---
title: "Percentage differential relay: 150 MVA transformer"
subject: "Switchgear and Protection"
chapter: 7
key: "semester_6/switchgear_and_protection:percentage-differential-150mva"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/percentage-differential-150mva
site: BCT Engineering
---

# Percentage differential relay: 150 MVA transformer

Switchgear and Protection · Chapter 7: Protective Relays

- Asked in: 2080 Chaitra, 6 marks
- Video: [percentage differential relay | in hindi | percentage differential protection of transformer](https://www.youtube.com/watch?v=faMk98Gaptw) — Mind of Engineer 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/percentage-differential-150mva
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-7

## Question

A 220/110 kV - 150 MVA transformer is protected by percentage differential relay. The HV and LV sides are delta and star connected respectively. The CT ratio of delta side is 400/5 and the ratio of star side is 1600/5. Determine (i) The CT secondary currents at full load, (ii) The relay current at full load, (iii) The relay current setting for 90% loading.

## Short answer

CT secondary currents: HV 4.92 A, LV line output 4.26 A (phase 2.46 A). Relay current at full load is 0.659 A. At 90% loading, relay current is 0.593 A; setting must exceed this.

## Answer

HV is delta connected, so its CTs are connected in **star**; LV is star connected, so its CTs are connected in **delta**. The relay current is the difference between the CT output line currents caused by the CT ratio mismatch.

**Data:** 150 MVA, 220/110 kV; HV (delta) CTs 400/5 (ratio 80); LV (star) CTs 1600/5 (ratio 320).

#### (i) CT secondary currents at full load
```text
I_HV = 150 × 10⁶ / (√3 × 220 × 10³) = 393.65 A
I_LV = 150 × 10⁶ / (√3 × 110 × 10³) = 787.30 A

HV CTs (star): secondary = 393.65 / 80 = 4.921 A
LV CTs (delta): secondary (phase) = 787.30 / 320 = 2.460 A
                output line current = √3 × 2.460 = 4.261 A
```

#### (ii) Relay current at full load
```text
I_relay = 4.921 − 4.261 = 0.659 A
```

#### (iii) Relay current setting for 90% loading
At 90% load all currents scale by 0.9:
```text
I_relay = 0.9 × 0.659 = 0.593 A
```
The relay setting must therefore be above **0.593 A** so that it does not operate at this loading (in practice a percentage bias is used to cover this mismatch).

**Answer:** (i) HV CT secondary **4.92 A**, LV CT secondary **2.46 A** (line output 4.26 A); (ii) relay current **0.659 A**; (iii) **0.593 A** at 90% load, so the setting must exceed this value.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The HV full-load current of a 150 MVA, 220 kV transformer is:
   A. 393.65 A
   B. 787.30 A
   C. 681.8 A
   D. 227.3 A
   Answer: A. I = 150e6/(sqrt(3) × 220e3) = 393.65 A. (Key point: Full-load HV current)

2. LV CTs (delta, 1600/5) have a phase secondary of 2.460 A. Their line output is:
   A. 2.460 A
   B. 1.420 A
   C. 4.261 A
   D. 4.921 A
   Answer: C. Delta line current = sqrt(3) × 2.460 = 4.261 A. (Key point: LV CT line output)

3. Relay current at full load is:
   A. 9.18 A
   B. 0.659 A
   C. 2.46 A
   D. 0 A
   Answer: B. 4.921 − 4.261 = 0.659 A due to CT ratio mismatch. (Key point: Relay current)

4. At 90% loading the relay current is:
   A. 0.659 A
   B. 0.593 A
   C. 0.732 A
   D. 0.066 A
   Answer: B. All currents scale by 0.9, so spill = 0.9 × 0.659 = 0.593 A; the setting must exceed this. (Key point: Setting at 90% load)

## Related in Switchgear and Protection

- [Percentage differential relay: 125 MVA transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apercentage-differential-125mva) — Switchgear and Protection, chapter 7
- [CT ratio for 33/6.6 kV star/delta (400/5)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Adifferential-ct-33-6-6kv-400) — Switchgear and Protection, chapter 7
- [CT ratio for 33/6.6 kV star/delta (300:5)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Adifferential-ct-33-6-6kv-300) — Switchgear and Protection, chapter 7
- [CT ratio and connection for 11/132 kV](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Adifferential-ct-11-132kv) — Switchgear and Protection, chapter 7
- [Differential protection: 11 kV, 100 MVA generator](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Agenerator-differential-11kv-6-ohm) — Switchgear and Protection, chapter 7
- [Percentage bias in differential relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apercentage-bias-differential) — Switchgear and Protection, chapter 7

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