Electrical Power Systems Technology

Power System Fundamentals 51

opposite side

sine θ = ——————

hypotenuse

Since this is true, the phase angle can be expressed as:

reactive power (var)

sine θ = —————————

apparent power (VA)

Therefore,

var = VA × sine θ.

We can determine either the phase angle or the var value by using

trigonometric functions. We also know that the cosine of an angle of a

right triangle is expressed as:

adjacent side

sine θ = ——————

hypotenuse

Thus, in terms of the power triangle:

true power (W)

sine θ = —————————

apparent power (VA)

Therefore, true power can be expressed as:

W = VA × cosine θ.

Sample Problem:

Given: a circuit has the following values: applied voltage = 240, cur-

rent = 12 amperes, power factor = 0.83.

Find: true power of the circuit.

Solution:

W = VA × cosine θ

= 240 V × 12 A × 0.83

W = 2390 watts

Note that the expression

true power

———————

apparent power