(McGraw-Hill) (Instructors Manual) Electric Machinery Fundamentals 4th Edition Episode 1 Part 4 pot

55

The resulting equivalent circuit referred to the primary at 50 Hz is shown below:

+

-

VP VS

IS

+

-

IP

RC jXM

REQ jXEQ

1.31 MΩ j473 kΩ

260 Ω j917 Ω

2-20. Prove that the three-phase system of voltages on the secondary of the Y-∆ transformer shown in Figure 2-

38b lags the three-phase system of voltages on the primary of the transformer by 30°.

SOLUTION The figure is reproduced below:

VC

VB

VA

VC'

VA'

VB' + +

+

+

+

+

- -

-

-

- -

- -

- -

- -

+ +

+ +

+ +

VA'

VB'

VC'

VA

VB

VC

56

Assume that the phase voltages on the primary side are given by

= ∠0° VA VφP = ∠ −120° VB VφP = ∠120° VC VφP

Then the phase voltages on the secondary side are given by

= ∠ ° ′ VA VφS 0 = ∠ − ° ′ VB VφS 120 = ∠ ° ′ VC VφS 120

where VφS = VφP / a . Since this is a Y-∆ transformer bank, the line voltage Vab on the primary side is

= − = ∠0° − ∠ −120° = 3 ∠30° Vab VA VB VφP VφP VφP

and the voltage = ∠ ° ′ Va′b′ = VA VφS 0 . Note that the line voltage on the secondary side lags the line

voltage on the primary side by 30°.

2-21. Prove that the three-phase system of voltages on the secondary of the ∆-Y transformer shown in Figure 2-

38c lags the three-phase system of voltages on the primary of the transformer by 30°.

SOLUTION The figure is reproduced below:

+ +

+ +

- -

- -

VA

VA'

VB VB'

VC VC'

Assume that the phase voltages on the primary side are given by

= ∠0° VA VφP = ∠ −120° VB VφP = ∠120° VC VφP