8/6/2019 6053 CD 01

1/35

Lesson 11:

Three Phase Transformers

A set of three similar single phase transformers may be connected to form a three-phasetransformer (three-phase transformer bank). The primary and secondary windings may be

connected in either star or delta configurations

8/6/2019 6053 CD 01

2/35

Three Phase TransformersThree Similar Single-phase Transformers

Connected to form a three phase TransformerFour possible connections/, /, , and /

Step up

Step down

One can be removed

Seldom used

Figure 11.2.1 a, b, c and d for 3 phase transformers connections

8/6/2019 6053 CD 01

3/35

Three Phase Transformer Bank

1.Three single-phase transformers connected in a three-phase bank.

2. Three sets of windings wrapped on a common core.

Ease of transportationInefficient magnetic circuit, less efficient

Higher capital cost than a single one

1-phase of the transformer at fault, the other two are not affected

8/6/2019 6053 CD 01

4/35

Figure 11.2.2 three-phase transformer structure

Usually 3-limb core structure

5-limb core may be used to reduce the overall height of a 3-limb coreMagnetic flux shares the magnetic circuit

Fault on one-phase very likely affects the other two

3-phase Transformer

8/6/2019 6053 CD 01

5/35

Tertiary Winding

A third set of windings usually exists in 3-phase transformer and used to:

Providing voltage to auxiliary power purposes in the substation or to supply localdistribution system

Power factor correction

Delta connected tertiary windings will provide a circuit for the third harmonics of theexciting current

8/6/2019 6053 CD 01

6/35

Wye / Wye connection

N n

A

B

C

a

b

c

IA

Ia

VAN

VAB

VCN

VBN Vbn

Van

Vcn

Vab

Figure 11.2.3

8/6/2019 6053 CD 01

7/35

Single Phase Diagram of 3 phase transformers

L o a dS u p p l y

N e t w o r k

T r a n s fo rm e r

Y -Y

Three-phase network supplies a load

through a transformer.

Transformer LoadSupply Network

Xtr_s

Van

Vload_an

VAN

Vnet_AN

Xnet

IA

Ia

N

n

A

a

Xtr_s

Van

Vload_an

VAN

IA

IaV

net_AN

Xnet

Equivalent circuit of the wye-wye

Single-phase equivalent circuit for phase

A of the three-phase wye-wye

transformer system

Figure 11.2.4 Single Phase Diagram of 3 phase transformers

8/6/2019 6053 CD 01

8/35

Wye / Delta connection

A

B

C

N

VAN

VAB

VBN

VBC

VCN

IA

Iba

Icb

VCA

a

b

c

a

b

c

Ia

Ic

Ib

Vab

Vbc

Vca

Iac

Figure 11.2.5

8/6/2019 6053 CD 01

9/35

Physical connections of 3 phase Transformers

Ia

Ib

Ic

Vab

Vbc

Vca

VCN

VBN

VAN

A

B

C

a

b

c

Icb

Iba

Iac

Transformer

AC

AC

AC

IC

IB

IA

VAN

VBN

VCN

Supply

Iab

Ibc

Ica

Load

VAB

VBC

VCA

Iac

Vca

Vbc

Vab

N

Figure 11.2.6 Wye-delta connected transformer

8/6/2019 6053 CD 01

10/35

Figure 11.2.7 Single-phase equivalent circuit of a wye-delta transformer

Xtr_s

Van Vs_an

VAN

IA Ia

Vp_AN

Xtr_p

Rtr_p

Rtr_s

Xm

Rc

Tspe

Y-

8/6/2019 6053 CD 01

11/35

Delta / Wye connection

A

B

C

n

a

b

c

VBC

IaIA

Ib

Ic

VAB

VCA Vca

Vab

Vbc

Van

Vbn

Vcn

IC

IB

ICA

IAB

IBC

Figure 11.2.8

8/6/2019 6053 CD 01

12/35

Delta / Delta connection

A

B

C

a

b

c

VAB

Ia

Iba

Iac

IA

IAB

ICA

Vab

Figure 11.2.9

8/6/2019 6053 CD 01

13/35

* Note: Phase shift lead between line-to-line voltages, VAB

and Vab

, and line-to-neutral voltages, VAN

and Van

, and line currents,

IA

and Ia.

AB and abZeroVAB

is in phase with Vab

Delta-Delta

AB and a30VAB

is in phase with Van

Delta-Wye

A and ab30VAN

is in phase with Vab

Wye-Delta

A and aZeroVAN

is in phase with Van

Wye-Wye

Windings Placed on the Same LegPhase Shift*Primary and Secondary Voltage Phase

RelationTransformer Connection

Table 11.2.1Three-phase Transformer Relations

8/6/2019 6053 CD 01

14/35

Three-phase transformer - Phase shift

Y-

VAB // Va

VAB

leads Vab

by 30o

-Y also provides line-to-line phaseshift

Y-Y and - connections have nophase shift

Figure 11.2.10

8/6/2019 6053 CD 01

15/35

Three-phase transformer - single-phase equivalent circuit

Validity conditions:

Identical transformers balancedsource and load

Only one phase variables are used, the other phases are similar.

