TRANSMISSION & DISTRIBUTION Three-Phase … 2 Book 2/4...phase, TP = AP. These relationships also apply to three-phase circuits. For example: A balanced three-phase load has a capacity

�T R A I N I N G

M A N U A L0 2 / 0 7 / 0 5

CombinationThree-Phase

Systems

Training Development Centre

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CC O M B I N A T I O N T H R E E -P H A S E S Y S T E M S

OBJECTIVE:Given a formula sheet, calculator andthe Construction Standards Manual, youwill be able to calculate voltage, currentand power values throughout abalanced wye/delta connected system.

WHY?When maintaining or troubleshooting three-phase systems or loads, you may be takingvoltage and current readings with measuringinstruments. Using your formulas, you canconvert the readings into values which helpyou determine maintenance ortroubleshooting activities.

LEARNING OBJECTIVES:1. Identify the three-phase services from

the Construction Standards Manual.

2. Calculate coil and line values in abalanced three-phase combinationcircuit.

3. Calculate the voltage, current or kVA in abalanced three-phase combinationcircuit.

4. Calculate the three-phase power factorand phase angle in a balanced three-phase combination circuit.

5. Calculate the voltage, current or kW in abalanced three-phase combinationcircuit.

Preface

Start Here

Intro to Hotsticks

Alternating Current

Street Lights

Single Phase Transformation

Three Phase Systems

Class 1 Rubber Gloves

DCRACF

RMSRINRIR

PACCXC

RXCSRX

PRX

SLIISL

MSLSLP

TOP

TRRPTR

TRLTWC

Standard Protection

Code

TPSYCO

DCOCTP

Copyright © 1998 by the Training and Development Centre, SaskPower. All rights reserved. 0 2 / 0 7 / 0 5

IN THIS MODULE:1. Coil and Line Values in a Balanced

Three-Phase Combination Circuit

2. Voltage, Current and Load in kVA

3. Three-Phase Power Factor and PhaseAngle

4. Voltage, Current or kW in a BalancedThree-Phase Combination Circuit

RESOURCES:• Calculator

• Construction Standards Manual

ESTIMATED TIME:1.5 Hours

PREREQUISITES:• Delta Connections

LEARNING STEPS:1. Cover the module.

2. Complete the Review Questions.

3. Clarify any questions or concerns youmay have.

Copyright © 1998 by the Training and Development Centre, SaskPower. All rights reserved.0 2 / 0 7 / 0 5

Three-Phase ServicesThere are many three-phase services available to customers today.The most basic is a three-phase, four wire star service. Typicallybuilt in three voltages, the most common is a 120/208 service.More complex three-phase services are delta 4W grounded,typically built as 120/240 4W delta.

Refer to Construction Standards Manual section A-08-00 formore information.

4 T R A I N I N G M A N U A L .

0 2 / 0 7 / 0 5Copyright © 1998 by the Training and Development Centre, SaskPower. All rights reserved.

Coil and Line Values in a Balanced Three-Phase Combination Circuit

When dealing with voltage and current in a three-phase system, wemust remember to convert voltage and current to coil or line valuesso that all variables correspond.

Consider the following:

A wye connected generator is connected to a line serving a deltaconnected load. Each coil in the generator has a voltage of 2400.The coil current is 26A.

What is the voltage and current in the coils of the three-phase deltaconnected load?

Solve:

If possible, always draw a diagram of the problem.

First, we will convert E and I to line values. We know that in awye connected system:

Eline = Ecoil x 1.73

Ecoil = 2400V

Eline = 4152V

Icoil = Iline

Icoil = 26A; therefore, Iline must equal 26A

Three-phase “Star -Delta” configuration.

C O M B I N A T I O N T H R E E - P H A S E S Y S T E M S 5 .

0 2 / 0 7 / 0 5 Copyright © 1998 by the Training and Development Centre, SaskPower. All rights reserved.

Next, let’s convert the line values to coil values in the delta load.

We know that in a delta connected system:

Eline = Ecoil

Eline = 4152V; therefore Ecoil must equal 4152V

I x II A

I I

I A

I A

coil line

line

coilline

coil

coil

17326

173261731503

.

.

..

==

=

=

=



Voltage, Current and Load in kVACalculating the load (in kVA) of a balanced three-phase system canbe accomplished using line values or coil values:

• Calculate the load of each coil individually and then add thethree values together.

For example, three-phase kVA equals three single-phase loadchecks added together.

• If the system is balanced, each coil will have the same kVAvalue. Therefore, we can utilize the following 3φ formula:

Three-phase kVA can also be calculated by using line values by thefollowing formula:

To prove this formula requires a detailed three-phase vector,whereby the 1.73 factor is derived as being two times cos 30degrees. Therefore, assume the formula as a given fact and use itat your own discretion on three-phase systems.

