CHAPTER 10: SINGLE-PHASE MOTORS¶

Example 10.1, Page number 341¶

In [1]:
import math
import cmath

#Variable declaration
hp = 0.25        #Power rating of the single-phase motor(hp)
V = 110.0        #Voltage rating of the single-phase motor(V)
I_sw = 4.0       #Starting winding current(A)
phi_I_sw = 15.0  #Phase angle by which I_sw lags behind V(degree)
I_rw = 6.0       #Running winding current(A)
phi_I_rw = 40.0  #Phase angle by which I_rw lags behind V(degree)

#Calculation
#Case(a)
I_s = I_sw*cmath.exp(1j*-phi_I_sw*math.pi/180)    #Starting current(A)
I_r = I_rw*cmath.exp(1j*-phi_I_rw*math.pi/180)    #Running current(A)
I_t = I_s+I_r                                     #Total starting current(A)
I_t_angle = cmath.phase(I_t)*180/math.pi          #Angle of total starting current(degree)
Power_factor = math.cos(I_t_angle*math.pi/180)    #Power factor
#Case(b)
Is_cos_theta = I_s.real                           #Component of starting winding current in phase with the supply voltage(A)
#Case(c)
Ir_sin_theta = I_r.imag                           #Component of running winding current that lags the supply voltage by 90°(A)
#Case(d)
phase = (phi_I_rw-phi_I_sw)                       #Phase angle between the starting and running currents(degree)

#Result
print('Case(a): Total starting current , I_t = %.2f∠%.f° A' %(abs(I_t),I_t_angle))
print('         Power factor = %.3f lagging' %Power_factor)
print('Case(b): Component of starting winding current in phase with the supply voltage , I_s*cosθ = %.2f A' %Is_cos_theta)
print('Case(c): Component of running winding current that lags the supply voltage by 90° , I_r*sinθ = %.2fj A' %Ir_sin_theta)
print('Case(d): Phase angle between starting and running currents , (θ_r-θ_s) = %.f° ' %phase)

Case(a): Total starting current , I_t = 9.77∠-30° A
Power factor = 0.866 lagging
Case(b): Component of starting winding current in phase with the supply voltage , I_s*cosθ = 3.86 A
Case(c): Component of running winding current that lags the supply voltage by 90° , I_r*sinθ = -3.86j A
Case(d): Phase angle between starting and running currents , (θ_r-θ_s) = 25°


Example 10.2, Page number 341¶

In [1]:
import math

#Variable declaration
hp = 0.25        #Power rating of the single-phase motor(hp)
V = 110.0        #Voltage rating of the single-phase motor(V)
I_s = 4.0        #Starting winding current(A)
phi_I_s = 15.0   #Phase angle by which I_sw lags behind V(degree)
I_r = 6.0        #Running winding current(A)
phi_I_r = 40.0   #Phase angle by which I_rw lags behind V(degree)

#Calculation
P_s = V*I_s*math.cos(phi_I_s*math.pi/180)   #Power dissipated by starting winding(W)
P_r = V*I_r*math.cos(phi_I_r*math.pi/180)   #Power dissipated in the running winding(W)
P_t = P_s+P_r                               #Total instantaneous power dissipated during starting(W)
P_r_d = P_r                                 #Total steady-state power dissipated during running(W)
n = hp*746/P_r*100                          #Efficiency(%)

#Result
print('Case(a): Power dissipated by the starting winding , P_s = %.f W' %P_s)
print('Case(b): Power dissipated in the running winding , P_r = %.1f W' %P_r)
print('Case(c): Total instantaneous power dissipated during starting , P_t = %.1f W' %P_t)
print('Case(d): Total steady-state power dissipated during running , P_r = %.1f W' %P_r_d)
print('Case(e): Motor efficiency , η = %.f percent' %n)

Case(a): Power dissipated by the starting winding , P_s = 425 W
Case(b): Power dissipated in the running winding , P_r = 505.6 W
Case(c): Total instantaneous power dissipated during starting , P_t = 930.6 W
Case(d): Total steady-state power dissipated during running , P_r = 505.6 W
Case(e): Motor efficiency , η = 37 percent


