0195136047.pdf

480 MAGNETIC CIRCUITS AND TRANSFORMERS

Transformers may be classified by their frequency range: power transformers, which usually

operate at a fixed frequency; audio and ultrahigh-frequency transformers; wide-band and narrow-

band frequency transformers; and pulse transformers. Transformers employed in supplying power

to electronic systems are generally known as power transformers. In power-system applications,

however, the termpower transformerdenotes transformers used to transmit power in ratings

larger than those associated with distribution transformers, usually more than 500 kVA at voltage

levels of 67 kV and above.

Conventional transformers have two windings, but others (known asautotransformers) have

only one winding, and still others (known asmultiwinding transformers) have more than two

windings. Transformers used in polyphase circuits are known aspolyphase transformers.Inthe

most popular three-phase system, the most common connections are the wye (star or Y) and the

delta (mesh or ) connections.

Figure 11.3.1 shows, schematically, a transformer having two windings withN 1 andN 2 turns,

respectively, on a common magnetic circuit. The transformer is said to beidealwhen:

• Its core is infinitely permeable.


• Its core is lossless.


• It has no leakage fluxes.


• Its windings have no losses.
  The mutual flux linking theN 1 -turn andN 2 -turn windings isφ. Due to a finite rate of change
  ofφ, according to Faraday’s law of induction, emf’se 1 ande 2 are induced in the primary and
  secondary windings, respectively. Thus, we have

e 1 =N 1

dφ

dt

; e 2 =N 2

dφ

dt

;

e 1

e 2

=

N 1

N 2

(11.3.1)

The polarity of the induced voltage is such as to produce a current which opposes the flux change,

according to Lenz’s law. For the ideal transformer, sincee 1 =v 1 ande 2 =v 2 , it follows that

v 1

v 2

=

e 1

e 2

=

N 1

N 2

=a;

V 1

V 2

=

E 1

E 2

=

N 1

N 2

=a (11.3.2)

whereV 1 ,V 2 ,E 1 , andE 2 are the rms values ofv 1 ,v 2 ,e 1 , ande 2 , respectively, andastands for the

turns ratio.When a passive external load circuit is connected to the secondary winding terminals,

the terminal voltagev 2 will cause a currenti 2 to flow, as shown in Figure 11.3.1. Further, we have

v 1 i 1 =v 2 i 2 ;

i 1

i 2

=

v 2

v 1

=

N 2

N 1

=

1

a

;

I 1

I 2

=

V 2

V 1

=

N 2

N 1

=

1

a

(11.3.3)

−

+

v 1 e 1 e 2 v 2

Mean path of magnetic flux

−

+

−

+

i 1 i 2

Secondary

(N 2 turns)

Primary

(N 1 turns)

Ferromagnetic core

Load

ZL

−

+

Mutual flux φ

Figure 11.3.1Schematic of two-winding transformer.