equivalent Y-representation

line-to-neutral = phase voltage

-Y transformation

Figure 11.2.11 a, b, c, and d

8/6/2019 6053 CD 01

16/35

Three-phase transformer - open delta connection

One phase can be removed

Operation at reduced load

Possible only in

-

connection

Figure 11.2.12 a, and b

58.03

30cos2

3

)30cos(2

)30cos(

)30cos(

==

=

=+=

=

+=

P

P

VIP

VIPPP

IVP

IVP

V

bcabV

cbcab

aabab

8/6/2019 6053 CD 01

17/35

Three-phase transformer unit

Balanced three-phase voltage

Balanced three-phase flux

Return leg can be removed

In-plan construction easy to

manufacture

Same operation as transformer bank

Figure 11.2.13 a, b, c, and d

8/6/2019 6053 CD 01

18/35

Example 11-1

Three-single phase transformers are connected grounded Y-Y to two three

phase loads connected in and Y

a) Draw single-line diagram.

b) The single-phase equivalent circuit with transformer referred to HV side.

Solution:

8/6/2019 6053 CD 01

19/35

240 120

VLS

VS

240120

120240

VLP

VP

a

b

c

100kVA5%

100kVA

5%

100kVA

5%SL1 = 75kVA

Pf = 0.9 lagging

SL2 = 24kVA

Pf = 0.9 leading

8/6/2019 6053 CD 01

20/35

VLP = 240x = 415.2V

VLS = 120x = 207.6V

300KVA

415/207.65%

Y-Y

SS1 SL2

~

a)

3

3

8/6/2019 6053 CD 01

21/35

kVA

S 251 = =KVA

S 82

240 120

100KVA

S1 S2

(J.05) ZbHV

b)

8/6/2019 6053 CD 01

22/35

c)

Sb=100KVA

S1p.u. S2p.u.

J.05Vb=240 Vb=120

Y-Y

1. Y-Y 2. Y- 3. -Y 4. -

aV

V

LS

LP ==S

P

V3

V3

8/6/2019 6053 CD 01

23/35

VLP

NP3

NP2

NP1

VP

a

b

c

Y-

NS2

NS3

NS1

a

b

cVLSVS

b

a

c

V L P

N P 1

N P 2

N P 3

N S 1

N S 2

N S 3

b

a

c

V SV P

PLPVV= 3 SLS

VV=

8/6/2019 6053 CD 01

24/35

aV

V

S

P =

aV

V

V

V

S

P

Ls

LP

3

3

==

LS

LP

V

Va

3=

The voltage ratio of each phase

The line voltage ratio

LS

P

LS

V

LS

LP

V

V

VV

Va

LP

=== 3

3

From the above

8/6/2019 6053 CD 01

25/35

Y-. The secondary voltage is shifted 30 relative to the primary voltage.

c

b

a H

HVVan LV

30

Vca

Vab

Vbc

a

c

b

LV

8/6/2019 6053 CD 01

26/35

Because of the phase shift. transformers can not be connected in

parallel unless they have proper phase sequence. (i.e. They are in

phase with each other).

Y Y parallel Y- ? NO

Y- parallel Y- ? Yes. However, you must identify the correctphase sequence.

8/6/2019 6053 CD 01

27/35

+

-V PV L P

V L S

V S

a

b

c

PLPVV = SLS VV = 3

LS

LP

s

P

LS

LP

V

Va

a

V

V

V

V 3

33===

S

P

LS

LP

LS

LP

V

V

V

V

V

Va

===

3

3From above we have

-Y

8/6/2019 6053 CD 01

28/35

For-Y connection, the secondary Voltage Lags the primary Voltage by30

V L S

+

-V L P

+

-

V P

a

b

c

N P 1V S

N S 3

N S 2

N S 1

a

b

c

-

PLPVV = SLS VV

=

aV

V

V

V

S

P

LS

LP ==

-for

8/6/2019 6053 CD 01

29/35

3- Phase Real Power Transformer

8/6/2019 6053 CD 01

30/35

Appliances Transformer

8/6/2019 6053 CD 01

31/35

Harmonics in Transformer

Harmonics in transformer occur due to the effect of saturation and Hysteresis which areto produce non-sinusoidal current if the applied voltage is sinusoidal.

Upon saturation, the flux waveform is flat topped and contains mainly 3rd harmonic

component.

8/6/2019 6053 CD 01

32/35

Effects of harmonic currents

(i) Additional I2R losses due to circulating currents .

(ii) Increased iron loss in core.

(iii) Magnetic interference with protective gear and communication circuits.

8/6/2019 6053 CD 01

33/35

Effects of harmonic voltages

(i) Increased dielectric stress.

(ii) Electric field interference with communication circuit.

(ii) Harmonic resonance may occur between the inductance of

transformer windings and the capacitance of a feeder to which it is

connected.

8/6/2019 6053 CD 01

34/35

In 3-ph Supply System (1/2)

Star-connected with isolated neutral the line voltage contains no 3rd

harmonic component and 3rd harmonic current is precluded.

Star connected with neutral wire, the 3rd harmonic currents can flow andstill no 3rd harmonic line voltages.

8/6/2019 6053 CD 01

35/35

In 3-ph Supply System (2/2)

Delta Connected, the 3rd harmonic emfs around the 3-phase windings aresummed, which causes a circulating 3rd harmonic current around the 3-phase

windings.

But the line voltages across any two lines contain no 3rd harmonic component,

since they are short circuited by the windings.