Basic Electronics and Electrical Engineering: Chapter 4: Synchronous Machines
EMF Equation of an Alternator
Synchronous Machines
Synchronous Machines: EMF Equation of an Alternator
EMF
EQUATION OF AN ALTERNATOR
Let,
ϕ = Flux per pole in
webers
P = Number of poles
N = Rotor speed in rpm
Z= No. of conductors
per phase = 2T, T is the No. of turns per coil
We know that number of
cycles per second is known as frequency.
f = N / 60 (rev /sec)
But time is reciprocal
of its frequency, dt = 1/f
= 60/N
In one revolution, each
stator‒conductor is cut by dϕ Webers, ie,
dϕ= ϕP
According to the
Faraday's second law, the total induced emf is directly proportional to the
rate of change of magnetic flux linkage.
Therefore, average emf
induced in one stator conductor, E = dϕ / dt
E = ϕP / (60/N) = ϕPN / 60
Since, there are Z‒
conductors in series per phase,
Average emf/phase = (ϕΡΝ/60)
× Z
But, N = 120f / P
emf/phase = (ϕΡZ/60) ×
(120f / P)
= 2 fϕZ
volts
RMS value of emf/phase
= Average value/phase × Form factor
= 2fϕZ × 1.11
Erms/phase = 2.22 fϕZ
If Kp and Kd
are the pitch factor and distribution factor of the armature winding.
Then, Erms/phase
= 2.22 fϕZ KpKd
Erms/phase = 2.22 KpKd fϕZ Volts ... (4.2)
In terms of the number
of turns
Erms/phase
= 4.44 KpKd fϕT
Volts
Basic Electronics and Electrical Engineering: Chapter 4: Synchronous Machines : Tag: Basic Engineering : Synchronous Machines - EMF Equation of an Alternator
Basic Electronics and Electrical Engineering: Chapter 4: Synchronous Machines
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