EE 740Professor Ali Keyhani

Lecture #5

Three Phase Transformer

Connections and Phase Shift

Problem 1: Three single-phase transformers, each rated 127/13.2 kV, 100 MVA with aleakage reactance of ten percent, are connected as a three-phase wye-wye connected bank.Draw the three-phase, single-phase (values specified in ohms) and the per unit equivalentcircuit.

13.2 kV127 kV

T1

T2 = T1

T3 = T1

300 MVAY-Y

219.71/22.83 kV

Problem 1: Three single-phase transformers, each rated 127/13.2 kV, 100 MVA with aleakage reactance of ten percent, are connected as a three-phase wye-wye connected bank.Draw the three-phase, single-phase (values specified in ohms) and the per unit equivalentcircuit.

ZbHV = (VbHV)2/Sb = 161.29 ZAHV = Zpu x ZbHV = j.10 x 161.29 = 16.129

300 MVA

Y-Y

219.71/22.83 kV

j16.129

j16.129

j16.1293-phase Eqt. Ckt.

j16.129

100 MVA

127/13.2 kV10%

1-phase Eqt. Ckt.

HV LVj.10

Per-unit Eqt. Ckt.

Problem 1: Three single-phase transformers, each rated 127/13.2 kV, 100 MVA with aleakage reactance of ten percent, are connected as a three-phase wye-delta connected bank.Draw the three-phase, single-phase (values specified in ohms) and the per unit equivalentcircuit.

13.2 kV127 kV

T1

T2 = T1

T3 = T1

300 MVAY-Y

219.71/13.2 kV

Three-phase transformer connections and phase shift.Y-YY--Y

American Standard:

High voltage terminals are marked with H1, H2 and H3. Also ABC for HV terminals.Low voltage terminals are marked with X1, X2 and X3. Also abc for LV terminals.

Dot Notations:

1) Place a dot on the terminals where the current enters the winding. The dotted terminal ispositive with respect to the other terminal.

2) Determine the direction of the flux using the right-hand-rule.3) According to Lenz’s law the flux generated in the second coil opposes the flux in the

first coil.4) Use RHR to determine the direction of the natural current by pointing the thumb in the

direction of the flux, then the right hand fingers will “curl” in the direction of the naturalcurrent. Place a dot where the natural current leaves the coil.

X3H3

X2

X1H1

H2

IcIC

IbIB

IaIA

VAN

VCN

VBN

Vcn

Vbn

Van

++

+ +

+ +

- -

- -

- -

C

A

B

c

b

a

(a) Core and coil arrangments

H1

H2

H3

X1

X2

X3

N

n

Ia

IA

IB IC

Ib Ic

Van

VAN

+

+

-

-

(b) Schematic representation showing phasor relationship for positive-sequence operation

nN

© Single-line diagram

Y Y

The phase of Y-Y or - transformers can be labeled so there is no phase shift betweenHV and LV variables.

Y- or -Y transformers have a 30 phase shift. The American Standards for labelingof the windings are:

“In either a Y- or -Y transformer, positive-sequence quantities on the HV sideshall lead their corresponding quantities on the low voltage side by 30 .

The following steps can be used for constructing the positive-sequence phasor diagramsfor Y- transformers.

Step 1) Assume positive sequence voltages are applied to the Y-winding.

Step 2) Identify the corresponding phasor voltages on the winding.

Step 3) For each single-phase transformer, the voltage across the low-voltage windingmust be in phase with the voltage across the high-voltage winding. Draw a line next toeach low-voltage winding parallel to the corresponding HV winding.

Step 4) Label the ends of the lines drawn in step 3 by inspecting the polarity marks.

Step 5) Bring the three lines labeled in step 4 together to complete the phasor diagramfor the low voltage winding. NoteVAN leads Van by 30 in accordance with theAmerican Standard.

X3H3

X2

X1H1

H2

C

A

B

c

b

a

(a) Core and coil arrangments

N

AN(Step 2)

b a(Step 3)

(Step 4) “a” connected to must be on the right side, and “b” on the left side of line a-b.

A

B

C

VANN

Step 1) Assume (+) sequence voltage

120

c

b a

n

Van

VAN

30

Step 2) Van is 30 behind VAN and abc sequence.

Step 5) For (+) sequence VAN (HV) leads Van (LV) by 30.

The negative sequence diagram is constructed from the following five steps:

Step 1) Draw the phasor diagram of the negative-sequence voltages which areassumed to be applied to the Y-winding.

Step 2) Identify the corresponding phasor voltages on the winding.

Step 3) For each single-phase transformer draw a line next to the low-voltage windingthat is parallel to the line drawn in step 2 next to the HV winding.

Step 4) Label the ends of the lines drawn in step 3 by inspecting the polarity marks.

Step 5) Bring the lines drawn in step 4 together to form the negative sequence phasordiagram for the low-voltage winding.

The HV phasor lags the LV phasor by 30 .

X3H3

X2

X1H1

H2

C

A

B

c

b

a

(a) Core and coil arrangments

N

AN(Step 2)

b a(Step 3)

(Step 4) “a” connected to must be on the right side, and “b” on the left side of line a-b.

A

B

C

VANN

Step 1) Assume (-) sequence voltage

120

c

b a

n

Van

VAN

30

Step 2) Van is 30 ahead of VAN and acb sequence.

Step 5) For (-) sequence VAN (HV) lags Van (LV) by 30.

N