--- title: "Three-phase transformer connections" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:three-phase-transformer-connections" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/three-phase-transformer-connections site: BCT Engineering --- # Three-phase transformer connections Electrical Machines I · Chapter 2: Transformer - Asked in: 2075 Baisakh, 5+3 marks - Video: [3-phase Transformer Connections | Star-to-Star, Delta-to-Delta, Star-to-Delta & Delta-to-Star](https://www.youtube.com/watch?v=CUpoOHMlMdY) — Electrical Deck - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/three-phase-transformer-connections - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2 ## Question Explain the different three phase transformer connections with neat sketch. Write their application also. ## Short answer Common connections are star-star (Y-y) for small HV units with tertiary, delta-delta (D-d) for large LV high-current loads, star-delta (Y-d) for step-down at substations, and delta-star (D-y) for distribution. Star gives a neutral; delta suppresses third harmonics. Phase shift is 0° for Y-y and D-d, 30° for Y-d and D-y. ## Answer A three-phase transformer (or bank of three single-phase units) can have its primary and secondary windings connected in **star (Y)** or **delta (Δ)**, giving four common connections. Let $K$ = turns ratio per phase ($N_2/N_1$) and $V_L$, $I_L$ = primary line voltage and current. In the sketches, S is one phase winding. #### 1. Star-Star (Y-y) ```text Primary (Y) Secondary (y) A B C a b c | | | | | | S S S S S S \ | / \ | / \ | / \ | / N n ``` - Phase voltage = $V_L/\sqrt3$, so less insulation is needed; a neutral is available on both sides. - Secondary line voltage = $KV_L$, with no phase shift (0°). - Problems: third-harmonic voltages in the phase voltages, and neutral shifting with unbalanced loads, unless the primary neutral is earthed or a tertiary delta winding is added. - **Use:** small high-voltage transformers, and interconnecting systems where both neutrals are needed (with a tertiary winding). #### 2. Delta-Delta (D-d) ```text Primary (D) Secondary (d) A ----+ a ----+ / \ / \ S S S S / \ / \ B +---S---+ C b +---S---+ c ``` - Line voltage = phase voltage; winding current = $I_L/\sqrt3$. - No third-harmonic problem (the third-harmonic current circulates inside the delta), and it handles unbalanced loads well. - If one unit fails, the remaining two can work in **open delta (V-V)** at 57.7% of the bank rating. - No neutral is available. **Use:** large low-voltage, high-current systems and industrial supply. #### 3. Star-Delta (Y-d) ```text Primary (Y) Secondary (d) A B C a ----+ | | | / \ S S S S S \ | / / \ \ | / b +---S---+ c N ``` - Primary star, secondary delta. Secondary line voltage = $\frac{KV_L}{\sqrt3}$, with a 30° phase shift. - The delta secondary suppresses third harmonics; the primary neutral can be earthed. - **Use:** step-down transformers at the **receiving end** of transmission lines (substations). #### 4. Delta-Star (D-y) ```text Primary (D) Secondary (y) A ----+ a b c / \ | | | S S S S S / \ \ | / B +---S---+ C \ | / n (neutral brought out) ``` - Primary delta, secondary star. Secondary line voltage = $\sqrt3 KV_L$, with a 30° phase shift. - The star secondary gives a neutral for a 3-phase, 4-wire supply. - **Use:** **distribution transformers** (e.g. 11 kV/400 V in Nepal) and step-up transformers at the **generating station**. #### Summary | Connection | Sec. line voltage | Phase shift | Main application | |---|---|---|---| | Y-y | $KV_L$ | 0° | Small HV units, with tertiary | | D-d | $KV_L$ | 0° | Large LV, high-current loads | | Y-d | $KV_L/\sqrt3$ | 30° | Step-down at substation | | D-y | $\sqrt3KV_L$ | 30° | Distribution, step-up at plant | Other connections: **open delta (V-V)** for emergencies or growing loads, and the **Scott (T-T)** connection for 3-phase to 2-phase conversion. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For a star-delta (Y-d) transformer with turns ratio K per phase, the secondary line voltage is: A. K V_L B. sqrt(3) K V_L C. K V_L / sqrt(3) D. K V_L / 3 Answer: C. Primary phase voltage is V_L/sqrt3 and the delta secondary line voltage equals its phase voltage, so V2 = K V_L/sqrt3. (Key point: Y-d secondary voltage) 2. Which connection is used for distribution transformers (e.g. 11 kV/400 V) because it gives a neutral for 3-phase 4-wire supply? A. Star-star B. Delta-delta C. Star-delta D. Delta-star Answer: D. Delta-star has a star secondary giving a neutral, with a delta primary that suppresses third harmonics. (Key point: Delta-star use) 3. If one unit of a delta-delta bank fails, the other two can still supply load in open delta (V-V) at what fraction of the bank rating? A. 57.7% B. 86.6% C. 66.7% D. 50% Answer: A. Open delta can deliver 57.7% (1/sqrt3) of the original bank rating. (Key point: Open delta) 4. What is the main problem of a star-star connection with unbalanced load or without a tertiary delta? A. Large phase shift of 30 degrees B. Third-harmonic voltages and neutral shifting C. Very high insulation requirement D. No neutral is available Answer: B. Third-harmonic voltages and shifting of the neutral occur unless the neutral is earthed or a tertiary delta is added. 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