---
title: "Sumpner's (back-to-back) test principle"
subject: "Electrical Machines I"
chapter: 2
key: "semester_4/electrical_machines_i:sumpner-test-two-identical"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/sumpner-test-two-identical
site: BCT Engineering
---

# Sumpner's (back-to-back) test principle

Electrical Machines I · Chapter 2: Transformer

- Asked in: 2082 Kartik (new course), 3+3 marks
- Video: [back to back test of transformer in hindi | sumpner's test of transformer | regenerative test](https://www.youtube.com/watch?v=l-UrV82raoM) — Mind of Engineer 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/sumpner-test-two-identical
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2

## Question

Explain the principle of Sumpner's test. Why is it necessary to use two identical transformers in Sumpner's test?

## Short answer

Sumpner's test connects two identical transformers back-to-back: primaries in parallel, secondaries in series opposition. Only losses are drawn from supply; wattmeters read total core and full-load copper losses. Two identical units are required to ensure equal secondary emfs cancel exactly and losses divide equally.

## Answer

**Sumpner's test (back-to-back test)** is a method of loading two identical transformers at full load to measure their temperature rise and efficiency, while drawing from the supply only the power needed for their losses.

#### Principle and connection

```text
 V1 supply        T1             T2
 o--[W1]--[A]--+--]  [--+-----+--]  [--+
               |  ]  [  |     |  ]  [  |
 o-------------+--]  [--+     |  ]  [  |
  primaries in          |  [W2][A2]    |
  parallel              |     |        |
                        +----(Vr)------+
         secondaries in series opposition,
         fed by low-voltage regulating supply
```

1. **Primaries in parallel** on rated voltage and frequency. Wattmeter $W_1$ reads the input on this side.
2. **Secondaries in series opposition.** With correct opposition, their emfs cancel round the secondary loop, so the voltmeter across the open point reads zero (no current flows). This is the "open-circuit" condition, and $W_1$ reads the **core loss of both transformers** ($2P_i$).
3. A small **auxiliary (regulating) voltage** $V_r$ is injected into the secondary loop and adjusted until **rated current** flows in the secondaries. Because the loop impedance is only the two leakage impedances, a small voltage (about 2× the SC voltage) is enough. Wattmeter $W_2$ reads the **full-load copper loss of both transformers** ($2P_{cu}$). The primaries carry the matching load current, which circulates between the two units.
4. Both units are now at rated voltage and rated current simultaneously, i.e. working at full load, but the supply provides only the losses.

$$
\eta_{each} = \frac{\text{output}}{\text{output} + \dfrac{W_1 + W_2}{2}}
$$

Running for several hours gives the **temperature rise (heat run)**.

#### Why two identical transformers are needed

- The test relies on the two secondary emfs being **equal and opposite**, so that no current flows in the loop without the injected voltage. Unequal ratios would cause an uncontrolled circulating current.
- Losses must divide **equally** between the two units, so that each gets half of $W_1$ and $W_2$; with different units the share could not be found.
- Each unit must be loaded to **its own rated current** at the same time; with the same current in series secondaries this is possible only if the ratings are equal.

Advantage: a large transformer can be heat-run at full load without a large load bank and with very small energy use.

## Check yourself

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

1. What is Sumpner's test used for?
   A. Measuring only the turns ratio
   B. Finding polarity of one transformer
   C. Testing a single transformer at no load only
   D. Full-load temperature rise and efficiency of two identical transformers drawing only loss power
   Answer: D. The supply meets only the losses, not the full-load power. (Key point: Purpose)

2. How are the transformers connected?
   A. Primaries in series; secondaries in parallel
   B. Primaries in parallel; secondaries in series opposition
   C. Both primaries and secondaries in series aiding
   D. Primaries in parallel; secondaries in series aiding
   Answer: B. Opposing emfs cancel, giving effectively open-circuit at rated voltage. (Key point: Connections)

3. What do W1 and W2 read?
   A. W1: copper loss; W2: core loss
   B. W1: output; W2: input
   C. W1: core loss of both (2Pi); W2: full-load copper loss of both (2Pcu)
   D. Both read core loss
   Answer: C. W1 is on the supply side at rated voltage; W2 is on the injected voltage supply at rated current. (Key point: Wattmeter readings)

4. Why are identical transformers needed?
   A. So that the test uses less energy only
   B. So that frequency matches
   C. So the injected voltage is not needed
   D. So emfs cancel, losses divide equally, and both carry rated current together
   Answer: D. Unequal units would give circulating current and unknown loss division. (Key point: Need for identical units)

## Related in Electrical Machines I

- [LV voltage of Δ–Y bank of 100 kVA transformers](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Adelta-star-bank-100kva-lv-voltage) — Electrical Machines I, chapter 2
- [Load sharing of 50 kVA and 25 kVA transformers in parallel](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aparallel-50kva-25kva-60kva-load) — Electrical Machines I, chapter 2
- [Conditions for parallel operation of transformers](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atransformer-parallel-conditions-reasons) — Electrical Machines I, chapter 2

## Related in other subjects

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- [Load sharing of two transformers in parallel](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aparallel-transformers-load-sharing) — Electrical Machines, chapter 2
- [Back-face test with given normals](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aback-face-normals-frontface) — Computer Graphics, chapter 7
- [Comparing two 750 kVA transformers](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Atransformer-purchase-comparison) — Industrial Power Distribution and Illumination, chapter 10