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- 1. GRI D Techni cal I nst i t ut e This document is the exclusive property of Alstom Grid and shall not be transmitted by any means, copied, reproduced or modified without the prior written consent of Alstom Grid Technical Institute. All rights reserved. Equivalent Circuits of Power Transformers
- 2. > Equivalent Circuits of Power Transformers Three Phase Transformers 1. Three single phase units 2. limb core type 4. Shell type 3. 5-limb core type
- 3. > Equivalent Circuits of Power Transformers Winding Polarity
- 4. > Equivalent Circuits of Power Transformers Transformer Equivalent Circuit
- 5. > Equivalent Circuits of Power Transformers
- 6. > Equivalent Circuits of Power Transformers Simplified Equivalent Circuit
- 7. > Equivalent Circuits of Power Transformers Two Winding Transformer (a) (b) (c)
- 8. > Equivalent Circuits of Power Transformers 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:
- 9. > Equivalent Circuits of Power Transformers Dy 1
- 10. > Equivalent Circuits of Power Transformers0 Positive Sequence Current Consider Dy 1 transformer Voltage ratio 1 : 1 Turns ratio : 13
- 11. > Equivalent Circuits of Power Transformers1 ( ) ( ) ( ) 150I 3 1a I 3 I 3 aI I 90I 3 aa I 3 aI 3 Ia I 30I 3 a1 I 3 Ia 3 I I 11 11 C 1 2 1 11 2 B 1 2 1 1 2 1 A ∠= − =−= −∠= − =−= ∠= − =−= 90II 1B −∠= 150II 1C ∠= 30II 1A ∠= 1IIa = 1aIIc = 1 2 IaIb =
- 12. > Equivalent Circuits of Power Transformers2 Negative Sequence Current Consider Dy 1 transformer Voltage ratio 1 : 1 Turns ratio : 13
- 13. > Equivalent Circuits of Power Transformers3 ( ) ( ) ( ) 150I 3 1a I 3 I 3 Ia I 90I 3 aa I 3 Ia 3 aI I 30I 3 a1 I 3 aI 3 I I 2 2 2 22 2 C 2 2 2 2 2 2 B 12 22 A −∠= − =−= ∠= − =−= −∠= − =−= 150II 2C −∠= 30II 2A −∠= 90II 2B ∠= 2IIa = 2aIIb = 2 2 IaIc =
- 14. > Equivalent Circuits of Power Transformers4 Example 210530530II 30530II 2)R(2 1)R(1 ∠=∠−=∠= −∠=−∠=
- 15. > Equivalent Circuits of Power Transformers5 Example continued … pu9066.824051205 IaaII pu9066.812052405 aIIaI 0III :FAt pu90104505905 2105.2401305.1201 IaaII pu90533052105 2105.1201305.2401 aIIaI pu9052105305 III :RAt 2 2 1C 21 2 B 21A )R(2 2 )R(1C )R(2)R(1 2 B )R(2)R(1A ∠=∠−∠= += −∠=∠−∠= += =+= ∠=∠+∠= ∠∠+−∠∠= += −∠=∠+∠= ∠∠+−∠∠= += −∠=∠+−∠= +=
- 16. > Equivalent Circuits of Power Transformers6 Example continued … AMPS8755.87x10I AMPS5.4375.87x5I AMPS5.4375.87x5I :RAt AMPS90931050x66.8I AMPS90931050x66.8I 0I :FAt AMPS87.5kV)(132CurrentBase AMPS1050(11kV)CurrentBase C B A C B A == == == == == = = =
- 17. > Equivalent Circuits of Power Transformers7 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.
- 18. > Equivalent Circuits of Power Transformers8
- 19. > Equivalent Circuits of Power Transformers9 Transformer Zero Sequence Impedance
- 20. > Equivalent Circuits of Power Transformers0 ‘b’ links closed for a delta winding as this forms a trap for I0in earthed star which induces current in delta. I0s in phase ∴ I0circulatesd round the delta and no I0 passes into the line.
