2 equivalent circuits of power transformers

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Equivalent Circuits of Power Transformers

> Equivalent Circuits of Power Transformers2

Three Phase Transformers

1. Three single phase units

2. limb core type 4. Shell type

3. 5-limb core type


Winding Polarity


Transformer Equivalent Circuit


Simplified Equivalent Circuit


Two Winding Transformer

(a)

(b)

(c)


Three Phase Transformers

Under balanced conditions all phases behave in a similar manner and can be considered independently.

Thus equivalent (single phase) circuit for both positive and negative sequence quantities is a single series impedance representing the primary and secondary leakage reactance.

(Resistance can usually be ignored.)

i.e. Same as single phase transformer

NB! Actual circuit:


Dy 1


Positive Sequence Current

Consider Dy 1 transformer

Voltage ratio 1 : 1

Turns ratio : 1

3


150I

3

1aI

3

I

3

aII

90I3

aaI

3

aI

3

IaI

30I3

a1I

3

Ia

3

II

1111

C

1

2

111

2

B

1

2

11

21

A

90II 1B

150II 1C

30II 1A 1IIa

1aIIc 12IaIb


Negative Sequence Current

Consider Dy 1 transformer

Voltage ratio 1 : 1

Turns ratio : 1

3


150I

3

1aI

3

I

3

IaI

90I3

aaI

3

Ia

3

aII

30I3

a1I

3

aI

3

II

2

2

222

2

C

2

2

22

22

B

1222

A

150II 2C

30II 2A

90II 2B

2IIa

2aIIb 22IaIc


Example

210530530II

30530II

2)R(2

1)R(1


Example continued …

pu9066.824051205

IaaII

pu9066.812052405

aIIaI

0III

:FAt

pu90104505905

2105.2401305.1201

IaaII

pu90533052105

2105.1201305.2401

aIIaI

pu9052105305

III

:RAt

22

1C

212

B

21A

)R(22

)R(1C

)R(2)R(12

B

)R(2)R(1A



AMPS 875 5.87 x 10I

AMPS 5.437 5.87 x 5I

AMPS 5.437 5.87 x 5I

:RAt

AMPS90931050 x 66.8I

AMPS90931050 x 66.8I

0I

:FAt

AMPS87.5 kV) (132Current Base

AMPS1050 (11kV)Current Base

C

B

A

C

B

A


Zero Sequence

The transformer response to zero sequence quantities depends upon:

a) The existence (or otherwise) of a neutral connection

b) The interconnection of the phase windings

c) Type of core (3-Limb, Shell etc)

The 3 or 4 terminal single phase equivalent circuit can be retained but

the above factors require consideration in order to determine the

connection of the circuit to the network.


Transformer Zero Sequence Impedance


‘b’ links closed for a delta winding as this forms a trap for I0 in

earthed star which induces current in delta.

I0s in phase

∴ I0 circulatesd round the delta and no I0 passes into the line.


‘a’ link closed

←path for zero sequence current

Link closed if I0 can flow from line into transformer winding

‘a’ link open

No I0 in neutral∴ none in line as I0 in each phaseis in phase

unearthed

I0 not possible in line asconsistent current distribution in delta not possible


General zero sequence equivalent circuit for two winding transformer

Primary Secondaryterminal terminal

On appropriate side of transformer:

Earthed star winding - Close link ‘a’Open link ‘b’

Delta winding - Open link ‘a’Close link ‘b’


Delta-star transformer Zero sequence equivalent circuit

There is a transfer of zero-sequence current between windings – the impedance presented being the zero sequence leakage inpedance.

Viewed from the star side, the Δ winding appears as a short circuit to zero sequence current.

Viewed from the delta side, the transformer appears as an open circuit (no zero sequence current in line connections).

Single phase equivalent circuit


Example



0 IaIaI

AMPS473pu18041.5 aIIaI

)A5.87I(

AMPS473 pu041.5 III

:R At

30II30II

AMPS9843

A1050I pu375.9IIII

pu125.332.0

0.1III

)R(22

)R(1C

)R(2)R(12

B

b

)R(2)R(1A

2)R(21)R(1

b021F

021

132 kV / 11 kV

Current Distribution


Transformer Sequence Impedances

For or transformers

ZM1 >> ZP1 or ZS1

ZM0 >> ZP0 or ZS0

Thus ZM1 and ZM0 are usually ignored.

Positive sequence

Equivalent cct

Zero sequence

Equivalent cct

Also Z1 = Z2 = Z0


For transformers

Similar to above but:

Z0 ≈ 0.85 Z1 for 3-limb core type

Z0 = Z1 for 5-limb core type

shell type

3 x 1 phase units


Zero Sequence Equivalent Circuits


Two Winding Transformer Zero Sequence Network


NOTE!

“Source” earthing arrangements can affect transformer zero sequence diagram.

Eg:


Measurement of Transformer Impedance(Two Winding Transformer)

Require two tests:(a) Open circuit test(b) Short circuit test

Consider equivalent circuit:

Open Circuit Test Short Circuit Test

Tests are repeated from secondary side.