Example 10.3, Page number 345¶

In [1]:
import math
import cmath

#Variable declaration
hp = 0.25        #Power rating of the single-phase motor(hp)
V = 110.0        #Voltage rating of the single-phase motor(V)
I_sw = 4.0       #Starting winding current(A)
phi_I_sw = 42.0  #Phase angle by which I_sw lead V(degree)
I_rw = 6.0       #Running winding current(A)
phi_I_rw = 40.0  #Phase angle by which I_rw lags behind V(degree)

#Calculation
#Case(a)
I_s = I_sw*cmath.exp(1j*phi_I_sw*math.pi/180)       #Starting current(A)
I_r = I_rw*cmath.exp(1j*-phi_I_rw*math.pi/180)      #Running current(A)
I_t = I_s+I_r                                       #Total starting current(A)
I_t_angle = cmath.phase(I_t)*180/math.pi            #Angle of total starting current(degree)
Power_factor = math.cos(I_t_angle*math.pi/180)      #Power factor
#Case(b)
angle = (phi_I_rw-(-phi_I_sw))                      #Angle between starting and running current(degree)
sin_angle = math.sin(angle*math.pi/180)             #Sine of the angle between starting and running currents
#Case(c)
T_ratio = sin_angle/math.sin(25*math.pi/180)        #Ratio of starting torque

#Result
print('Case(a): Total starting current , I_t = %.2f∠%.1f° A' %(abs(I_t),I_t_angle))
print('         Power factor = %.3f ' %Power_factor)
print('Case(b): Sine of the angle between starting and running currents = %.4f ' %sin_angle)
print('Case(c): Steady state starting current has been reduced from 9.88∠-30° A to %.2f∠%.1f° A' %(abs(I_t),I_t_angle))
print('         The power factor has raised from 0.866 lagging to %.3f' %Power_factor)
print('         The ratio of starting torques , T_cs/T_rs = %.2f ' %T_ratio)

Case(a): Total starting current , I_t = 7.66∠-8.9° A
Power factor = 0.988
Case(b): Sine of the angle between starting and running currents = 0.9903
Case(c): Steady state starting current has been reduced from 9.88∠-30° A to 7.66∠-8.9° A
The power factor has raised from 0.866 lagging to 0.988
The ratio of starting torques , T_cs/T_rs = 2.34


Example 10.4, Page number 345¶

In [1]:
#Variable declaration
T_r = 1.0       #Rated torque(lb-ft)
P_in = 400.0    #Rated input power(W)
V = 115.0       #Rated input voltage(V)
I_t = 5.35      #Rated input current(A)
Speed = 1750.0  #Rated speed(rpm)
hp = 1.0/3      #Rated hp
T_s = 4.5       #Starting torque(lb-ft) From Locked-Rotor data
T_br = 2.5      #Breakdown torque(lb-ft) From Breakdown-Torque data

#Calculation
T_s_r = T_s/T_r      #Ratio of starting to rated torque
T_br_r = T_br/T_r    #Ratio of breakdown to rated torque
P_o = hp*746         #Power output(W)
n = P_o/P_in*100     #Rated load efficiency(%)
S = V*I_t            #VA rating of the motor
cos_theta = P_in/S   #Rated load power factor
hp = T_r*Speed/5252  #Rated load horsepower

#Result
print('Case(a): Ratio of starting to rated torque , T_s/T_r = %.1f ' %T_s_r)
print('Case(b): Ratio of breakdown to rated torque , T_br/T_r = %.1f ' %T_br_r)
print('Case(c): Rated load efficiency , η = %.1f percent' %n)
print('Case(d): Rated load power factor , cosθ = %.4f ' %cos_theta)
print('Case(e): Rated load horsepower , hp = %.4f hp' %hp)

Case(a): Ratio of starting to rated torque , T_s/T_r = 4.5
Case(b): Ratio of breakdown to rated torque , T_br/T_r = 2.5
Case(c): Rated load efficiency , η = 62.2 percent
Case(d): Rated load power factor , cosθ = 0.6501
Case(e): Rated load horsepower , hp = 0.3332 hp