# Chapter 6:AC Motor Drives¶

## Example 6.1,Page no:153¶

In [1]:
import math

#Variable declaration
V=400.0 #[Voltage] volt
P=4.0 #[poles]
f=50.0 #[Frequency]  Hz
Pout=10.0 #[Power out]  hp

#Calculation
Pout=Pout*735.5 #[Power out] in W
Snl=1.0/100.0 #No load Slip
Sfl=4.0/100.0 #Full load slip
Ns=120.0*f/P #[Synchronous speed] rpm
N1=Ns*(1.0-Snl) #[Speed at no load]  rpm
N2=Ns*(1.0-Sfl) #[Speed at full load]  rpm

f2=Sfl*f #[Frequency at full load]   Hz
omega_n=N2*2*math.pi/60.0 #[Angular velocity]   rad/s
T=Pout/omega_n #[Full load torque]   N-m

#Result
print"(a)  Synchronous speed ",Ns,"rpm"
print"(b)  Speed at no load : ",N1,"rpm"
print"(c)  Speed at full load in rpm : ",N2,"rpm"
print"(d)  Frequency of rotor current at full load : ",f2,"Hz"
print"(e)  Full load Torque : ",round(T,2),"N-m\n\n"
print"NOTE:Answer of Part (C) full load speed in the book is wrong."

(a)  Synchronous speed  1500.0 rpm
(b)  Speed at no load :  1485.0 rpm
(c)  Speed at full load in rpm :  1440.0 rpm
(d)  Frequency of rotor current at full load :  2.0 Hz
(e)  Full load Torque :  48.77 N-m

NOTE:Answer of Part (C) full load speed in the book is wrong.


## Example 6.2,Page no:153¶

In [2]:
import math
#Variable declaration
P=6.0 #poles
f1=50.0 #[Input frequency]  Hz
Pg=80.0 #[Power of induction motor]  KW
f2=100.0 #[alternation/min]

#Calculation
f2=f2/60.0 #[Frequency]   Hz
Ns=120*f1/P #[Synchronous speed]  rpm
Ns=Ns/60.0 #rps
S=f2/f1 #[Slip]
print"Slip is : ",S
N=Ns*(1.0-S) #[Motor speed]   rps
print"Motor speed : ",round(N*60.0,2),"rpm"
Pm=Pg*(1-S) #[Mechanical power developed]   KW
print"Developed mechanical power  : ",round(Pm,3),"kW"
CuLoss=S*Pg #[Rotor copper loss]   KW
CuLoss_per_phase=CuLoss/3.0 #KW
print"Rotor Copper Loss per phase : ",round(CuLoss_per_phase*1000,1),"W"
I2=65 #A
r2=CuLoss_per_phase*1000.0/I2**2 #ohm/phase
print"Rotor resistance per phase  : ",round(r2,2),"ohm/phase"
T=Pg*1000.0/2.0/math.pi/Ns #N-m

#Result
print"Torque developed  : ",round(T,2),"N-m"

Slip is :  0.0333333333333
Motor speed :  966.67 rpm
Developed mechanical power  :  77.333 kW
Rotor Copper Loss per phase :  888.9 W
Rotor resistance per phase  :  0.21 ohm/phase
Torque developed  :  763.94 N-m


## Example 6.3,Page no:154¶

In [3]:
import math
#Variable declaration
N=288.0 #[Full load speed]   rpm
f=50.0 #[Supply frequency]   Hz
CuLoss=275.0 #[Copper loss]  W
Ns=300.0 #[Synchronous speed]  rpm(For S=0.03:0.05)

#Calculation
P=120.0*f/Ns #poles
print"No. of poles : ",P
S=(Ns-N)/Ns #Slip
print"Slip : ",S
S=2.0*S #(as rotor reistance doubled, slip is doubled)
print"Slip for full load if rotor resiatance doubled : ",S
#CuLoss=I2**2*r2
CuLoss=2*CuLoss #KW(rotor resiatance doubled & current constant)

#Result
print"New value of rotor copper loss : ",CuLoss,"W"

No. of poles :  20.0
Slip :  0.04
Slip for full load if rotor resiatance doubled :  0.08
New value of rotor copper loss :  550.0 W


## Example 6.4,Page no:158¶

In [4]:
import math
#Variable declaration
T_directStartBYTfl=1.5 #[ratio]

#Calculation
K=math.sqrt(T_directStartBYTfl) #Ratio of full load torque to starting torque direct starting
#Vapplied=1/K*Vline
VappliedBYVline=1/K
LineCurrentBYIfl=1/K**2*4 #V

#Result
print"Applied voltage is ",round(VappliedBYVline,3),"* Line voltage."
print"Line current at starting is ",round(LineCurrentBYIfl,2)," * full load current."