To give Zo/c’ = Zs + ZM

Zs/c’ = Zs + ZPZM

ZP + ZM

In pu Zo/c ≈ Zo/c’ and Zs/c ≈ Zs/c’


Star/Delta Transformer

Zero sequence impedance

Open circuit test:

Short circuit test:


ZM can be ignored for positive and negative sequence network.

ZM0 cannot be ignored for zero sequence network

Eg:

Zero Sequence Network

Typically:

Z0 = (ZS0 + ZM0) = 50 – 100% for 3-limb core type

= 100 – 500% for 5-limb core type

(400%) shell type

3 x 1 phase units

Non-Earthed Star Winding


Interconnected Star (Zig-Zag) Windings

Positive sequence current distribution

Zig-zag / Star transformer


Consider ampere-turns on ‘A’ Phase zig-zag winding

For ampere-turn balance

Zig-zag / star transformer has 30° phase shift for positive sequence quantities

30IT3033

IT

)a1(3

IT3

TxIa

3

TxI.T.A

2

2

30 I (a) I Thus

T (a) I 30 IT

A.T.Star A.T.zag-Zig


Zy 11

Zy 1

Zd 0


As with / connections the / connection introduces opposite

phase shifts for positive and negative sequence components.

Positive (and negative) sequence impedance:

Determined in usual manner by:

a) Open circuit test

b) Short circuit test

From both sides of transformer.

Again magnetising impedance can usually be ignored.

Thus equivalent single phase circuit:

Zig-Zag Transformers


Zig-Zag TransformersZero Sequence Current Distribution

Net ampere turns on each phase = 0

∴ current in secondary winding = 0

Zero sequence current can flow in zig-zag winding without regard to any other winding.

Leakage flux is very small, therefore inductive reactance to zero sequence current is small.


Zig-Zag Transformers

As there is no transfer of zero sequence current across the transformer, the zero sequence impedance viewed from the star side is high (effectively the zero sequence magnetising impedance)

Zero sequence equivalent circuit:


Zig-Zag Earthing Transformers

Positive (and negative) sequence impedance is very high.

Equivalent circuit:

Zero sequence impedance is very low.

Equivalent circuit:


Three Winding Transformer

Equivalent circuits can be found by performing open circuit and short circuit tests on each pair of windings in turn with the third winding open circuit.

Primary to Secondary Test

Primary to Tertiary Test

Secondary to Tertiary Test

etc


Three Winding TransformerEquivalent Circuit


Three Winding TransformerFor positive (negative) sequence tests

Thus, from the short circuit tests,

Primary to Secondary

Primary to Tertiary

Secondary to Tertiary

From these equations


Three Winding TransformerZero Sequence Impedance

Each winding requires consideration in similar manner to two winding transformers.

Eg:

NB!

All impedances must be expressed to common base quantities

The star point of the above impedance network is a fictitious point and does not represent the system neutral


Primary Tertiary Secondary

IPO induces current in secondary and tertiary current in delta ITO – proportion of IPO not converted into secondary zero sequence current.

ie. Proportion trapped in delta

‘b’ link closed for delta

‘a’ link closed for star


Positive Sequence Network

Negative Sequence Network

Zg2 ZT2 ZP2 ZT2

ZS2

F2

N2

LOAD

Zg1 ZT1 ZP1 ZT1

ZS1

F1

N1

LOAD



Zg0 a ZT0 a 3Zn1 3Zn2 a ZP0 ZT0 a

3Zn b b b

b

a

b

3Zn3 F0

N0


Auto Transformers

Has a single winding per phase, part of which is common to bothprimary and secondary

A

B

C

series-commonwinding

serieswinding

commonwinding

HV

SIDE

LV

SIDE


The positive (negative) sequence is obtained in similar way to two winding transformers.

For auto transformers with delta winding (ie. similar to 3 winding transformer):

Equivalent star impedances


Auto TransformersZero Sequence Impedance

Similar to 2/3 winding transformers

Eg. For autotransformer with earthed neutral and delta winding


Auto Transformers

ZN is common to both HV and LV system

Zero sequence network:

Where n = HV voltage ratioLV

If PU → ZN referred to LV base quantities

If ZN in ohms → ZH, ZL & ZT must be referred to LV network


Positive Sequence Network

Negative Sequence Network

Zg1 ZT1 ZL1 ZT1

ZH1

F1

N1

LOAD

E1

Zg2 ZT2 ZL2 ZT2

ZH2

F2

N2

LOAD



Zg0 a ZT0 a 3Zn1 a

n

1n 3Zn2 ZL0 ZT0 n

Z3 2n

a

b

a

b

F0

N0

ZH0

3Zn b b b

2n

1n 3Zn2


Typical Transformer Impedances

2 Winding Transformers

1 MVA 4.75 → 6%

5 MVA 6 → 7.5%

10 MVA 9 → 11%

15 MVA 10 → 15%

30, 45, 60 MVA 10 → 12.5%

90 MVA 15 → 22.5%

120 MVA 15 → 20%

210, 425 MVA 17%

600 MVA 14 → 17%

800 MVA 14 → 16%

Auto Transformers with Delta Tertiaries

ZH ZL ZT

120 MVA; 275/132 kV 17.5% -2.5% 20.5%

500 MVA; 400/132 kV 20% -8% 60%

1000 MVA; 400/275 kV 21% -5% 89%