Chapter 11: Dynamics of Electric Machines

Example 11.7, Page 646

In [1]:
import math

#Variable declaration
KVA=71500;#Kilo Volt-Ampere
V_r=13800;#in Volts
X_af=0.57;#in per unit
X_la=0.125;#in per unit
X_lf=0.239;#in per unit
X_ld=0.172;#in per unit

#Calculations&Results
X_ds=X_la+((X_af*X_lf*X_ld)/(X_lf*X_ld+X_af*X_ld+X_af*X_lf));#subtransient reactance(in per unit)
E_phy=1.;#generated voltage (in per unit)
I_ds=E_phy/X_ds;#short circuit current (in per unit)
X_d=X_la+((X_af*X_lf)/(X_af+X_lf));#transient reactance (in per unit)
I_d=E_phy/X_d;#transient current (in per unit)
I_rated=KVA*1000/(math.sqrt(3)*V_r);#in Amperes
I_dsa=I_ds*I_rated;#sub transient current (in Amperes)
print 'sub-transient current (in Amperes)=%.2f'%I_dsa
I_da=I_d*I_rated;#transient current (in Amperes)
print 'transient current (in Amperes)=%.2f'%I_da
#Answer varies due to rounding-off errors
sub-transient current (in Amperes)=14238.48
transient current (in Amperes)=10195.69

Example 11.8, Page 652

In [2]:
import math

#Variable declaration
f=60.;#in Hertzs
P=4.;#no. of poles
P_m=0.9;
H=10;#in Joule/Volt-Amperee

#Calculations&Results
N_s=f*120/P;#synchronous speed in (rpm)
w_s=2*math.pi*N_s/f;#(in rad/sec)
P_dm=P_m/math.sin(18*math.pi/180);
t_c=P/f;#fault clearing time (in sec)
delta_o=18*2*math.pi/360;#in rad
delta_m=math.degrees(delta_o+((w_s/(P*H))*P_m*t_c**2))
P_d=P_dm*math.sin(delta_m*math.pi/180);
print '(a) power generated (in per unit)=%.2f'%P_d
delta_2=math.pi-delta_o;
delta_c=math.acos(((P_m/P_dm)*(delta_2-delta_o))+math.cos(delta_2));
t_cn=math.sqrt((delta_c-delta_o)*4*H/(w_s*P_m));
print '(b) critical fault clearing time (in sec)=%.3f'%t_cn
(a) power generated (in per unit)=0.95
(b) critical fault clearing time (in sec)=0.581