Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 24

A magnetic circuit may be defined as the 'complete closed path followed by any
group of magnetic flux lines' (Hughes, 2005).
Total magnetic flux F through an area may be obtained from the flux density
normal to it. In many cases of practical interest the flux density is indeed normal to
the area of interest. If, in addition, the flux density is uniform over the area, the total
flux is given simply by

F ¼ Ba ð 2 : 8 Þ

where a is the area.
We are particularly interested here in magnetic circuits containing ferro-
magnetic materials. It was noted above (2.3) that these materials are characterised
by high values of relative permeability m r . The behaviour of these materials is
described by the linear relationship of (2.3) for flux densities up to around 1 T.
They are then subject to saturation, which effectively reduces the relative perme-
ability as flux density increases further.
Consider the effect of applying a magnetic field of strength H to part of a mag-
netic circuit of length l . It is assumed that the flux density B is uniform and normal to a
constant cross-sectional area a . From (2.5) the m.m.f. will be simply
F ¼ Hl
From (2.3) and (2.8) we have

Bl
m r m 0 ¼

l
m r m 0 a F ¼ S F

F ¼ ð 2 : 9 Þ

The quantity S is known as reluctance. It can be determined easily for the
various sections of a magnetic circuit. Equation (2.9) has the same form as the
familiar expression of Ohm's Law: V ¼ RI . A magnetic circuit may therefore be
analysed using electric circuit methods, with the following equivalences:

Electric circuits Magnetic circuits

voltage V m.m.f. F

current I flux F

resistance R reluctance S

2.2.3 Electromagnetic induction
The key to electric power generation was Faraday's discovery of electromagnetic
induction in 1831. Faraday's Law is usually expressed in terms of the electromotive
force (e.m.f.) e induced in a coil of N turns linked by a flux f . Setting flux linkage
l ¼ N F we have

d l

d t ¼ N d

d t

e ¼ ð 2 : 10 Þ

This equation encapsulates the key idea that it is the change of flux which
creates the e.m.f., rather than flux per se as Faraday had expected. The polarity of