Environmental Engineering Reference
the induced e.m.f. is governed by Lenz's Law, which states that 'the direction of an
induced e.m.f. is such as to tend to set up a current opposing the motion or the
change of flux responsible for inducing that e.m.f.' (Hughes, 2005).
It is useful for power system analysis to recast (2.10) in terms of coil voltage
drop v and coil current i . From (2.5) and (2.9)
We then have
d t ¼ L d i
d ð Li Þ
v ¼ e ¼
d t ¼
ð 2 : 11 Þ
where L is the inductance of the coil. It may be seen from comparison of (2.10)
and (2.11) that inductance may be defined as 'flux linkage per ampere causing it'.
2.2.4 Electricity supply
The discovery of electromagnetic induction paved the way for electricity supply on
a useful scale. The first schemes appeared in Britain and the United States at about
the same time (1882), supplying the newly developed electric lighting. The voltage
was induced in stationary coils, linked by flux produced on a rotating member
or rotor . The general arrangement is shown schematically in Figure 2.12. The
constant rotor flux is seen as an alternating flux by the stationary coils as a result of
the rotor's rotation. It follows from Faraday's Law that an e.m.f. will be induced in
each stator coil.
The machine shown in Figure 2.12 is known as a synchronous generator or
alternator . Alternators have provided almost all of the world's electricity to date.
However, in spite of the alternator's extreme simplicity, the pioneers of electricity
supply decided to provide a direct - rather than an alternating - voltage. This required
brushes and a commutator to be fitted to the alternator to achieve rectification. The
added complexity of the resulting direct current (DC) generator contributed to poor
supply reliability. A further difficulty with DC supply arises when a switch is opened,
perhaps to disconnect a load. The attempt to reduce the current to zero in a short time
creates a large voltage; this is a direct consequence of Faraday's Law as expressed in
Equations (2.10) and (2.11). This voltage appears across the switch, creating an arc.
This problem can be overcome by suitable switch design, but adds to the difficulty
and expense of DC supply. The much greater currents to be interrupted under short-
circuit conditions create a very severe system protection problem.
Challenging as these problems were, the greatest limitation of the early DC
supply systems was that power had to be supplied, distributed and consumed at the
same voltage. This was typically 110 V, which was deemed to be the highest safe
value for consumers. Extra load required cables of ever increasing cross-sectional
area for a given power. It soon became clear that distribution at such a low voltage
was untenable. However, a move to a higher distribution voltage - and lighter