Applied voltage is  0.816 * Line voltage.
Line current at starting is  2.67  * full load current.


## Example 6.5,Page no:158¶

In [5]:
import math

#Variable declaration
Ist=300.0 #[Starting current]  A
X=50/100.0 #[Percentage tapping]   tapping
Imotor=X*Ist #[Motor current]  A

#Calculation

Iline=X**2*Ist #A
ratio=X**2 #Ratio of starting Torque 50% tapping to full voltage torque

#Result
print"(a)  Motor current  : ",Imotor,"A"
print"(b)  Line current  : ",Iline,"A"
print"(c)  Ratio of starting Torque 50% tapping to full voltage torque : ",ratio

(a)  Motor current  :  150.0 A
(b)  Line current  :  75.0 A
(c)  Ratio of starting Torque 50% tapping to full voltage torque :  0.25


## Example 6.6,Page no:163¶

In [6]:
import math
#Variable declaration
V=400.0                  #[Volatge]   volt
P=8.0                    #[pole]
f=50.0                   #[Frequency]    Hz
r1=1.2                   #[Resistance]   ohm
r2dash=1.2               #[R2]  ohm
x1=2.5                   #[Resistance parameter 3]   ohm
x2dash=2.5               #[Resistance]   ohm
N=720.0 #rpm

#Calculation
Ns=120.0*f/P                                      #rpm
S=(Ns-N)/Ns                                       #full load slip
S2=2.0-S                                          #Slip during plugging
V1=V/math.sqrt(3.0)                                 #V
I2dash1=V1/math.sqrt((r1+r2dash/S2)**2.0+(x1+x2dash)**2.0)                     #A(Initial braking current)
Ifl=V1/math.sqrt((r1+r2dash/S)**2.0+(x1+x2dash)**2.0)                         #A(Full load current)

RatioCurrent=I2dash1/Ifl                                                   #ratio of initial braking current to full load current
Tfl=3.0*Ifl**2*r1/(2.0*math.pi*S*Ns/60.0)                                       #N-m
T2dash=3.0*I2dash1**2.0*r2dash/(2.0*math.pi*S2*Ns/60.0)                            #N-m(initail braking T)
RatioT=T2dash/Tfl                                                         #ratio of initial braking Torque to full load Torque
#Let R be the additional resistance
I2dash=2*Ifl                                                               #A
#I2dash=V1/math.sqrt((r1+r2dash/S2+R/S2)**2+(x1+x2dash)**2)                #A(Initial braking current)
R=(math.sqrt(V1**2.0/I2dash**2.0-(x1+x2dash)**2.0)-r1-r2dash/S2)*S2              #in ohm
Ractual=R/2.0**2.0                                                             #ohm
T_braking=3*I2dash**2*(r2dash+R)/(2.0*math.pi*S2*Ns/60.0)                      #N-m(initail braking T)
TbBYTfl=T_braking/T2dash #ratio

#Calculation
print"(a)  Initial Braking current : ",round(I2dash1,2),"A"
print"     Full load current is:",round(Ifl,2),"A"
print"     Ratio is ",round(RatioCurrent,3)
print"     Full load troque=",round(Tfl,2),"N-m"
print"     Initial Braking torque: ",round(T2dash,2),"N-m"
print"     Ratio of braking ",RatioT," times of full  load Torque.\n"
print"(b)  Actual additional rotor resistance per phase  :",round(Ractual,3),"ohm\n"
print"(c)  Braking torque in N-m : ",round(T_braking,2),"N-m"
print"     Ratio of braking torque to full load torque : ",round(TbBYTfl,2)

(a)  Initial Braking current :  43.42 A
Full load current is: 7.31 A
Ratio is  5.941
Full load troque= 61.21 N-m
Initial Braking torque:  44.1 N-m
Ratio of braking  0.720412943871  times of full  load Torque.

