and turn off the power supply.
10. Connect a capacitor of 4.4 F in parallel across each phase of the RL series-load as
shown in Fig. 1-5, and repeat Steps 2 and 3. Print the waveforms that are observed on
the oscilloscope. All the phase angles can also be seen using the LVDAM phasoranalyzer on the PC. Print these diagrams in phase related groups (E1 and I1, E2 and
I2, E3 and I3). Return the voltage to zero and turn off the power supply.
8
To DAQ
4
a
+
connections,
4, 6 are reversed
in diagram.
A
I1
4
+
0-208V
V
E1
To DAQ
5
To
Osc.
To DAQ
2.5Aac Note: W2
Ia
a
i
I3
+
Ia
250Vac
b
W1
1
2 3
W2
6
5
Van
4
To DAQ
+
To
Osc.
Vcn
Vab
Ib
Vbc
+
Vca
I2
+
e
n
To DAQ
0-208V E2
c
To DAQ
Vbn
Ib
6
E3
L
O
A
D
Ic
b
+
c
Ic
Figure 1-5. The power-factor correction circuit.
11. Connect the circuit as shown in Fig. 1-6 with the resistive load unit connected in
delta, and have your instructor check the circuit. Be sure to note the high and low
sides of the load elements and the meters
Depending on the orientations of the components, there is one correct set of results that
2.5Aac
To DAQ
+
4
A
I1
+
0-208V
To DAQ
5
0-208V
6
V
E1
E2
W1
W2
4 5 6
1 2 3
250Vac
To DAQ
+
Ib
Vbc
b
Ibc +
To Osc
c
+
Vab
Vca
E3
e
To DAQ
To Osc
I3
Zab Iab
+
Zbc
Ic
To DAQ
+
Use same phase current
as line (phase) current
in step 3 (300
To DAQ
,resistors).
Zca
Ica
a
Ia
i
I2
Figure 1-6. The Delta connected circuit.
is relatively easy to explain. There are several other data sets that do not correspond to
the normal conventions of describing 3-phase power circuits. These variations will have
to be explained in your report.
12. Set the resistance of each section to 600 . Turn on the power supply and adjust the
line voltage to obtain the same phase (and line) voltage as the line voltage in Step
2 where the load is connected in wye (The value of E3 in Fig. 1-6, should be the same
as E1 in Fig. 1-4, Step 2, i.e. 120 Vac). Record the value of source voltage.Measure
and record the values as before.
14. Return the voltage to zero and turn off the power supply.
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V. Safety
1. Locate the poster that shows the security-procedures and emergency-contact
information. Note the sections for fire and medical emergencies.
2.
Locate the fire extinguisher in the lab. Consul the internet (or other source) and the
label on the extinguisher to identify the classes of extinguisher, what types of fire they
are used for and the type of extinguisher in the lab.
VI. QUESTIONS
1.
Derive the transformation that will change a wye-connected circuit to a deltaconnected circuit as shown in the introduction. Assume that each circuit has an
equivalent power rating and a three-phase balanced load. Using this transformation
(ratio), calculate the equivalent delta connected R, C, L, load-components for the wyeconnected circuits (and corresponding measurements) of Step 10 (i.e. transform Fig.
1-5 into a delta circuit similar to Fig. 1-6). Make sure all units (Ohms, Farads, and
Henries) are indicated. Hint: do the initial calculation in terms of Ohms (XC and XL
at 60 Hz). Include a hand-drawn (freehand) sketch of the 2 circuits in your report. In
the drawings include the load-side voltage and current measurement devices shown in
Figs. 1-5 and 1-6.
2.
Calculate and tabulate the theoretical and experimental power and power factors (PF)
for Step 10 (Fig. 1-5, Power-Factor Correction). How well (%) do the experimental
readings from 1) the dual-wattmeters, 2) the 2-wattmeters readings (LabVolt DAQ),
3) the single-phase readings (LabVolt DAQ) and 4) the phasor analyzer (LabVolt
DAQ), compare with a theoretical calculation of power and power factor based on the
2-wattmeter method? The theoretical power calculation is based on the four equations
given in the introduction (page 1) of this experiment. Sketch the 3-phase phasor
diagram that corresponds to the circuit of Step 10 (Fig. 1-5). A freehand drawing is
acceptable. Indicate the angles of the phasors. If necessary, include a sample
calculation to explain each table entry.
3.
Does the value of the neutral current measured in Step 4 satisfy the equations given in
the Introduction of this lab?
10
4.
For Fig. 1-4 (Steps 1-9, R, C, L, RL loads), Calculate the theoretical value of the power
and power factor for each circuit based on the specified phase voltage given in the
procedure and the specified impedance. Re-calculate the power factor of each circuit
using the observed values the load-angle taken from the oscilloscope and the LabVolt phasor analyzer. Include the print outs of the waveforms taken from the
oscilloscope. For each of the 4 circuits put the three values of the power-factor in a
table. For each circuit, which of the experimentally-derived values, oscilloscope or
phasor, differs the most (percentage) from the theoretical value? Include a sample
calculation for the RL load circuit and the oscilloscope trace for each entry.
5.
Compare the power factor variation in Steps 9 and 10 (RL and RLC loads) and
comment on the results. Which circuit transfers the most power for the least amount
of current? Calculate the exact capacitor value that would yield unity power factor for
the circuit of Fig. 1-5. Show your calculation. Why is unity power factor desirable?
6.
Calculate the theoretical power in each phase (resitive load) and the total power
consumed by the load for Step 12 (Fig.1-6). Do these values agree with your
experimental data? Does the ratio of the loads in Step 5 and Step 12 (wye and delta
circuits) support the derivation in Question 1? Is the assumption of an equal power
dissipation per-phase valid? Sketch the phasor diagram of the 3-phase delta connected
system. Show Vline, Iline, Vphase, Iphase and the associated angles and magnitudes.
Indicate the phasors used in the 2-wattmeter method. Could the same phasors be used
when applying the 2-wattmeter method to describe the wye-connected system? A
freehand drawing is acceptable. Why are the phase angles of the oscilloscope and the
Lab-Volt phasor analyzer different?
7.
Where are the security-procedures and emergency-contact information posted?
8.
Where is the fire extinguisher in the lab located? What type (class) of extinguisher is
it? What types of fire are treated with each class of extinguisher?
9.
What route should be taken to exit the lab and building in case of fire?
11
ELEC 331, Data Tables for Experiment 1
Table 1 Data for Wye Connected Load (* print-out of graphical display or oscilloscope trace is required)
Vab
Ia
R
XL
XC W1 W2 Vph Iph
Ineutral P3,Q ph
Vcb c
ph