- 21. > Equivalent Circuits of Power Transformers1 ‘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 phase is in phase unearthed I0 not possible in line as consistent current distribution in delta not possible
- 22. > Equivalent Circuits of Power Transformers2 General zero sequence equivalent circuit for two winding transformer Primary Secondary terminal terminal On appropriate side of transformer: Earthed star winding - Close link ‘a’ Open link ‘b’ Delta winding - Open link ‘a’ Close link ‘b’
- 23. > Equivalent Circuits of Power Transformers3 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
- 24. > Equivalent Circuits of Power Transformers4
- 25. > Equivalent Circuits of Power Transformers5 Example
- 26. > Equivalent Circuits of Power Transformers6 Example continued … ( ) 0IaIaI AMPS473pu18041.5aIIaI )A5.87I( AMPS473pu041.5III :RAt 30II30II AMPS9843 A1050Ipu375.9IIII pu125.3 32.0 0.1 III )R(2 2 )R(1C )R(2)R(1 2 B b )R(2)R(1A 2)R(21)R(1 b021F 021 =+= =∠=+= = =∠=+= ∠=−∠= = ==++= ==== 132 kV / 11 kV Current Distribution
- 27. > Equivalent Circuits of Power Transformers7 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
- 28. > Equivalent Circuits of Power Transformers8 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
- 29. > Equivalent Circuits of Power Transformers9 Zero Sequence Equivalent Circuits
- 30. > Equivalent Circuits of Power Transformers0 Two Winding Transformer Zero Sequence Network
- 31. > Equivalent Circuits of Power Transformers1 NOTE! “Source” earthing arrangements can affect transformer zero sequence diagram. Eg:
- 32. > Equivalent Circuits of Power Transformers2 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’
- 33. > Equivalent Circuits of Power Transformers3 Star/Delta Transformer Zero sequence impedance Open circuit test: Short circuit test:
- 34. > Equivalent Circuits of Power Transformers4 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
- 35. > Equivalent Circuits of Power Transformers5 Interconnected Star (Zig-Zag) Windings Positive sequence current distribution Zig-zag / Star transformer
- 36. > Equivalent Circuits of Power Transformers6 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 30IT303 3 IT )a1( 3 IT 3 T xIa 3 T xI.T.A 2 2 °∠=°∠= −= −= 30I(a)IThus T(a)I30IT A.T.StarA.T.zag-Zig ∠= =°∠ =
- 37. > Equivalent Circuits of Power Transformers7 Zy 11 Zy 1 Zd 0
- 38. > Equivalent Circuits of Power Transformers8 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
- 39. > Equivalent Circuits of Power Transformers9 Zig-Zag Transformers Zero 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.
- 40. > Equivalent Circuits of Power Transformers0 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:
- 41. > Equivalent Circuits of Power Transformers1 Zig-Zag Earthing Transformers Positive (and negative) sequence impedance is very high. Equivalent circuit: Zero sequence impedance is very low. Equivalent circuit:
- 42. > Equivalent Circuits of Power Transformers2 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
- 43. > Equivalent Circuits of Power Transformers3 Three Winding Transformer Equivalent Circuit
- 44. > Equivalent Circuits of Power Transformers4 Three Winding Transformer For positive (negative) sequence tests Thus, from the short circuit tests, Primary to Secondary Primary to Tertiary Secondary to Tertiary From these equations
- 45. > Equivalent Circuits of Power Transformers5 Three Winding Transformer Zero 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
- 46. > Equivalent Circuits of Power Transformers6 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
- 47. > Equivalent Circuits of Power Transformers7 Positive Sequence Network Negative Sequence Network Zg2 ZT2 ZP2 ZT2 ZS2 F2 N2 LOAD Zg1 ZT1 ZP1 ZT1 ZS1 F1 N1 LOAD
- 48. > Equivalent Circuits of Power Transformers8 Zero Sequence Network Zg0 a ZT0 a 3Zn1 3Zn2 a ZP0 ZT0 a 3Zn b b b b a b 3Zn3 F0 N0
- 49. > Equivalent Circuits of Power Transformers9 Auto Transformers Has a single winding per phase, part of which is common to both primary and secondary A B C series-common winding series winding common winding HV SIDE LV SIDE
- 50. > Equivalent Circuits of Power Transformers0 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
- 51. > Equivalent Circuits of Power Transformers1 Auto Transformers Zero Sequence Impedance Similar to 2/3 winding transformers Eg. For autotransformer with earthed neutral and delta winding
- 52. > Equivalent Circuits of Power Transformers2
- 53. > Equivalent Circuits of Power Transformers3 Auto Transformers ZN is common to both HV and LV system Zero sequence network: Where n = HV voltage ratio LV If PU → ZN referred to LV base quantities If ZN in ohms → ZH, ZL & ZT must be referred to LV network
- 54. > Equivalent Circuits of Power Transformers4 Positive Sequence Network Negative Sequence Network Zg1 ZT1 ZL1 ZT1 ZH1 F1 N1 LOAD E1 Zg2 ZT2 ZL2 ZT2 ZH2 F2 N2 LOAD
- 55. > Equivalent Circuits of Power Transformers5 Zero Sequence Network 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 ( ) 2 n 1n −− 3Zn2
- 56. > Equivalent Circuits of Power Transformers6 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%

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