Is the 10 kVA Transformer Overloaded?
A small eatery has a 10 kVA, 2300/230 V single-phase transformer. The open-circuit test on the LV side gives 230 V, 1.2 A, and 90 W. The short-circuit test on the HV side gives 60 V, 4.35 A, and 120 W. The connected load is 6 kW at 0.70 power factor lagging. After three hours the transformer case is hot to touch, and the owner wants to buy a 15 kVA replacement. The electrician measures the load current and finds it is consistent with 6 kW at 0.70 power factor. The transformer is indoors, with a cardboard box stored against its ventilation slots. The owner asks whether the transformer is overloaded, what its efficiency is at the measured load, and whether the replacement is justified. The electrician must also state what additional checks should be made before condemning the transformer.
1. Calculate the load kVA, the load fraction of the transformer rating, and the copper loss at the measured load.
Read the worked answer
The load apparent power is S = P/pf = 6/0.70 = 8.57 kVA. The transformer rating is 10 kVA, so the load fraction is 8.57/10 = 0.857, or 85.7%. The rated HV current is 10,000/2300 = 4.35 A, which matches the short-circuit test current. At the measured load the HV current is 8571/2300 = 3.73 A. Copper loss varies with the square of the load current, so P_cu = 120 × (0.857)² = 88 W. The core loss remains approximately 90 W. The transformer is not overloaded at this load, although it is close to its most efficient loading.
2. Calculate the efficiency at the measured load and at full load at 0.70 power factor. At what load fraction does maximum efficiency occur?
Read the worked answer
At the measured load, output is 6000 W and losses are 90 W core plus 88 W copper = 178 W. Input = 6178 W, so efficiency = 6000/6178 × 100 = 97.1%. At full load at 0.70 power factor, output is 7000 W, copper loss is 120 W, and total loss is 210 W. Input = 7210 W, so efficiency = 7000/7210 × 100 = 97.1%. Maximum efficiency occurs when copper loss equals core loss: load fraction x = √(90/120) = 0.866. That is 8.66 kVA, very close to the present 8.57 kVA. The transformer is therefore operating near its best efficiency, not in a dangerous overload.
3. Advise the owner on whether to buy the 15 kVA transformer and list the checks that should be made first.
Read the worked answer
A 15 kVA replacement is not justified by the measured load alone. The transformer is at 85.7% of rating, and its calculated efficiency is normal. The hot case may be caused by the cardboard box blocking ventilation, a high ambient temperature, poor terminal connections, or a high supply voltage. First remove the obstruction and clean the ventilation slots. Measure the ambient temperature and the case temperature with an infrared thermometer, and check the terminal screws for tightness and discoloration. Measure the load voltage and current, and check for harmonic-producing equipment. An insulation-resistance test and a winding-resistance check would help if the transformer is suspected of internal damage. Only if the load grows beyond about 10 kVA, or if the temperature remains excessive after ventilation and connection checks, should a larger transformer be considered.