Remember, using coil values:

and using line values:

To find three-phase kVA, always use line or coil values for Eand I; however, do not use a mix. This will prevent confusion.

kVAE x I xline line

3173

1000∅ =.

kVAE x I xcoil coil

33

1000∅ =

kVAE x I xline line

3173

1000∅ =.

kVAE x I xcoil coil

33

1000∅ =

Coil R Coil Y Coil BE x I E x I E x Icoil coil coil coil coil coil

1000 1000 1000⎛⎝⎜

⎞⎠⎟

+ ⎛⎝⎜

⎞⎠⎟

+ ⎛⎝⎜

⎞⎠⎟



Example:

A delta connected, three-phase generator supplies a balanced three-phase load. Each coil has a current value of 32.6A and a voltageof 2400.

Calculate the three-phase capacity of the generator.

Because we are dealing with coil values, we use:

If you already know two of the three variables in a three-phasekVA formula (three phase kVA, E or I), the unknown variable canbe calculated.

Simply isolate the unknown variable on one side of the equal signand solve.

You may also convert your coil values to line values and usethe line values formula.

kVAE x I x

kVA V x A x

kVA kVA

coil coil3

3

3

31000

2400 32 6 31000

234 72

∅

∅

∅

=

=

=

.

.



Example:

A balanced three-phase delta connected load is supplied by a three-phase line. The line voltage is 2400 volts and the capacity of thethree phase load is 172.65kVA. What is the line current and coilcurrent?

Solve for I using line values:

Calculate Icoil:

Since the system is delta connected:

I I

I A

I A

coilline

coil

coil

=

=

=

1734158

17324 03

....

kVA E x I x

kVAE x

I

kVAV x

I

A I

line line

lineline

line

line

3

3

1731000

1000173

1000 172 652400 173

4158

∅

∅

=

=

=

=

.

( ).

( ) ..

.



Three-Phase Power Factor and Phase Angle

Previously, in AC circuits, we learned that the phase angle isthe angular displacement by which voltage and current are out ofphase with each other. We also learned:

• In a purely resistive circuit, E and I are in phase or:

• In a purely inductive circuit, I lags E by 90 degrees or:

lagging

• In a purely capacitive circuit, I leads E by 90 degrees or:

leading

The power factor (p.f.) is simply the cosine of expressed as apercentage value.

Consider the following:

In a balanced three-phase system with resistive and inductive load,I lags E by 30 degrees.

Because 30 degrees is the angular displacement, the power factoris calculated as follows:

The P.F. is lagging.

cos . .. . .. . .

30 1000 8660 10086 6%

° ==

=

x p fx p f

p f

∠θ

∠θ = °90

∠θ = °90

∠θ = °0

( )∠θ



Example:

If the power factor of an inductive three-phase wye connected loadis 92%, what is the angular displacement of E and I?

The three-phase vector drawing would look like this (I lags E in aninductive load):

Where the coil voltages are:

EOY

EOR

EOB

Where the coil currents are:

IOY

IOR

IOB

p f. . cos

. (cos ).

10092231

1

= ∠θ

= ∠θ° = ∠θ

−



Example:

A delta connected three-phase inductive load has a phase angle of40 degrees. What is the power factor of the system?

The three-phase vector drawing is as follows:

p f xp f x. . cos. . . .

= °= =

40 1000 766 100 76 6%



Voltage, Current or kW in a Balanced Three-Phase Combination Circuit

While studying AC, we learned that true power (watts) is theproduct of supplied power (VA) and the power factor (p.f.). Wealso learned that in a purely resistive circuit where E and I are inphase, TP = AP. These relationships also apply to three-phasecircuits.

For example:

A balanced three-phase load has a capacity of 74kVA and I lags Eby 24 degrees. Calculate the TP of the system:

Given:

A balanced three-phase load connected in delta uses 171.75kW andhas an angular displacement of 17.5 degrees where I lags E. Whatis the coil current of the load if the line voltage is 24,947?

First of all, let us determine the kVA of the system:

p fp fp f

AP TPp f

AP kW

AP kVA

. . cos

. . cos .

. . .

. ...

.

= ∠θ= °=

=

=

=

17 50 95

171 750 95

180 79

p fp fp f

TP AP x p fTP kVA xTP kW

. . cos

. . cos

. . .

. ..

.

= ∠θ= °=

===

240 9135

74 0 913567 6



Now, isolate Icoil in the three-phase capacity formula:

Given:

A wye connected, balanced, three-phase load uses 5400 watts andis purely resistive. The line current is measured at 0.75A. What isthe coil voltage of the load?

Purely resistive means that E and I are in phase.Therefore TP = AP.

Now, let’s isolate Ecoil:

Because the system is wye connected:

I I A

E kVAA x

E V

coil line

coil

coil

= =

=

=

0 755 4 1000

0 75 32400

.. ( )

.

kVA E x I x

kVAI x

E

coil coil

coilcoil

3

3

31000

10003

∅

∅

=

=( )

54001000

5 4

5 4

W kW

AP kVA

=

=

.

