CHAPTER 10: SYNCHRONOUS MOTOR

Example 10.1, Page number 335

In [1]:
import math

#Variable declaration
V = 2.5*10**3          #Supply voltage(V)
R_r = 0.12             #Per phase resistance(ohm)
X_r = 3.2              #Syncronous reactance(ohm)
I_a = 185.0            #Line current(A)
pf = 0.8               #Leading power factor

#Calculation
phi = math.acos(pf)                                                #Angle(radians)
phi_deg = phi*180/math.pi                                          #Angle(degree)
V_t = V/3**0.5                                                     #Terminal voltage per phase(V)
Z_s = complex(R_r,X_r)                                             #Impedance per phase(ohm)
beta = math.atan(X_r/R_r)                                          #Angle(radians)
beta_deg = beta*180/math.pi                                        #Angle(degree)
E_r = I_a*abs(Z_s)                                                 #Resultant voltage due to impedance(V)
E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(beta+phi))**0.5            #Excitation voltage per phase(V)

#Result
print('Excitation voltage per phase , E = %.2f V' %E_f)
print('\nNOTE : Changes in answer is due to precision i.e more number of decimal places')
print(' ERROR : Line current I_a = 185 A not 180 A as given in textbook question')

Excitation voltage per phase , E = 1846.18 V

NOTE : Changes in answer is due to precision i.e more number of decimal places
 ERROR : Line current I_a = 185 A not 180 A as given in textbook question

Example 10.2, Page number 335-337

In [1]:
import math

#Variable declaration
kVA = 1200.0        #kVA ratings
V = 14.0*10**3      #Supply voltage(V)
R_r = 4.8           #Per phase resistance(ohm)
X_r = 35.0          #Syncronous reactance(ohm)
pf = 0.95           #Leading power factor

#Calculation
phi = math.acos(pf)                                  #Angle(radians)
phi_deg = phi*180/math.pi                            #Angle(degree)
Z_s = complex(R_r,X_r)                               #Impedance per phase(ohm)
I_a = kVA*10**3/(3**0.5*V)                           #Armature current(A)
E_r = I_a*abs(Z_s)                                   #Resultant voltage due to impedance(V)
V_t = V/3**0.5                                       #Terminal voltage per phase(V)
b = math.atan(X_r/R_r)                               #Beta value(radians)
b_deg = b*180/math.pi                                #Beta value(degree)
E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(b-phi))**0.5 #Excitation voltage per phase(V)
sin_delta = (E_r/E_f)*math.sin(b-phi)
delta = math.asin(sin_delta)*180/math.pi             #Torque angle(degree)

#Result
print('Excitation voltage per phase , E_f = %.2f V' %E_f)
print('Torque angle , δ = %.2f°' %delta)

Excitation voltage per phase , E_f = 7483.23 V
Torque angle , δ = 12.12°

Example 10.3, Page number 343-344

In [1]:
import math

#Variable declaration
V = 440.0          #Supply voltage(V)
R_a = 1.5          #Per phase armature resistance(ohm)
X_a = 8.0          #Synchronous reactance(ohm)
P = 4.0            #Number of poles
f = 50.0           #Supply frequency(Hz)
pf = 0.9           #Leading power factor
I_a = 50.0         #Armature current(A)

#Calculation
V_t = V/3**0.5                                            #Terminal voltage per phase(V)
phi = math.acos(pf)                                       #Angle(radians)
phi_deg = phi*180/math.pi                                 #Angle(degree)
Z_s = complex(R_a,X_a)                                    #Impedance per phase(ohm)
E_r = I_a*abs(Z_s)                                        #Resultant voltage due to impedance(V)
beta = math.atan(X_a/R_a)                                 #Beta value(radians)
beta_deg = beta*180/math.pi                               #Beta value(degree)
E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(beta+phi))**0.5   #Excitation voltage per phase(V)
P_dm = (((E_f*V_t)/abs(Z_s))-((E_f**2*R_a)/abs(Z_s)**2))  #Maximum power per phase(W)

#Result  
print('Maximum power per phase , P_dm = %.1f W' %P_dm)
print('\nNOTE : ERROR : In textbook solution E_f = 513.5 V is taken instead of 533.337089826 V')

Maximum power per phase , P_dm = 10205.3 W

NOTE : ERROR : In textbook solution E_f = 513.5 V is taken instead of 533.337089826 V

Example 10.4, Page number 344

In [1]:
#Variable declaration
P = 4.0        #Number of poles
f = 50.0       #Supply frequency(Hz)
V_t = 1500.0   #Terminal voltage per phase(V)
E_f = 1000.0   #Excitation voltage per phase(V)
Z_s = 12.0     #Synchronous impedance per phase(ohm)
R_a = 1.5      #Armature resistance(ohm)

#Caclulation
P_dm = ((E_f*V_t/Z_s)-(E_f**2*R_a/Z_s**2))  #Maximum power(W)
N_s = 120*f/P                               #Synchronous speed(rpm)
T_dm = 9.55*P_dm/N_s                        #Maximum torque(N-m)

#Result 
print('Maximum power developed , P_dm = %.f W' %P_dm)
print('Maximum toruqe , T_dm = %.1f N-m' %T_dm)

Maximum power developed , P_dm = 114583 W
Maximum toruqe , T_dm = 729.5 N-m