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

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

 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.