# CHAPTER 8: STARTING, CONTROL AND TESTING OF AN INDUCTION MOTOR¶

## Example 8.1, Page number 273¶

In :
#Variable declaration
T_st = '1.5*T_f'         #Starting torque
s = 0.03                 #Slip

#Calculation
I_sc_I_f = (1.5/s)**0.5  #I_sc/I_f

#Result
print('Short circuit current , I_sc = %.2f*I_f' %I_sc_I_f)

Short circuit current , I_sc = 7.07*I_f


## Example 8.2, Page number 274-275¶

In :
#Variable declaration
T_ratio = 50.0/100    #Ratio of starting torque to full load torque T_st/T_f
s_f = 0.03            #Full load slip
I_ratio = 5.0         #Ratio of short circuit current to full load current I_sc/I_f

#Calculation
x = (1/I_ratio)*(T_ratio/s_f)**0.5  #Percentage of taping

#Result
print('Percentage tapings required on the autotransformer , x = %.3f ' %x)

Percentage tapings required on the autotransformer , x = 0.816


## Example 8.3, Page number 277¶

In :
#Variable declaration
T_ratio = 25.0/100           #Ratio of starting torque to full load torque T_st/T_f
I_ratio = 3.0*120/100        #Ratio of short circuit current to full load current I_sc/I_f

#Calculation
s_f = T_ratio*3/I_ratio**2   #Full load slip

#Result
print('Full load slip , s_f = %.2f ' %s_f)

Full load slip , s_f = 0.06


## Example 8.4, Page number 281-282¶

In :
#Variable declaration
Z_icr = complex(0.04,0.5)       #Inner cage impedance per phase at standstill(ohm)
Z_ocr = complex(0.4,0.2)        #Outer cage impedance per phase at standstill(ohm)
V = 120.0                       #Per phase rotor induced voltage at standstill(V)

#Calculation
#For case(i)
Z_com = (Z_icr*Z_ocr)/(Z_icr+Z_ocr)      #Combined impedance(ohm)
I_2 = V/abs(Z_com)                       #Rotor current per phase(A)
R_2 = Z_com.real                         #Combined rotor resistance(ohm)
T = I_2**2*R_2                           #Torque at stand still condition(synchronous watts)
#For case(ii)
s = 0.06                                 #Slip
R_ocr = Z_ocr.real
X_ocr = Z_ocr.imag
R_icr = Z_icr.real
X_icr = Z_icr.imag
Z_com6 = complex(R_ocr/s,X_ocr)*complex(R_icr/s,X_icr)/complex(R_ocr/s+R_icr/s,X_ocr+X_icr)  #Combined impedance(ohm)
I2_6 = V/abs(Z_com6)                     #Rotor current per phase(A)
R2_6 = Z_com6.real                       #Combined rotor resistance(ohm)
T_6 = I2_6**2*R2_6                       #Torque at 6% slip(synhronous watts)

#Result
print('(i)  Torque at standstill condition , T = %.2f syn.watt' %T)
print('(ii) Torque at 6 percent slip , T_6 = %.2f syn.watt' %T_6)
print('\nNOTE : Changes in answer is due to precision i.e more number of decimal places')

(i)  Torque at standstill condition , T = 31089.35 syn.watt
(ii) Torque at 6 percent slip , T_6 = 15982.06 syn.watt

NOTE : Changes in answer is due to precision i.e more number of decimal places


## Example 8.5, Page number 285¶

In :
#Variable declaration
V = 210.0      #Supply voltage(V)
f = 50.0       #Supply frequency(Hz)
P = 50.0       #Input power(W)
I_br = 2.5     #Line current(A)
V_L = 25.0     #Line voltage(V)
R_1 = 2.4      #DC resistance between any two terminal(ohm)

#Calculation
V_br = V_L/3**0.5             #Phase voltage(V)
P_br = P/3                    #Power per phase(W)
R_eq = P_br/I_br**2           #Equivalent resistance(ohm)
R_2 = R_eq-(R_1/2)            #Per phase rotor resistance(ohm)
Z_eq = V_br/I_br              #Equivalent impedance(ohm)
X_eq = (Z_eq**2-R_2**2)**0.5  #Equivalent reactance(ohm)
X_1 = 0.5*X_eq                #For practical cases reactances(ohm)

#Result
print('Equivalent resistance , R_eq = %.1f ohm' %R_eq)
print('Equivalent impedance , Z_eq = %.1f ohm' %Z_eq)
print('Equivalent reactance , X_eq = %.1f ohm' %X_eq)
print('Per phase rotor resistance , R_2 = %.1f ohm' %R_2)
print('Reactances for practical cases , X_1 = X_2 = %.1f ohm' %X_1)

Equivalent resistance , R_eq = 2.7 ohm
Equivalent impedance , Z_eq = 5.8 ohm
Equivalent reactance , X_eq = 5.6 ohm
Per phase rotor resistance , R_2 = 1.5 ohm
Reactances for practical cases , X_1 = X_2 = 2.8 ohm


## Example 8.6, Page number 287¶

In :
import math

#Variable declaration
V = 210.0        #Supply voltage(V)
f = 50.0         #Supply frequency(Hz)
P = 4.0          #Number of poles
P_0 = 400.0      #Input power(W)
I_0 = 1.2        #Line current(A)
V_0 = 210.0      #Line voltage(V)
P_fw = 150.0     #Total friction and windage losses(W)
R = 2.2          #Stator resistance between any two terminals(ohm)

#Calculation
R_1 = R/2                                   #Per phase stator resistance(ohm)
P_scu = 3*I_0**2*R_1                        #Stator copper loss(W)
P_core = P_0-P_fw-P_scu                     #Stator core loss(W)
#Alternate approach\n",
phi_0 = math.acos(P_core/(3**0.5*V_0*I_0))  #Power factor angle(radians)
phi_0_deg = phi_0*180/math.pi               #Power factor angle(degree)
R_01 = (V_0/3**0.5)/(I_0*math.cos(phi_0))   #No-load circuit resistance per phase(ohm)
X_0 = (V_0/3**0.5)/(I_0*math.sin(phi_0))    #Magnetizing reactance per phase(ohm)

#Result
print('Stator core loss , P_core = %.1f W' %P_core)
print('No-load circuit resistance per phase , R_0 = %.1f ohm' %R_01)
print('Magnetizing reactance per phase , X_0 = %.f ohm' %X_0)

Stator core loss , P_core = 245.2 W
No-load circuit resistance per phase , R_0 = 179.8 ohm
Magnetizing reactance per phase , X_0 = 122 ohm


## Example 8.7, Page number 290¶

In :
#Variable declaration
P_1 = 6.0       #Number of pole
P_2 = 4.0       #Number of pole
f = 50.0        #Supply frequency(Hz)
P = 60.0        #Power(kW)

#Calculation
#For case(i)
s = P_2/(P_1+P_2)          #Combined slip
#For case(ii)
N_cs = 120*f/(P_1+P_2)     #Combined synchronous speed(rpm)
#For case(iii)
P_0 = P*P_2/(P_1+P_2)      #Output of 4-pole motor(kW)

#Result
print('(i)   Combined slip , s = %.1f ' %s)
print('(ii)  Combined synchronous speed , N_cs = %.f rpm' %N_cs)
print('(iii) Output of the 4-pole motor , P_0 = %.f kW' %P_0)

(i)   Combined slip , s = 0.4
(ii)  Combined synchronous speed , N_cs = 600 rpm
(iii) Output of the 4-pole motor , P_0 = 24 kW