Transformer Power Losses

Electricity and Magnetism Level 3

A transformer has two basic types of power losses (heat dissipation): core losses and copper (winding) losses.

The core losses are essentially fixed, as long as the transformer is energized. The copper losses are proportional to the square of the load current flowing through the transformer.

When the transformer is energized but un-loaded, the total power losses are $P$
With 50% of rated load current, the total power losses are $3P$
With 100% of rated load current, the total power losses are $\alpha P$

What is the value of $\alpha$ ?

The answer is 9.

1 solution

Steven Chase
Sep 30, 2017

Power loss equation:

$P_{loss} = P_{core} + \beta I_{load}^2$

At no-load:

$P_{NL} = P_{core} + \beta 0^2 = P_{core} = P \\ P_{core} = P$

50% Load:

$P_{50} = P_{core} + \beta (\frac{1}{2} I_{FL})^2 = 3P \\ P + \frac{1}{4} \beta I_{FL}^2 = 3P \\ \beta I_{FL}^2 = 8P$

100% Load:

$P_{100} = P_{core} + \beta (I_{FL})^2 = P + 8P = \boxed{9P}$

Transformer Power Losses

The answer is 9.

1 solution

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