A three phase 3600 rmin Yconnected 6 pole synchronous genera

A three phase, 3600 r/min, Y-connected, 6 pole synchronous generator has a field current of 200 A with distributed windings for both armature and field: Field Winding: Factor: 0.912 Series Turns: 100 Armature Winding: Factor=0.94 Series Turns: 25 h = 1 = 4 m, r = 0.2m g = 0.02 Find the peak fundamental mmf in the airgap peak flux airgap (phase a) line to line voltage between phases b and c

Solution

1. finding the fundamental mmf in the airgap

F_{1f =} (4*K_f*n_f*I)/ P*pi

K_f = winding factor for field = 0.912

N_f = 100

I = 200

F_{1f =} (4*0.912*100*200)/6*3.14

₌ 3872.611 ATs/pole

therefore peak fundamental mmf in airgap is 3872.611 ATs/pole

2. finding peak flux airgap

first calculating peak value of fundamental flux density

B_1p= u₀H=u₀F_1f /g= (4pi*3872.61)/0.02

=0.243T

hence value of flux = phi = (4*B_1p*l*r)/P

=( 4*0.2431*4*0.2)/6

= 0.129Wb

therefore peak flux airgap is 0.129 Wb

3. Line to line voltage between b and c

first calculating E_ph,

E_{ph =} 1.414 *f*N_ph *k_w*phi

N=120*f/P , hence f = NP/120 = 3600*6/120= 180 Hz

N_ph= armature winding series turns = 25 , K_w = armature winding factor=0.94

E_ph = 1.414 *180*25*0.94*0.129

= 771V

therefore E_l ,which is line to line voltage = 1.732* E_ph = 1.732* 771

= 1335.372 V

therefore line to line voltage between phase b and c is 1335.372 V