(b)  Actual additional rotor resistance per phase  : 6.456 ohm

(c)  Braking torque in N-m :  112.52 N-m
Ratio of braking torque to full load torque :  2.55


## Example 6.7,Page no:169¶

In [7]:
import math

#Variable declaration
V=400.0 #[Volatge]   volt
P=8.0 #[pole]
f=50.0 #Frequency   Hz
r1=0.1 #Resistance  ohm
r2dash=0.1 #Resistance ohm
x1=0.4 #Resistance  ohm
x2dash=0.4 #Resistance  ohm
J=10.0 #Inertia of motor   Kg-m**2

#Calculation
Sm=r2dash/math.sqrt(r1**2+(x1+x2dash)**2)
Ns=2*f/P #rps
omega_ms=2*math.pi*Ns #rad/s
V1=V/math.sqrt(3) #V
Tmax=1.5*V1**2/(2.0*math.pi*Ns)*(1.0/(r1+math.sqrt(r2dash**2+(2*x2dash)**2))) #N-m
tau_m=J*omega_ms/Tmax #sec
ts=tau_m*(1.5*Sm+0.25/Sm) #sec
E=0.5*J*omega_ms**2 #Watt-s
Etot=2*E #Watts-s
tb=tau_m*(0.7/Sm+0.334*Sm) #sec
E=1.4*J*omega_ms**2 #Watt-s
E=2*E/1000 #KW-s(taking cU loss into account)

#Result
print"(a)  Starting time : ",round(ts,2),"seconds"
print"(b)  Energy dissipated during starting : ",round(Etot/1000,2),"kW-s"
print"(c)  Pluggingfg time  : ",round(tb,2),"secs"
print"(d)  Energy dissipated during plugging : ",round(E,2),"kW-s"

(a)  Starting time :  1.54 seconds
(b)  Energy dissipated during starting :  61.69 kW-s
(c)  Pluggingfg time  :  3.97 secs
(d)  Energy dissipated during plugging :  172.72 kW-s


## Example 6.8,Page no:177¶

In [8]:
import math
#Variable declaration
V=400.0 #[Voltage]   volt
P=4.0 #[pole]
f=50.0 #Frequency   Hz
r1=0.64 #Resistances  ohm
r2=0.08 #Resistance  ohm
x1=1.1 #Resistance  ohm
x2=0.12 #Resistance  ohm
T1=40.0 #Load torque    N-m
N=1440.0 #Speed   rpm
n=2.0*f/P #[Load torque at1300] rps
n=n*60.0 #rpm
N1=1300.0 #[Motor speed]   rpm
#Calculation
Tload=T1*(N1/N)**2 #N-m
S=(n-N1)/n #slip
r2dash=r2*2**2 #ohm
x2dash=x2*2**2 #ohm
#Tload=3*I2dash**2*r2dash/(2*math.pi*S*n/60)
I2dash=math.sqrt(Tload/3/r2dash*(2*math.pi*S*n/60)) #A
I2=2*I2dash #A
I1=I2dash #A
V1=I1*(r1+r2dash+r2dash*(1-S)/S+(1j)*(x1+x2dash)) #Vplt
StatorVoltage=abs(V1)*math.sqrt(3) #Volt

#Result
print"(a)  Load torque : ",round(Tload,1),"N-m"
print"Rotor current:",round(I2,2),"A"
print"Stator Applied Voltage  : ",round(StatorVoltage,1),"V"

(a)  Load torque :  32.6 N-m
Rotor current: 53.34 A
Stator Applied Voltage  :  158.3 V


## Example 6.9,Page no:177¶

In [9]:
import math
#Variable declaration
V=400.0 #[Voltage]   volt
P=4.0 #[pole]
f=50.0 #[Frequecy]   Hz
r1=0.64 #[Resistance]  ohm
r2=0.08 #[Resistance]  ohm
x1=1.1 #[Resistance]   ohm
x2=0.12 #[Resistance]  ohm
T1=40.0 #[Torqu]   N-m
N=1440.0 #[Speed]   rpm
N1=1300.0 #[Motor speed]  rpm

