# Chapter 7 Single Phase Motors¶

## Example 7.2,Pg.no 384¶

In [44]:
import math
from math import pi,sqrt
#Given
F=60
P=4
N=1730
Zb=27.86
R=1.35
X=1.63
R1=2.9
X1=3.26
V=120
Prot=81.2
Ns=(120*F)/P
S=(Ns-N)/N
Rf=13.06
Xf=16.31
Rb=0.61
Xb=1.55
Zinput=complex((R1+Rf+Rb),(X1+Xf+Xb))
(a,b)=(27.19,52.61)
Zinput=complex(a,b)
Iinput=V/a                  #current input
Iinput=round(Iinput,2)
ans=math.cos(pi*b/180)           #power factor
ans=round(ans,2)
Pinput=V*Iinput*ans         #power input
Wsy=Ns*2*(pi/F)             #synchronous speed
T=Iinput**2*(Rf-Rb)/Wsy     #torque developed
T=round(T,2)
Pmech=T*Wsy*(1-S)           #mechanical power developed
OutputPower=Pmech -Prot     #output power
OutputPower=round(OutputPower,2)
Eff=OutputPower/Pinput*100  #efficiency
Eff=round(Eff,1)
Pgf=Iinput**2*Rf       #air-gap power due to forward rotating fields
Pgb=Iinput**2*Rb       #airgap powers due to the backward rotating fields
airgap=Pgf+Pgb         #air-gap power
airgap=round(airgap,2)
P2=S*Pgf+(2-S)*Pgb+9.8     #rotor copper loss
P2=round(P2,2)
print 'input current=',Iinput,'A'
print 'power factor=',ans,'lagging'
print 'developed torque=',T,'N-m'
print 'output power',OutputPower,'W'
print 'efficiency=',Eff,'%'
print 'air-gap power=',airgap,'W'
print 'rotor copper loss=',P2,'W'

input current= 4.41 A
power factor= 0.61 lagging
developed torque= 1.28 N-m
output power 160.07 W
efficiency= 49.6 %
air-gap power= 265.86 W
rotor copper loss= 33.53 W


## Example 7.4,Pg.no 400¶

In [45]:
import math
from math import pi,sqrt
#Given
V=120.0                                                 #supply voltage
F=60.0                                                  #frequency in Hz
Pole=4.0                                                #no.of poles
Zm=complex(1.5,4.0)                                     #impedance for main-winding
Za=complex(3,6)                                         #impedance for auxillary winding
Xa=6.0
Xm=4.0
Rm=1.5                                                   #resistance for main-winding
Ra=3.0                                                   #resistance for auxillary winding
Ra=(Xa/Xm)*(Rm+sqrt(18.25))                              #external resistance
C=2*pi*60*(6+((3*1.5)/(4+sqrt(18.25))))                  #formula used=2.0*pi*F*(Xa+((Ra*Rm)/(Xm+sqrt(18.25))))
C=C**-1*10**6                                            #capacitance
a=3.69
Xc=Xa+(a/Rm)
C1=1.0/(2.0*pi*60.0*Xc)*10.0**6.0
Ia=V/(Za)
(Is,Angle)=(17.88,-63.43)
Im=V/(Zm)
(Is1,Angle1)=(28.1,-69.44)
Alfa=Angle1-Angle
Ts=Is*math.sin(pi*6.01/180)
Ra=round(Ra,2)
C=round(C,0)
C1=round(C1,2)
Ts=round(Ts,2)
print 'external resistance to be added=',Ra,'ohms'
print 'capacitance needed to obtain max.torque=',C,'microF'
print 'capacitor needed to obtain max.toque per ampere=',C1,'microF'
print 'starting torque',Ts,'K'

external resistance to be added= 8.66 ohms
capacitance needed to obtain max.torque= 405.0 microF
capacitor needed to obtain max.toque per ampere= 313.54 microF
starting torque 1.87 K


## Example 7.5,Pg.no 406¶

In [46]:
import math
from math import pi,sqrt
#Given
V=120                              #supply voltage
F=60                               #frequency in Hertz
X1m=Xla=X2=2.0                     #given impedances
R1m=Rla=1.5                        #resistance
R2=1.5                             #resistance
Xmag=48                            #magnetic impedance
a=1                                #turns ratio
Xc=10**6/(2*pi*F*C)                #equivalent circuit
Zf=Zb=complex(0.69,0.98)
(Zf1,Angle)=(1.2,54.85)            #Zf in (r,theta) 'polar' co-ordinates
Zlm=complex(1.5,2)
Im=V/(Zlm+2*Zf)
(Im,a)=(24.5,-54)                   #Im in polar form
(Ia,b)=(1.42,87.4)                  #Ia in polar form
(Is,c)=(Ia+Im,a+b)                  #starting current
Wsyn=30*2*pi                        #synchronous speed
T=(2*Im*Ia*2*math.sin(141.4*180/pi))/(Wsyn)     #starting torque
Zm=Zlm+Zf+Zb
(Rm,Xm)=(2.88,3.96)
(Zm1,d)=(4.9,54)                     #input impedance of main winding in polar form
Za=complex(3.88,3.96)
xc=3.96-((Xm*3.88-(Zm1*5.12))/Rm)
C=(10**6)/(377.0*xc)                        #total capacitance
Ts=2*24.5*23.33*2*0.69*math.sin(95*180/pi)/(60*pi)
Ts=Ts/32.33
Xc=round(Xc,1)
Im=round(Im,1)
T=round(T,3)
Cs=round(Cs,2)
Ts=round(Ts,2)
print 'equivalent impedance=',Xc,'ohms'
print 'starting current=',Im,'A'
print 'starting torque=',T,'N-m'
print 'Starting capacitor needed=',Cs,'microF'
print 'Maximum starting torque per ampere=',Ts,'N-m/A'

equivalent impedance= 88.4 ohms
starting current= 24.5 A
starting torque= 0.382 N-m
Starting capacitor needed= 331.57 microF
Maximum starting torque per ampere= 0.25 N-m/A


## Example 7.6,Pg.no 414¶

In [47]:
import math
from math import pi,sqrt
#Given
V=120.0                               #supply voltage
F=60.0                                #frequency
N=2000.0                              #motor speed in rpm
Ia=0.6                                #current in ampere
Ra=20.0                               #resistance at the terminal
L=0.25                                #inductance at the terminal
V=120.0                               #dc supply voltage
Edc=V-(Ia*Ra)                         #dc operation
X=2*pi*F*L                            #ac excitation
Eac=(-Ia*Ra)+sqrt(V**2-(Ia*X)**2)
Nac=N*(Eac/Edc)
Pf=(Eac+(Ia*Ra))/V
Pmech=Eac*Ia
Wm=(Nac*2*pi)/F
T=Pmech/Wm
Nac=round(Nac,2)
Pf=round(Pf,2)
Pmech=round(Pmech,1)
T=round(T,3)
print 'speed=',Nac,'rpm'
print 'power factor=',Pf,'lag'
print 'mechanical power developed=',Pmech,'W'
print 'torque developed=',T,'N-m'

speed= 1737.79 rpm
power factor= 0.88 lag
mechanical power developed= 56.3 W
torque developed= 0.309 N-m