Page 74 - Electric Machinery Fundamentals

5U ELECTRIC MACH1NERY FUNDAMENTALS

S = VI (1- 62)

The units of apparent power are volt-amperes (VA), where I VA = 1 V X I A. As
with reactive power, apparent power is given a distinctive set of units to avoid
confusing it with real and reactive power.

Alternative Forms of the Power Equations

If a load has a constant impedance, then Ohm's law caD be used to derive alterna-
tive expressions for the real, reactive, and apparent powers supplied to the load.
Since the magnitude of the voltage across the load is given by
V= [Z (1-63)
substituting Equation (1-63) into Equations (1- 60) to (1- 62) produces equations
for real, reactive, and apparent power expressed in terms of current and impedance:
p = / 2ZCOS e (1-64)
Q = / 2Z sin e (1-65)

S = / 'Z (1- 66)
where Izi s the magnitude of the load impedance Z.
i
Since the impedance of the load Z can be expressed as
Z = R + jX = IZI cos e + jlZI in e
s
we see from this equation that R = IZI cos e and X = Izi sin e, so the real and
reactive powers of a load can also be expressed as

P = [' R (1- 67)
Q = [ 2X (1-68)
where R is the resistance and X is the reactance of load Z.

Complex Power
For simplicity in computer calculations, real and reactive power are sometimes
represented together as a complex power S, where

s = P + j Q (1-69)
The complex power S supplied to a load can be calculated from the equation
S = VI' (1-70)

where the asterisk represents the complex conjugate operator.
To understand this equation, let's suppose that the voltage applied to a load
is V = V L IX and the current through the load is I = / L [3. Then the complex
power supplied to the load is