Page 93 - Electric Machinery Fundamentals

TRANSFORMERS 69

which steps the voltage down from transmission levels to distribution levels (from
2.3 to 34.5 kV), is called a substation transformer. Finally, the transformer that
takes the distribution voltage and steps it down to the final voltage at which the
power is actually used (110, 208, 220 V, etc.) is called a distribution transformer.
All these devices are essentially the same- the only difference among them is
their intended use.
In addition to the various power transformers, two special-purpose trans-
fOlTIlerS are used to measure voltage and current in electric machinery and power
systems. The first of these special transformers is a device specially designed to
sample a high voltage and produce a low secondary voltage directly proportional
to it. Such a transformer is called a potential transformel: A power transformer
also produces a secondary voltage directly proportional to its primary voltage; the
difference between a potential transformer and a power transformer is that the
potential transformer is designed to handle only a very small current. The second
( type of special transformer is a device designed to provide a secondary current
much smaller than but directly proportional to its primary current. This device is
called a current transformer. Both special-purpose transformers are discussed in a
later section of this chapter.

2,3 THE IDEAL TRANSFORMER
An ideal transformer is a lossless device with an input winding and an output
winding. The relationships between the input voltage and the output voltage, and
between the input current and the output current, are given by two simple equa-
tions. Figure 2-4 shows an ideal transformer.
The transformer shown in Figure 2-4 has N p turns of wire on its primary
side and Ns turns of wire on its secondary side. The relationship between the volt-
age vp(t) applied to the primary side of the transformer and the voltage vs(t) pro-
duced on the secondary side is

(2-1)

where a is defined to be the turns ratio of the transformer:
N
a = ::....e. (2-2)
Ns
The relationship between the current ip(t) flowing into the primary side of the
transformer and the current isCt) flowing out of the secondary side of the trans-
former is
(2-3a)

or (2-3b)

l