#Calculation
r2dash=r2*2**2 #ohm
x2dash=x2*2**2 #ohm
S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip
print"(a)  Slip for maximum torque at 50 Hz : ",round(S,4)
V1=V/math.sqrt(3) #volt/phase
ns=2*f/P #rps
Tmax=1.5*V1**2/(2*math.pi*ns)*(1/(r1+math.sqrt(r1**2+(x1+x2dash)**2))) #Nm
print"Maximum torque at 50 Hz  : ",round(Tmax,1),"N-m"
n=ns*(1-S) #rps
N=n*60 #rpm
print"Speed at 50 Hz  : ",round(N,2),"rpm"
f=25 #Hz
x1=x1/2 #ohm
x2dash=x2dash/2 #ohm
S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip
print"(b)  Slip for maximum torque at 25 Hz : ",round(S,4)
V1=V1/2 #volt/phase
ns=2*f/P #rps
Tmax=1.5*V1**2/(2*math.pi*ns)*(1/(r1+math.sqrt(r1**2+(x1+x2dash)**2))) #Nm
print"Maximum torque at 25 Hz: ",round(Tmax,2),"N-m"
n=ns*(1-S) #rps
N=n*60 #rpm

#Result
print"Speed at 25 Hz : ",round(N,3),"rpm"

(a)  Slip for maximum torque at 50 Hz :  0.1877
Maximum torque at 50 Hz  :  217.2 N-m
Speed at 50 Hz  :  1218.43 rpm
(b)  Slip for maximum torque at 25 Hz :  0.3147
Maximum torque at 25 Hz:  153.71 N-m
Speed at 25 Hz :  513.945 rpm


## Example 6.10,Page no:178¶

In [10]:
import math

#Variable declaration

V=400.0 #[Voltage[   volt
P=4.0 #[pole]
f=50.0 #[Frequency]  Hz
r1=0.64 #[Resistance]   ohm
r2=0.08 #[Resistance]  ohm
x1=1.1 #[Resistance]  ohm
x2=0.12 #[Resistance]  ohm
T1=40.0 #[Troque]  N-m
N=1440.0 #[Speed]   rpm
N1=1300.0 #[Motor speed]  rpm

#Calculation
r2dash=r2*2**2 #ohm
x2dash=x2*2**2 #ohm
S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip
V1=V/math.sqrt(3) #volt/phase
ns=2*f/P #rps
Tst1=3*V1**2*r2dash/(2*math.pi*ns*((r1+r2dash)**2+(x1+x2dash)**2)) #N-m
f=25 #Hz
x1=x1/2 #ohm
x2dash=x2dash/2 #ohm
V1=V1/2 #volt/phase
ns=2*f/P #rps
Tst2=3*V1**2*r2dash/(2*math.pi*ns*((r1+r2dash)**2+(x1+x2dash)**2)) #N-m

#Calculation
print"Starting torque at 50 Hz  : ",round(Tst1,2),"N-m"
print"Starting torque at 25 Hz  : ",round(Tst2,2),"N-m"

Starting torque at 50 Hz  :  95.36 N-m
Starting torque at 25 Hz  :  105.44 N-m


## Example 6.11,Page no:179¶

In [11]:
import math
#Variable declaration
V=400.0 #[Voltage] volt
P=4.0 #[pole ]
f=50.0 #[Frequency]   Hz
r2dash=1.0 #[Rotor resistance]   ohm/phase
#Neglecting r1,x1,x2
f1=400.0 #[Frequency]   Hz
S=4.0/100.0 #[Slip]
t2=1.5 #[Time]  ms

#Calculation
t2=t2*10**-3 #sec
t=1.0/f1 #sec
t1=t-t2 #sec
R=2.0 #ohm(additional resistance)
R2dash=(r2dash*t1+(r2dash+R)*t2)/t #ohm
V1=V/math.sqrt(3) #volt
T=3*V1**2*S/R2dash #N-m

#Result
print"Torque : ",round(T,1)," synch.watts"

Torque :  2909.1  synch.watts


## Example 6.12,Page no:179¶

In [12]:
import math

#Variable declaration
V1=400.0 #[Volatge]   volt
P=4.0 #[pole]
f=50.0 #[Frequency]   Hz
Sm=10.0/100.0 #[slip]
S1=0.04 #[slip]
N2=900.0 #[Speed]  rpm
#r2dash=0.01*x2 #ohm/phase
r2dash=0.01  #[Stator resistance]
r1dash=0.1   #[Stator resistance]

#Calculation
Ns=120.0*f/P #rpm
N1=Ns*(1-S1) #rpm
S2=(Ns-N2)/Ns #slip
T2ByT1=(N2/N1)**2
#T=3/(2*math.pi*ns)*[V1**2/((rdash/S2)**2+xdash**2)]*(rdash/S2)
#T2/T1=V2**2/V1**2*S1/S2*[(1+625*r1dash**2)/(1+6.25*r1dash**2)]
V2=math.sqrt(T2ByT1*V1**2*S2/S1/((1+625*r1dash**2)/(1+6.25*r1dash**2))) #volt

