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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

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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-to-

line 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:

)30(cos

) and between angle(cos1

LL

aabaab

IV

or

IVIVP

)30(cos

) and between angle(cos2

LL

ccbccb

IV

or

IVIVP

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 load-

angle, , is the same for each load.

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Figure 1-2 shows the phasor diagram that corresponds to the 3-phase system given in Fig.

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

circuit.

L

D

Osc.

-120o

Vbc

30o

(b) Oscilloscope representation of 1-phase

equivalent wye connected circuit (with

lagging PF).

Van

Vab

Ia

Vbn

Vcn 120o

Ib

Ic

Vca

150o

-90o

(a) Phasor diagram of 3-phase wye system.

+

Ia

t (ms)

16.7ms

8.33ms

Van Vpk

Ipk

Figure 1-2. Phasor diagram of 3-phase system and the voltage and current waveforms of

a single phase (lagging PF, 60 Hz).

Figure 1-1. A 3-phase wye connected source and load.

b

a

To Osc.

Osc. To I3 i

+

E3

Three-Phase Wye Connected Source

1 2 3

4 5 6

V

A

0-208V

0-208V

Van

250Vac

Ia

n

c

5

0o

Ic

To DAQ

Three-Phase Wye

Connected Load

+

+

Vcn -240o

bc V

Ib

Load a

Za

Load c

Zc Load b

Zb Vca

Vab Van

Vbn -120o

In

n

4

Zan

Zcn

Zbn

Zab Zca

+

Zbc

Vbc

b

a

c

a

b c

Van

Ia

Ib

n

+

+

+ +

+

Vca

Vab

IabVca

VabIca

Vbc

Ibc

Ic

Ia

IbIc

Vbc

Vca

Vab

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∅∆

𝑃∅𝛥 ∙ 𝑉∅∆

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. PRE-LAB CALCULATIONS

1. 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 wye-

connected 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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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

Warning:

High voltages are present in this experiment!

DO NOT make any connection while the power is on.

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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.

L O A D

To Osc.

Osc. To

I3 i

To DAQ

e

E3

To DAQ

1 2 3 4 5 6

V

A

W I3

0-208V

0-208V

2.5Aac

250Vac 1 W 2

4

5

6 I2

To DAQ

To DAQ

E2

I1

To DAQ

To DAQ

E1

+

+

+

+

a

b

b

+

c

a

c

Vcn

+

Note: W2

connections,

4, 6 are reversed

in diagram.

Ic

Van

Ia

+

Vbn n

Ib

Ic

Ib

Ia

Vab

Vca Vbc DMM

M Neutral

I4 0 – 300 Ω A

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 phasor-

analyzer 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

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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 phasor-

analyzer 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 phasor-

analyzer 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.

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L O A D

To Osc.

Osc. To

I3 i

To DAQ

e

E3

To DAQ

1 2 3 4 5 6

W 1 W 2

V

A

0-208V

0-208V

2.5Aac

250Vac

4

5

6 I2

To DAQ

To DAQ

E2

I1

To DAQ

To DAQ

E1

+

+

+

+

a

b

c

a

b c

Ia

Ib

Vab

Ic

Vbc Vca

+ +

+

4

Van

Ic Ib

Ia

Vcn Vbn

n

Note: W2

connections,

4, 6 are reversed

in diagram.

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

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.

To Osc

i

To DAQ

To DAQ

V

A

0-208V

0-208V

2.5Aac

250Vac

4

5

6 I2

To DAQ

To DAQ

E2

I1

To DAQ

To DAQ

E1

+

+

+

+

Use same phase current

as line (phase) current

in step 3 (300

,resistors).

Ia

e

To Osc

Zab

a

1 2 3

4 5 6

W 1 W 2 E3

I3

Zca

Zbc

b

Vca Vab

Vbc +

+

Ica

+ c

Ibc

Iab

Ib

Ic

Figure 1-6. The Delta connected circuit.

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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 delta-

connected 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 wye-

connected 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?

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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 Lab-

Volt 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?

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ELEC 331, Data Tables for Experiment 1

Table 1 Data for Wye Connected Load (* print-out of graphical display or oscilloscope trace is required)

R

() XL

() XC

() W1

(W)

W2

(W)

Vph (V)

Iph

(A)

Ineutral

(A)

P3,Q

3,S3

(W,

Var,

VA)

ph

Lab-

Volt

Phasor

(deg

or rad)

ph

Oscillo-

scope

(deg or

rad)

Vab

(V)

Ia

(A)

Vab,

Ia

ref

Vab

Vcb

(V) c

(A)Vcb,

Ic

ref

Vab

P1,

S1

(W,

VA)

P2,

S2

(W,

VA)

300 0 0 * 208 * *

Open 1 ph C

0 0 *

300|| 600 3-ph

0 0 * 120

0 0 600 * 208

0 300||600||1200

0 *

300

300||600||1200

0 * * * *

300

300||600||1200

600 * *

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Table 2. Data for Delta Connected Load (* print-out of graphical display is required) I ph is same as 300 load above

R

()

XL

()

XC

()

W1 (W)

W2 (W)

Vph (V)

Iph (A) N.B See

Iph

above

P3, Q3,

S3 (W,

Var,

VA)

ph

Lab-Volt Phasor (deg or rad)

e-Vab,i-Ia

Oscillo-

scope

(deg or rad)

Vab (V)

Ia (A)

Vab,

Ia

ref

Vab

Vcb (V)

c

(A)Vcb,

Ic

ref

Vab

P1,

S1

(W,

VA)

P2,

S2

(W,

VA)

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 2-

Wattmeter method. All numerical data can be recorded in a LabVolt data table, copied to Notepad and printed.

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