.

kVA E x I x

kVAE x

I

In a delta system E E so E V

kVAV x

I

A I

coil coil

coilcoil

line coil coil

coil

coil

3

3

31000

10003

24 947

180 79 100024 947 3

2 42

∅

∅

=

=

= =

=

=

( )

, , ,

. ( ),

.



SummaryTo summarize this module, you have learned:

• How to identify three-phase services from the ConstructionStandards Manual.

• Coil and line values in a balanced three-phase combinationcircuit.

• Voltage, current or kVA in a balanced three-phasecombination circuit.

• Three-phase power factor and phase angle in a balancedthree-phase combination circuit.

• Voltage, current or kW in a balanced three-phasecombination circuit.

Now...

• Complete the Review Questions.

• Clarify any questions or concerns you may have.



REVIEW QUESTIONS

Combination Three-Phase Systems

Calculate coil and line values in a balancedthree-phase combination circuit.

1. A three-phase delta connected generator supplies a balancedthree-phase, Wye connected load. Using the drawing below:

(a) Calculate Ecoil of the generator.

(b) Calculate Icoil of the three-phase load.

(c) Calculate Eline and Iline.

This section is review of your Power Line Apprenticeshipwritten exams. Complete the questions, and verify your answerswith the Review Question Solutions located at the end of thismodule.



Calculate the voltage, current or kVA in abalanced three-phase combination circuit.

2. Calculate the capacity of a three-phase, wye connected generatorwith a coil current of 17.3A and a coil voltage of 14.45kV.

3. A three-phase, delta connected, balanced load has a capacity of39.8kVA. The line voltage is 4152 volts. The value of Icoil is:

(a) 1.9A.

(b) 3.2A.

(c) 3.98A.

(d) 5.54A.

4. The three-phase generator below has a capacity of 18.6kVA. Theline voltage is:

(a) 120 volts.

(b) 208 volts.

(c) 277 volts.

(d) 347 volts.



Calculate the three-phase power factor andphase angle in a balanced three-phasecombination circuit.

5. In a purely __________________ system, I lags E by ______degrees.

6. In a purely resistive three-phase system:

(a)

(b)

(c)

(d)

7. In a delta connected motor, I lags E by 13.5 degrees. The powerfactor is:

(a) 13.5%.

(b) 23.5%.

(c) 92.2%.

(d) 97.2%.

8. A wye connected load has a leading power factor of 90.3%. Theangular displacement of E and I is:

(a) 20.1 degrees.

(b) 25.4 degrees.

(c) 27.6 degrees.

(d) 31 degrees.

∠θ = °90

∠θ = °45

∠θ = °30

∠θ = °0



Calculate the voltage, current or kW in abalanced three-phase combination circuit.

9. A delta connected generator supplies a motor with a 75% laggingpower factor. On each winding, there is 100 volts and 20A.

(a) Calculate Eline.

(b) Calculate Iline.

(c) Calculate A.P.

(d) Calculate T.P.

10. A three-phase delta connected alternator is rated at 50kVA, 600volts at full load.

(a) Calculate T.P. with a 70.7% p.f.

(b) Calculate Icoil.

(c) Calculate Iline.

(d) Calculate Ecoil.



11. A wye connected generator feeds a motor with an 85% leadingpower factor. On each winding, there are 200 volts and 6A.

(a) Calculate the line voltage.

(b) Calculate the line current.

(c) Calculate A.P.

(d) Calculate T.P.

12. The star connected alternator shown below supplies a motor witha phase angle of 45 degrees.

(a) Calculate the line voltage.

(b) Calculate the line current.



(c) Calculate the apparent power of the circuit.

(d) Calculate the true power of the alternator.

13. Three coils are connected delta across a 416 volt, three-phasesupply. The line current is 12A and the power delivered to thethree coils is 6000 watts.

(a) Calculate A.P.

(b) Calculate the power factor.

(c) Calculate Icoil.

(d) Calculate Ecoil.




Copyright © 1998 by the Training and Development Centre, SaskPower. All rights reserved. 0 2 / 0 7 / 0 5

1a. Ecoil = 4152V

1b. Icoil = 17.3A

1c. 17.3A

2. 750kVA

3. b

4. b

5. Inductive, 90

6. a

7. d

8. b

9a. 100V

9b. 34.6A

9c. 5.99kVA

9d. 4.49kW

10a. 35.35kW

10b. 27.84A

10c. 48.17A

10d. 600V

11a. 346V

11b. 6A

11c. 3.59kVA

11d. 3.05kW

12a. 600.31V

12b. 80A

12c. 83.08kVA

12d. 58.73kW

13a. 8.64kVA

13b. 69%

13c. 6.94A

13d. 416V

REVIEW QUESTION SOLUTIONS

Combination Three-Phase Systems

Documents

TRANSMISSION & DISTRIBUTION Three-Phase … 2 Book 2/4...phase, TP = AP. These relationships also apply to three-phase circuits. For example: A balanced three-phase load has a capacity