#Result
print"Stator applied voltage: ",round(V2,2),"V"

Stator applied voltage:  302.65 V


## Example 6.13,Page no:180¶

In [13]:
import math
#Variable declaration
P=4.0 #[pole]
f=50.0 #[Frequency]  Hz
S=4/100.0 #[slip]
T=1000.0 #[Torque]  synch.Watts
f1=25.0 #[New I/P frequency]   Hz

#Calculation
Tnew=T*f/f1 #synch.watts

#Result
print"Torque : ",Tnew,"synch.Watts"

Torque :  2000.0 synch.Watts


## Example 6.14,Page no:181¶

In [14]:
import math
#Variable declaration
P=4.0 #pole
f=50.0 #[Frequency]    Hz
r1=0.04 #[Resitance]  ohm
r1dash=0.04 #[Rotor Resistance]  ohm
r2dash=0.04 #[Rotor resistance]  ohm
x1=0.2 #[Reactance]  ohm
x2dash=0.2 #[Reactace]  ohm
f1=20.0 #[New Frequency]   Hz

#Calculation
k=f1/f #ratio of frequencies
Tmax20BYTmax50=(r1+math.sqrt(r1**2+(x1+x2dash)**2))/(r1/k+math.sqrt((r1/k)**2+(x1+x2dash)**2))
Tst20BYTst50=((r1+r2dash)**2+(x1+x2dash)**2)/k/((r1/k+r2dash/k)**2+(x1+x2dash)**2)
#at 20 Hz :
x11=x1*f1/f #ohm
x22dash=x2dash*f1/f #ohm
Ir20ByIr50=(f1/f)*(math.sqrt((r1+r2dash/r1dash)**2+(x1+x2dash)**2))/(math.sqrt((r1+r2dash/r1dash)**2+(x11+x22dash)**2))

#Result
print"(a)  Ratio of max torque at 20 Hz to max Torque at 50 Hz : ",round(Tmax20BYTmax50,3)
print"(b)  Ratio of starting torque at 20 Hz to starting Torque at 50 Hz : ",Tst20BYTst50
print"(c)  Ratio of rotor current at 20 Hz to rotor current  at 50 Hz : ",round(Ir20ByIr50,3)
print"\nNOTE:Answer of rotor current ratio is wrong in the book."

(a)  Ratio of max torque at 20 Hz to max Torque at 50 Hz :  0.863
(b)  Ratio of starting torque at 20 Hz to starting Torque at 50 Hz :  2.08
(c)  Ratio of rotor current at 20 Hz to rotor current  at 50 Hz :  0.424

NOTE:Answer of rotor current ratio is wrong in the book.


## Example 6.15,Page no:182¶

In [17]:
import math
#Variable declaration
P=4.0 #[pole]
f=50.0 #Frequency]  Hz
S=0.04 #[slip]
r1=0.04 #[Resistance]  ohm
r1dash=0.04 #[Resistance]  ohm
r2dash=0.04 #[Resistance]  ohm
x1=0.2 #ohm
x2dash=0.2 #ohm
f1=30.0 #[Frequency new ]  Hz

#Calculation
import numpy as np
k=f1/f #ratio of frequencies
S1=k*S #slip
#For 50 Hz
#T=3*V1**2*S*r2dash/(2*math.pi*ns)/[(S*r1+r2dash)**2+S**2*(x1+x2dash)**2]
#For 30 Hz
#T=3*V1**2/(2*math.pi*ns)*S/(0.6*S1)/[(S/0.6+S/0.6/S1)**2+S**2]
#0.16445*S1**2-0.74*S1+0.00445=0
p=[0.16445,-0.074,0.00445] #polynomial for S1
S1=np.roots(p)
S1=S1[1] #as another value is for unstable region
Ns=2*f1/P*60 #rpm
N=Ns-S1*Ns #rpm

#Result
print"Motor speed at 30 Hz operation m : ",round(N),"rpm (approx)"

Motor speed at 30 Hz operation m :  836.0 rpm (approx)


