Chapter 10 : Fractional Kilowatt Motors

Example 10.1, Page No 148

In [1]:
import math
#initialisation of variables
# to compute the ratio of E_mf/E_mb,V_f/V_b,T_f/T_b,gross total torque,T_f/total torque, T_b/total torque

  
R_lm=3.0 
X_lm=5.0 
R_2=1.5 
X_2=2.0 
s=1-.97         #slip

#Calculations
a=complex(R_2/s,X_2) 
b=complex(R_2/(2-s),X_2) 
c=abs(a)/abs(b) 
print(c,'E_mf/E_mb') 
a=(1.0/2)*complex((R_lm+R_2/s),(X_lm+X_2)) 
b=(1.0/2)*complex((R_lm+R_2/(2-s)),(X_lm+X_2)) 
c=abs(a)/abs(b) 
print(c,'V_f/V_b') 
d=(2.0-s)/s 
print(d,'T_f/T_b') 
Z_tot=a+b 
V=220.0 
I_m=V/abs(Z_tot) 
P=6.0 
f=50.0 
n_s=120.0*f/P 
w_s=2*math.pi*n_s/60 
T_f=(I_m**2*R_2/(2*w_s))*(1/s) 
T_b=(I_m**2*R_2/(2*w_s))*(1/(2-s)) 
T_tot=T_f-T_b 
print(T_tot,'gross total torque(Nm)') 
a=T_f/T_tot 
b=T_b/T_tot 

#Results
print(a,'T_f/T_total') 
print(b,'T_b/T_total') 

(23.38275544101299, 'E_mf/E_mb')
(6.727447444111447, 'V_f/V_b')
(65.66666666666661, 'T_f/T_b')
(13.316745850891841, 'gross total torque(Nm)')
(1.0154639175257731, 'T_f/T_total')
(0.015463917525773207, 'T_b/T_total')

Example 10.2, Page No 149

In [2]:
import math
#initialisation of variables
# to calculate parameters of the ckt model, line current, power factor, shaft torque and efficiency

  
V_0=215.0 
I_0=3.9 
P_0=185.0 
R_1=1.6 
V_sc=85 
I_sc=9.8 
P_sc=390.0 
X=(V_0/I_0)*2.0         #magnetisation reactance
phi_sc=math.degrees(math.acos(P_sc/(V_sc*I_sc)))
I_e=V_sc/complex(0,X) 
I_SC=I_sc*complex(math.cos(math.radians(phi_sc*(-1))),math.sin(math.radians(phi_sc*(-1)))) 
I_m=I_SC-I_e 
Z=V_sc/I_m 
R_2=(Z.real)-R_1     #real(Z)=R=R1+R2
print(R_2,'R_2(ohm)') 
print((Z.imag),'X_1+X_2(ohm)') 

#Calculations
n=1500.0     
nn=1440 
s=(n-nn)/n 
a=1.55/s 
b=1.55/(2-s) 
Z_ftot=(complex(0,X/2))*(complex(a+.8,(Z.imag)/2))/((complex(0,X/2))+(complex(a+.8,(Z.imag)/2))) 
Z_btot=(complex(0,X/2))*(complex(b+.8,(Z.imag)/2))/((complex(0,X/2))+(complex(b+.8,(Z.imag)/2))) 
Z_tot=Z_ftot+Z_btot 
I_m=V_0/Z_tot 
I_L=abs(I_m) 
print(I_L,'line current(A)') 
pf=math.cos(math.radians(math.degrees(math.atan((I_m.real)/(I_m.imag)))))
print(pf,'pf') 
P_in=V_0*I_L*pf 
I_mf=I_m*complex(0,X/2)/complex(39.55,59.12) 
I_mb=I_m*complex(0,X/2)/complex(1.59,59.12) 
T=(1/157.1)*(abs(I_mf)**2*38.75-abs(I_mb)**2*.79) 
P_m=157.1*(1-s)*T 
P_L=185 
P_out=P_m-P_L 
eff=P_out/P_in 

#Results
print(eff*100,'efficiency(%)') 
T_shaft=P_out/157.1     
print(T_shaft,'shaft torque(Nm)') 

(3.0828571185946845, 'R_2(ohm)')
(8.051321578491317, 'X_1+X_2(ohm)')
(6.261296470855541, 'line current(A)')
(0.6818110490832134, 'pf')
(72.4748020932455, 'efficiency(%)')
(4.234260916702234, 'shaft torque(Nm)')

Example 10.3, Page No 149

In [3]:
import math
#initialisation of variables
#to compute ampitudes of forward and backward stator mmf waves,magnitude of auxillary currrent and its ph angle diff

