Electrical Power Systems Technology

52 Electrical Power Systems Technology

is the power factor of a circuit; therefore, the power factor is equal to the co-
sine of the phase angle (pf = cosine θ).
Right triangle relationships can also be expressed as equations that
determine the value of any of the sides of the power triangle when the
other two values are known. These expressions are as follows:

W = VA^2 – var^2

VA = W^2 – var^2

var = VA^2 – W^2

Sample Problem:
Given: total reactive power = 54 var, applied; voltage = 120 volts;
current = 0.5 amperes.
Find: true power of the circuit.
Solution:

W = VA^2 – var^2

120 x 0.5^2 – 54^2

3600 – 2916

26.15 watts

Appendix B should be reviewed in order to gain a better understand-
ing of the use of right triangles and trigonometric ratios for solving AC cir-
cuit problems.

POWER RELATIONSHIPS IN THREE-PHASE AC CIRCUITS

To illustrate the basic concepts of three-phase power systems, we
will use the example of a three-phase AC generator. This type of genera-
tor will be discussed in more detail in Chapter 6. A simplified pictorial
diagram of a three-phase generator is shown in Figure 2-20. A three-phase