## Example 6.16,Page no:183¶

In [18]:
import math
#Variable declaration
P=6.0 #[pole]
f=50.0 #[Frequency]   Hz
S=0.04 #[slip]
Ton=40.0 #[Torque]  N-m
Toff=30.0 #[Torque at off chopper]  N-m
t_onBYt_off=1.0    #[ratio]

#Calculation
Ns=2*f/P*60 #rpm
N=Ns*(1.0-S) #rpm
Tavg1=(Ton+Toff)/2.0 #N-m
Navg=math.sqrt((N**2)*Tavg1/Ton) #rpm
N1=800.0 #rpm
T=Ton*(N1/N)**2 #N-m
Tavg2=32.0 #N-m
#Tavg=32=(Ton*t_on+T*t_off)/(t_on+t_off) #N-m
tonBYtoff=(T-Tavg2)/(Tavg2-Ton) #

#Result
print"Part(a) : "
print"Average torque  : ",Tavg1,"N-m"
print"Average speed  : ",round(Navg),"rpm"
print"Part(b) : "
print"Ratio ton/toff is : ",round(tonBYtoff,4)

Part(a) :
Average torque  :  35.0 N-m
Average speed  :  898.0 rpm
Part(b) :
Ratio ton/toff is :  0.5278


## Example 6.17,Page no:184¶

In [19]:
import math
from scipy import integrate
#Variable declaration
Vrms=415.0 #[rms voltage]  volt
f=50.0 #[Frequency]   Hz

#Calculation
def f(t):
return(1)
X=integrate.quad(f,0,2*math.pi/3.0)
Vdc=Vrms/math.sqrt(1.0/math.pi*X[0])

#Result
print"Value of Vdc  : ",round(Vdc,2),"V"

Value of Vdc  :  508.27 V


## Example 6.18,Page no:184¶

In [20]:
import math
#Variable declaration
V=400.0 #[Volatge]   volt
f=50.0 #[Frequency]  Hz
P=4.0 #[poles]
N1=1350.0 #[Rotor speed]  rpm
N2=900.0 #[Rotor speed] rpm
Rs=1.5 #[Resisatance]  ohm
R=4.0 #[Resistance]   ohm
X=4.0 #[Stator resistance]  ohm

#Calculation
ns=2*f/P*60.0 #rpm
S=(ns-N1)/ns #slip
T=3.0/2.0/math.pi/(ns/60)*((V/math.sqrt(3))**2*(P/S)/((Rs+P/S)**2+(R+X)**2))
T2=T*(N2/N1)**2 #N-m
Snew=(ns-N2)/ns #slip
V=math.sqrt((T2/3.0*2.0*math.pi*(ns/60.0))*((Rs+P/Snew)**2+(R+X)**2)/(P/Snew))*math.sqrt(3)

#Calculation
print"Torque at 900 rpm  : ",round(T2,2),"N-m"
print"Voltage at speed of 900 rpm  : ",round(V,1),"V"

Torque at 900 rpm  :  10.14 N-m
Voltage at speed of 900 rpm  :  176.8 V


## Example 6.19,Page no:195¶

In [21]:
import math
#Variable declaration
V=415.0 #[Voltage]   volt
P=4.0 #[pole]
f=50.0 #[Frequency]   Hz
N=1370.0 #[Speed]  rpm
r1=2.0 #[Resistance]   ohm
r2dash=3.0 #[Resitance]  ohm
x1=3.5 #[Resitance]  ohm
x2dash=3.5 #ohm
X0=55.0 #ohm

#Calculation
Ns=120.0*f/P #rpm
S=(Ns-N)/Ns #slip
Nfl=Ns-N #rpm
Z=(r1+1j*x1)+1j*X0*(r2dash/S+1j*x2dash)/(r2dash/S+1j*(X0+x2dash)) #ohm
Istator=V/math.sqrt(3)/abs(Z) #A
I2dash=Istator*(1j*X0/(r2dash/S+1j*(X0+x2dash))) #A
Tfl=3*abs(I2dash)**2*r2dash/2/math.pi/S/(Ns/60) #N-m
#Torque is equal so stator current will be same.
N=1200 #rpm
Ns=N+Nfl #rpm
f_inv=4*Ns/120 #Hz

#Result
print"Part(a) : "
print"Slip speed  : ",Nfl,"rpm"
print"Stator current: ",round(Istator,2),"A"
print"Motor torque : ",round(Tfl,2),"N-m"
print"Part(b) : "
print"Stator current: ",round(Istator,2),"A"
print"Inverter frequency  : ",round(f_inv,2),"Hz"