  
N_m=80.0
N_a=100.0 
I_m=15*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) 
I_aa=7.5*complex(math.cos(math.radians(45)),math.sin(math.radians(45)))  
I_a=7.5*complex(math.cos(math.radians(60)),math.sin(math.radians(60))) 
F_m=N_m*I_m 
F_a=N_a*I_a 
F_aa=N_a*I_aa     #mmf at 45 angle

#Calculations
F_f=(1.0/2)*(F_m+1j*F_aa) 
a=abs(F_f) 
print(a,'forward field(AT)') 
F_b=(1.0/2)*(F_m-1j*(F_aa)) 
b=abs(F_b) 
print(b,'backward field(AT)') 
#1200+100*I_a*complex(sind(a),cosd(a))=0
#equating real and imaginery parts
#100*I_a*cosd(a)=0 
a=90 
print(a,'phase angle diff') 
I_a=-1200.0/(100*math.sin(math.radians(a))) 

#Results
print(I_a,'auxillery current(A)') 

(427.1146783547173, 'forward field(AT)')
(904.8884193832665, 'backward field(AT)')
(90, 'phase angle diff')
(-12.0, 'auxillery current(A)')

Example 10.4 Page No 150

In [4]:
import math
#initialisation of variables
#to determine value of capacitor

  
f=50.0 
w=2*math.pi*f 
Z_lm=complex(3,2.7) 
Z_la=complex(7,3) 

#Calculations
I_m=(-1)*math.degrees(math.atan((Z_lm.imag)/(Z_la.imag))) 
a=90.0 
I_a=a+I_m 
c=1/(w*((Z_lm.real)-(Z_la.real)*math.cos(math.radians((-1)*I_a)))) 

#Results
print(c,'value of capacitor(F)') 

(-0.0018916018169502632, 'value of capacitor(F)')

Example 10.6, Page No 151

In [5]:
import math
#initialisation of variables
#to calculate starting torque and atarting current,motor performance

  
V_a=110*complex(math.cos(math.radians(90)),math.sin(math.radians(90))) 
V_m=220*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) 
R_1=3 
R_2=2.6 
X_1=2.7 
X_2=2.7 
X=110 
V_f=(1.0/2)*(V_m-1j*V_a)
V_b=(1.0/2)*(V_m+1j*V_a) 

#Calculations
Z_f=(complex(0,X)*complex(R_2,X_2))/(complex(0,X)+complex(R_2,X_2)) 
Z_b=Z_f 
Z_ftot=complex(R_1,X_1)+Z_f 
Z_btot=complex(R_1,X_1)+Z_b 
I_f=V_f/Z_ftot 
I_b=V_b/Z_btot 
T_s=(2/157)*(Z_f.real)*(abs(I_f)**2-abs(I_b)**2) 
print(T_s,'starting torque(Nm)') 
I_m=I_f+I_b 
I_a=1j*(I_f-I_b) 
print(abs(I_a),'starting current(A)') 
s=0.04 

Z_f=(complex(0,X)*complex(R_2/s,X_2))/(complex(0,X)+complex(R_2/s,X_2)) 
Z_b=(complex(0,X)*complex(R_2/(2-s),X_2))/(complex(0,X)+complex(R_2/(2-s),X_2)) 
Z_ftot=complex(R_1,X_1)+Z_f 
Z_btot=complex(R_1,X_1)+Z_b 
I_f=V_f/Z_ftot 
I_b=V_b/Z_btot 
w_s=157.1 
T_s=(2/157.1)*(abs(I_f)**2*(Z_f.real)-abs(I_b)**2*(Z_b.real)) 
print(T_s,'starting torque(Nm)') 
I_m=I_f+I_b 
m=math.degrees(math.atan((I_m.imag)/(I_m.real)))
I_a=1j*(I_f-I_b) 
a=math.degrees(math.atan((I_a.imag)/(I_a.real)))
P_m=w_s*(1.0-s)*T_s 
P_L=200.0 
P_out=P_m-P_L 
P_min=V*abs(I_m)*math.cos(math.radians(m)) 
P_ain=V*abs(I_a)*math.cos(math.radians(a))
P_in=P_min+P_ain 
n=P_out/P_in 
print(n,'efficiency') 

r=Z_ftot/Z_btot     #r=V_mf/V_bf
#V_mf+V_bf=220
V_mf=220/(1+r) 
V_mb=220-V_mf 
V_a=1j*(V_mf-V_mb) 

#Results
print(abs(V_a),'V_a(V)')

(0.0, 'starting torque(Nm)')
(14.313452498677325, 'starting current(A)')
(3.5887587638431966, 'starting torque(Nm)')
(0.12798421082025385, 'efficiency')
(176.4417668704772, 'V_a(V)')