Page 134 - Electrician - TT (Volume 2)

ELECTRICIAN - CITS

Emf equation of the alternator

Objectives: At the end of this lesson you shall be able to:
• explain the emf equation to calculate the induced emf in an alternator

Equation of induced emf: The emf induced in an alternator depends upon the flux per pole, the number of
conductors and speed. The magnitude of the induced emf could be derived as stated below
Let Z = No.of conductors or coil sides in series/phase in an alternator
P = No.of poles
¦ = frequency of induced emf in Hz

Ø = flux per pole in webers
kf = form factor = 1.11 - if emf is assumed to be sinusoidal
N = speed of the rotor in r.p.m.
According to Faraday’s Law of Electromagnetic Induction we have the average emf induced in a conductor is
equal to rate of change of flux linkage
d
=
dt
change of total flux
=
time durat ion in which the flux change takes place
In one revolution of the rotor (ie in 60/N seconds), each stator conductor is cut by a flux equal to PØ webers.
Hence the change of total flux = dØ = PØ and the time duration in which the flux changes takes place
= dt = 60/N seconds.

Hence the average emf induced in a conductor
= d = P volts -------- Eq 1

dt 60
N
120

Substituting the value for in eqn 1
P
we have the average emf induced in a conductor =
P 120
= volts 2 = volts
P60 ------ Eq. 2

If there are Z conductors in series per phase we have the average emf per phase = 2؃Z volts.
Then r.m.s. value of emf per phase = average value x form factor
= V x K
AV
F
= V x 1.11
AV
= 2؃Z x 1.11
= 2.22؃Z volts.
Alternatively r.m.s. value of emf per phase = 2.22ئ2T volts

= 4.44؃T volts
where T is the number of coils or turns per phase and Z = 2T.

121

CITS : Power - Electrician & Wireman - Lesson 76-85