Electrical Power Systems

80 Electrical Power Systems
4.3 MODEL O GENERATOR
An elementary two-pole three-phase synchronous generator model is shown in ig. 4.1. The
rotor and stator are made of high permeability iron to achieve a high ratio of flux density to
mmf. igure 4.1 is highly schematic. igure 4.1 shows each phase winding as if it were a single
turn (the coils aa¢, bb¢ and cc¢) coil placed in a single pair of stator slots. Infact, it is a multiturn
coil physically distributed in a number of stator slots. These three coils aa¢, bb¢ and cc¢, displaced
from each other by 120 electrical degrees. The concentrated full-pitch coils shown here may be
considered to represent distributed windings producing sinusoidal mmf waves concentrated on
the magnetic axes of respective phases. When the rotor is excited to produce an air gap flux (f o
per pole) and is rotating at constant angular velocity (w), the flux linkage of the coil varies with
the position of the rotor mmf axis wt. The flux linkage for an N-turn concentrated coil aa¢ will
be maximum at wt = 0 and zero at wt = p/2. The flux linkage with coil a is given as:
l a = Nf o cos (wt) ...(4.1)
ig. 4.1: Elementary two-pole 3-phase synchronous generator.
The voltage induced in the coil aa¢ is given as:
Ea = - d
( )
dt la = Nfow sin (wt)
\ Ea = Emax cos wt -
p
2
HG I KJ
...(4.2)