Page 96 - Electric Machinery Fundamentals

72 ELECTRIC MACHINERY FUNDAMENTALS

IL
+
I
V
V L L
ZL ZL =
IL
I
(a)
Ip Is
+
+
I. • I
Vp
I I
Z'L = Vp ( ZL (
Ip "

(b)
FIGURE 2- 5
(a) Definition of impedance. (b) Impedance scaling through a transformer.

The same relationship applies to reactive power Q and apparent power S:

I Qin = Vplp sin () = Vs1s sin e = Qout I (2-10)

and I Sin - Vplp = \I.<;ls = SOUl I (2-11)

Impedance Transformation through a Transformer
The impedance of a device or an element is defined as the ratio of the phasor volt-
age across it to the phasor cutTent flowing through it:
V
Z= - L (2-12)
L I L
One of the interesting properties of a transformer is that, since it changes voltage
and cunent levels, it changes the ratio between voltage and current and hence the
apparent impedance of an element. To understand this idea, refer to Figure 2- 5. If
the secondary current is called Is and the secondary voltage V , then the imped-
s
ance of the load is given by
(2-13)