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A 66.7 MVA transformer has an efficiency of 99.3 percent when it delivers full power to a load with a power factor of 100 percent.

(1) Calculate the losses in the transformer under these conditions.

Answer :

The losses in a 66.7 MVA transformer with an efficiency of 99.3% at full power and a power factor of 100% are calculated to be 470 kW.

To calculate the losses in the transformer under these conditions, one must first understand what the efficiency percentage represents. The efficiency of a transformer is the ratio of the output power to the input power. Here, if the transformer efficiency is 99.3%, it means that 99.3% of the input power is being converted to output power, and the rest is lost as heat or other forms of energy loss.

Since the provided transformer has a maximum apparent power (also known as Volt-Amperes, VA) of 66.7 MVA (Mega Volt Amperes) and the power factor is 100%, the real power delivered at full load is also 66.7 MW (Mega Watts). Given that the efficiency is 99.3%, the output power is 99.3% of the input power.

To find the input power, one uses the formula:
Input Power = Output Power / Efficiency. To find the losses:
Losses = Input Power - Output Power. Plugging in the numbers:
Input Power = 66.7 MW / 0.993 and then calculating the losses from these figures.

Here's the calculation:

  1. Input Power = 66.7 MW / 0.993 = 67.170 MW
  2. Losses = 67.170 MW - 66.7 MW
  3. Losses = 0.470 MW or 470 kW

Therefore, the losses in the transformer when it is operating at full power with a power factor of 100% and an efficiency of 99.3% are 470 kW.

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