--- title: "Transformer vector groups and fault current" subject: "Power System Analysis II" chapter: 5 key: "semester_5/power_system_analysis_ii:transformer-vector-group-fault-current" source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/transformer-vector-group-fault-current site: BCT Engineering --- # Transformer vector groups and fault current Power System Analysis II · Chapter 5: Unsymmetrical Faults on Power Systems - Asked in: 2071 Chaitra, 5 marks - Video: [H2 Power System: Transformer Vector Groups](https://www.youtube.com/watch?v=sM5x5fMHSMI) — iMooX at - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/transformer-vector-group-fault-current - Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-5 ## Question How do the different vector groups of transformer affect the fault current in the power system network? ## Short answer Transformer vector groups determine the zero-sequence path. A Yg-Δ provides a low-impedance earth path on the grounded side but blocks zero-sequence on the delta side. Unearthed windings or Δ-Δ arrangements block zero-sequence current, drastically reducing L-G fault current. Positive/negative impedance magnitudes are unchanged, so L-L fault currents remain unaffected. Neutral earthing impedance adds 3Zn and further limits earth faults. ## Answer The **vector group** of a transformer (Yy, Yd, Dy, Dd, with the neutral earthed or not) decides how the zero-sequence current can flow through it and what phase shift it gives. This changes the zero-sequence network and therefore the earth-fault current. The positive and negative sequence impedances are the same for all groups. #### Effect on sequence networks - **Positive and negative sequence:** every group behaves as a series leakage reactance $X_T$. Only a phase shift of $\pm 30^\circ$ appears in Dy/Yd units (positive sequence shifted one way, negative the other). The magnitudes of balanced and L-L fault currents are not changed. - **Zero sequence:** zero-sequence currents are in phase in all three lines, so they need a return path through an earthed neutral or a circulating path inside a delta. | Vector group | Zero-sequence equivalent | Effect on earth fault current | |---|---|---| | Yg–Yg (both neutrals earthed) | Series $Z_0$ between both sides | Zero-seq current passes through; fault fed from both sides | | Yg–Δ | Yg side connected to reference through $Z_0$; Δ side open | Acts as an earthing source on the Yg side; blocks zero seq to the Δ side | | Y–Δ (Y not earthed) | Open on both sides | No zero-seq path; no earth fault current through it | | Yg–Y (one neutral isolated) | Open circuit | Blocks zero-seq current | | Δ–Δ | Open on both sides | No earth fault current through it | | Neutral earthed through $Z_n$ | $3Z_n$ in series in zero-seq path | Earth fault current reduced | #### How it affects fault current 1. **L-G fault current** $I_f = \dfrac{3E}{Z_1+Z_2+Z_0+3Z_f}$ depends strongly on $Z_0$. A Δ-winding or an unearthed star makes $Z_0$ seen from that side very large (open), so the L-G fault current falls sharply; for an isolated system it becomes almost zero. 2. A **Δ/Yg** transformer feeding a fault on its star side provides a low-impedance zero-sequence path, so the L-G current can even exceed the three-phase fault current when $Z_0 < Z_1$. 3. **Yg–Yg** units let the zero-sequence current pass to the other side, so earth faults are fed from both sides and are seen by relays on both sides. 4. **Neutral impedance** $Z_n$ appears as $3Z_n$ and is used deliberately to limit earth fault current. 5. **Phase shift** of Dy/Yd units shifts the positive and negative sequence currents by $\pm30^\circ$. The current magnitudes on the other side are the same, but the phase currents are distributed differently, e.g. an L-G fault on the star side of a Dy transformer appears as current in two lines on the delta side. 6. **L-L faults** have no zero-sequence component, so the vector group does not change their magnitude. #### Example For a generator connected through a Δ/Yg step-up transformer, an L-G fault on the HV side is fed only through the transformer's own $Z_0$ (the generator's zero sequence is isolated by the delta). An L-G fault on the delta side gives almost no fault current if neither the generator nor the delta side has an earthed neutral. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which sequence quantity does the transformer vector group mainly change? A. The positive sequence series reactance B. The zero sequence path and impedance C. The negative sequence reactance magnitude D. None; it only affects the voltage ratio Answer: B. Positive and negative sequence behave as series leakage reactance for all groups; zero sequence flow depends on grounding and delta windings. (Key point: Sequences affected by vector group) 2. How does a Yg-delta transformer appear in the zero sequence network? A. Open on both sides B. Series Z0 passing current to the delta side C. Yg side connected to reference through Z0, delta side open D. Delta side connected to reference, Yg side open Answer: C. The delta circulates zero sequence current, which gives a path to ground on the Yg side but blocks flow to the delta side. (Key point: Delta winding and zero sequence) 3. What happens to the L-G fault current if the zero sequence impedance seen from the fault becomes very large (unearthed star or delta)? A. It falls sharply, nearly to zero for an isolated system B. It rises sharply C. It is unchanged D. It becomes equal to the three-phase current Answer: A. If = 3E/(Z1 + Z2 + Z0 + 3Zf), so a huge Z0 makes If tiny. (Key point: Effect on L-G fault current) 4. How does a neutral impedance Zn enter the zero sequence network? A. As Zn in series B. As Zn/3 in series C. As 3Zn in series D. As Zn in parallel Answer: C. The neutral carries 3I0, so Zn appears as 3Zn and is used to limit earth fault current. 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