Part(a) :
Slip speed  :  130.0 rpm
Stator current:  7.52 A
Motor torque :  24.45 N-m
Part(b) :
Stator current:  7.52 A
Inverter frequency  :  44.33 Hz


## Example 6.20,Page no:196¶

In [22]:
import math
#Variable declaration
Is=6.0 #[Stator current]  A
f=40.0 #[Frequency]   Hz
SlipSpeed=100.0 #[Slip speed]   rpm
V=415.0 #[Volage]  volt
P=4.0 #[pole]
r1=2.0 #[Resistance]   ohm
r2dash=3.0#[Resistance]  ohm
x1=3.5 #[Resistance]  ohm
x2dash=3.5 #[Resistance]  ohm
X0=55.0 #[Resistance]   ohm
N=1370.0 #[Motor speed]  rpm

#Calculation
Ns=120.0*50.0/P #rpm
S=(Ns-N)/Ns #slip
I2dash=Is*X0/abs(r2dash/S+1j*(X0+x2dash)) #A
T=3.0*I2dash**2.0*r2dash/(2.0*math.pi*S*(Ns/60.0)) #N-m
Ns2=120*f/P #rpm
MotorSpeed=Ns2-SlipSpeed #rpm

#Result
print"Rotor current  :",round(I2dash,3),"A"
print"Full  load torque : ",round(T,2),"N-m"
print"Motor speed  : ",MotorSpeed,"rpm"

Rotor current  : 4.855 A
Full  load torque :  15.58 N-m
Motor speed  :  1100.0 rpm


## Example 6.20,Page no:205¶

In [23]:
import math
#Variable declaration
Pout=2500.0 #[Power out]  hp
V=2300.0 #[Voltage]   volt
P=20.0 #[pole]
f=50.0 #[Frequency]  Hz
Xs=1.77 #[ohm/phase]

#Calculation
Pout=Pout*735.5/1000.0 #KW
V=V/math.sqrt(3) #Volt/phase
cos_theta=1.0
I=Pout*10**3.0/3.0/V/cos_theta #A
Ixs=I*Xs #V
E=math.sqrt(V**2+Ixs**2) #V
Pout_max=3*V*E/Xs/1000.0 #KW
Tmax=Pout_max*1000.0 #synch. Watts
ns=2*f/P #rps
Tmax=Pout_max*1000.0/2.0/math.pi/ns #N-m

#Result
print"Maximum torque  : %.3e"%Tmax,"N-m"

Maximum torque  : 1.117e+05 N-m


## Example 6.21,Page no:206¶

In [24]:
import math
#Variable declaration
Pout=2500.0 #[Power out]  hp
V1=2300.0 #[Volatge]  volt
P=20.0 #[pole]
f=50.0 #[Frequency]   Hz
Xs=1.77 #[ohm/phase]

#Calculation
Pout=Pout*735.5/1000.0 #KW
print Pout
V=V1/math.sqrt(3) #Volt/phase
cos_theta=1
I=Pout*10**3.0/3.0/V/cos_theta #A
Ixs=I*Xs #V
E=math.sqrt(V**2.0+Ixs**2) #V
dell=math.acos(V/E) #degree
Pout=3*V*E/Xs*math.cos(dell) #W

#Result
print"Part(a) Power output  : %.3e"%Pout,"W"
T=Pout #synch. Watts
N=300 #rpm
ns=N/60.0 #rps
T=T/2.0/math.pi/ns #N-m
print"        Torque in N-m :%.2e"%T,"N-m"
f1=25 #Hz
N1=2*f1/P*60 #rpm
print"Part(b) Speed  : ",N1,"rpm"
T=T*(N1/N)**2 #N-m
print"        Torque  : %.3e"%T,"N-m"
Vapplied=V1*f1/f #Volts
print"Part(b) Applied voltage  : ",Vapplied,"VoltS"
Pout=T*2*math.pi*N1/60 #W
print"Part(b) Power output:",round(Pout/1000,2),"kW"

1838.75
Part(a) Power output  : 2.989e+06 W
Torque in N-m :9.51e+04 N-m
Part(b) Speed  :  150.0 rpm
Torque  : 2.378e+04 N-m
Part(b) Applied voltage  :  1150.0 VoltS
Part(b) Power output: 373.59 kW