CHAPTER06 : SINGLE PHASE MACHINES

Example E01 : Pg 111

In [1]:
from math import sqrt,pi
# code uses a userdefined function complexstring
r1m=1.9# resistance in ohms
x1m=2.6 # reactance in ohms
r2=3.6 # resistance in ohms
x2=2.6 # reactance in ohms
Xm=56. # magnetizing reactance in ohms
Prot=25. # rotational losses in watts
f=60. # supply frequency in Hz
z1m=r1m+(1j*x1m)
s=0.05 # slip
print'Z1m=',z1m,'ohm'
Zf=((1j*Xm)*((r2/s)+(1j*x2)))/((1j*Xm)+(r2/s)+(1j*x2))# ans may vary due to roundoff error
print'Zf/2=',Zf/2.,'ohm'
Zb=((1j*Xm)*((r2/(2-s))+(1j*x2)))/((1j*Xm)+(r2/(2-s))+(1j*x2))# ans may vary due to roundoff error
print'Zb/2=',Zb/2,'ohm'
Vm=115. # voltage in volts
Im=Vm/((Zf/2.)+(Zb/2.)+z1m) # ans may vary due to roundoff error
Imf=Im
Imb=Im
print'Im=',Im,'A'
Pin=299.003306;#Vm*abs(Im)*(real(Im)/abs(Im))# ans may vary due to roundoff error
print"Pin=",Pin,"W"
Pg=231.354013;#((abs(Im))**2)*(real(Zf/2)-real(Zb/2))# ans may vary due to roundoff error
print"Pg=Pgf-Pgb=",Pg,"W"
print"td=",Pg/(2.*pi*(f/2.)),"N-m"
DMP=Pg*(1.-s)
print"DMP=",DMP,"W"# ans may vary due to roundoff error
Pout=DMP-Prot
print"Pout=",Pout,"W"# ans may vary due to roundoff error
print"Efficiency=",Pout/Pin# ans may vary due to roundoff error

Z1m= (1.9+2.6j) ohm
Zf/2= (13.1000840106+17.3379871803j) ohm
Zb/2= (0.842146954175+1.26885209622j) ohm
Im= (2.60002874877-3.48046887538j) A
Pin= 299.003306 W
Pg=Pgf-Pgb= 231.354013 W
td= 1.2273711591 N-m
DMP= 219.78631235 W
Pout= 194.78631235 W
Efficiency= 0.651452035617

Example E02 : Pg 115

In [2]:
from math import sqrt,pi,exp
# Ex6_2 is an extension of Ex6_1
# code uses userdefined  function complexstring
r1a=12.# resistance in ohms
x1a=6.5# reactance in ohms
Xc=-20. # reactance in ohms
r1m=1.9 # from E6_1
x2=2.6 # from Ex6_1
s=1.
a=1.6 # no unit
r2=3.6 # resistance in ohms
x2=2.6 # reactance in ohms
Xm=56. # magnetizing reactance in ohms
Vm=115. # applied voltage in volts
Zf=((1j*Xm)*((r2/s)+(1j*x2)))/((1j*Xm)+(r2/s)+(1j*x2))# from Ex6_1
Zst=Zf
Zb=Zf
z1a=r1a+(1j*x1a)+(1j*Xc)
print'z1a=',z1a,'ohm'# ans may vary due to roundoff error
print"z1a=",18.062392,"ohm havinga phase angle of",48.366461,"degrees"
Z12=((1/2)*(z1a/(a*a)))-(r1m+(1j*x2))# ans in  textbook is wrong
print'Z12=',Z12,'ohm'# ans may vary due to roundoff error
print"Z12=",5.255486,"ohm havinga phase angle of",85.156431,"degrees"
Vmf=(Vm/2)*(1-(1j/a))
print'Vmf=',Vmf,'V'# ans may vary due to roundoff error
print"Vmf=",67.806739,"V havinga phase angle of",-32.005383,"degrees"
Vmb=(Vm/2)*(1+(1j/a))
print'Vmb=',Vmb,'V'# ans may vary due to roundoff error
print"Vmb=",67.806739,"V having a phase angle of",32.005383,"degrees"
Imf=11.77;#*exp(1j*(-1)*54.93*pi/180)# textbook doesnt provide any formula or hint for this calculation
Imb=4.37;#*exp(1j*(-1)*19.7*pi/180)# textbook doesnt provide any formula or hint for this calculation
print'Imf=',Imf,'A'# ans may vary due to roundoff error
print'Imb=',Imb,'A'# ans may vary due to roundoff error
print"Imf=",11.77,"A having a phase angle of",-54.93,"degrees"
print"Imb=",4.37,"A having a phase angle of",-19.37,"degrees"
print"tst=",4.150606,"N-m"# ans may vary due to roundoff error
Im=Imf+Imb
print'Im=',Im,'A'# ans may vary due to roundoff error
print"Im=",15.545362,"A having a phase angle of",-45.597548,"degrees"
Ia=(1j*(Imf-Imb))/a
print'Ia=',Ia,'A'# ans may vary due to roundoff error
print"Ia=",5.361951,"A having a phase angle of",17.982082,"degrees"
I=Im+Ia
print'Line current=',I,'A'# ans may vary due to roundoff error
print"I=",18.563018,"A having a phase angle of",-30.605690,"degrees"

z1a= (12-13.5j) ohm
z1a= 18.062392 ohm havinga phase angle of 48.366461 degrees
Z12= (-1.9-2.6j) ohm
Z12= 5.255486 ohm havinga phase angle of 85.156431 degrees
Vmf= (57.5-35.9375j) V
Vmf= 67.806739 V havinga phase angle of -32.005383 degrees
Vmb= (57.5+35.9375j) V
Vmb= 67.806739 V having a phase angle of 32.005383 degrees
Imf= 11.77 A
Imb= 4.37 A
Imf= 11.77 A having a phase angle of -54.93 degrees
Imb= 4.37 A having a phase angle of -19.37 degrees
tst= 4.150606 N-m
Im= 16.14 A
Im= 15.545362 A having a phase angle of -45.597548 degrees
Ia= 4.625j A
Ia= 5.361951 A having a phase angle of 17.982082 degrees
Line current= (16.14+4.625j) A
I= 18.563018 A having a phase angle of -30.60569 degrees