(V)
(A)
(V)
(A)
(A)
3,S3 LabOscilloVab, (V) (A)
()
()
() (W) (W)
(W, Volt
scope
Ia
Var, Phasor (deg or
ref
VA) (deg
rad)
Vab
or rad)
300
0
0
*
208
*
Open
0
0
*
1 ph C
300|| 0
0
*
120
600
3-ph
0
0
600
*
208
0
300|| 0
*
600||
1200
300
300|| 0
*
*
*
600||
1200
300
300|| 600
*
*
600||
1200
12

Vcb,
Ic
ref
Vab
*
*
P1,
S1
(W,
VA)
P2,
S2
(W,
VA)
Table 2. Data for Delta Connected Load (* print-out of graphical display is required)
P3, Q3, ph
R
XL
XC
W1 W2 Vph
Iph
e-Vab,i-Ia Vab Ia
S3
(W,
(A)
Lab-Volt Oscillo- (V) (A)
() () () (W) (W) (V)
scope
N.B Var,
Phasor
VA)
(deg or
See
(deg or
rad)
Iph
rad)
I ph is same as 300  load above
Vcb
c

 P1,
Vab, (V)
(A) Vcb, S1
(W,
Ia
Ic
VA)
ref
ref
Vab
Vab
P2,
S2
(W,
VA)
above
600 0
0
*
*
120
*
*
E3, I3 are phase parameters. E1, I1, E2, I2 are the line (line-to-line) parameters: Vab, Ia, Vcb and Ic. E2 is oriented to support the 2Wattmeter method. All numerical data can be recorded in a LabVolt data table, copied to Notepad and printed.
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