Chapter4 - Permanent magnet generators

Example 4.1 Page 216

In [1]:
from math import pi, floor
# Given data
kf=0.12  #  in Nm/A
V=48 #in volt

#Calculations
omega_mo=V/kf#in radian/sec
No=omega_mo*60/(2*pi)#in rpm
print "No load speed =",floor(No),"rpm" 

No load speed = 3819.0 rpm

Example 4.2 Page 216

In [2]:
from __future__ import division
# Given data
Tst=1  #  in N-m
Ist=5 #in Ampere
V=28 #in volt

#Calculations
kf=Tst/Ist #in Nm/A
omega_m=V/kf#in radian/sec
No=omega_m*60/(2*pi)#in rpm
print "No load speed = %0.2f rpm  "%No

No load speed = 1336.90 rpm

Example 4.3 Page 217

In [3]:
# Given data
Ra=0.8 #in Ω
Vdd=2 #in volt
V=28 #in volt
T1=0.3  #  in N-m
Tst=1  #  in N-m
Ist=5 #in Ampere

#Calculations
#We know : Tst = fi_1*Ist  and T1 = IL*fi_2
#Deviding these two eqn we have
IL=(T1/Tst)*Ist/0.8 #in Ampere
Ebo=V #in volt
NLbyNo=(V-IL*Ra-Vdd)/(0.8*Ebo) # temporary calculation for NL
No=1337 #in rpm
NL=NLbyNo*No #in rpm
print "Speed of motor = %0.f rpm"%NL 

Speed of motor = 1462 rpm

Example 4.4 page 217

In [4]:
# Given data
ke=0.12 #in Nm/A
V=48 #in volt
Rph=0.15 #in Ω
Vdd=2 #in volt

#Calculations
omega_mo=V/ke#in radian/sec
No=omega_mo*60/(2*pi)#in rpm
print "No load speed = %0.1f rpm "%No 

Ist=(V-Vdd)/(2*Rph) #in Ampere
Tst=ke*Ist  #  in N-m
print "Starting Torque = %0.1f N-m"%Tst 

No load speed = 3819.7 rpm 
Starting Torque = 18.4 N-m

Example 4.5 Page 218

In [5]:
# Given data
Vs=120 #in volt
V=60 #in volt
Ra=2.5 #in Ω
T=0.5  #  in N-m
N=6000#in rpm

#Calculations

omega_mo=2*pi*N/60#in radian/sec
ke=Vs/omega_mo #in Nm/A
Ia=T/ke #in Ampere
E=V-Ia*Ra #in Volt
omega_m=E/ke#in radian/sec
N=omega_m/(2*pi/60) #in rpm
print "Speed = %0.2f rpm "%N 
#Note : answer is wrong in the book because calculation is not accurate. .

Speed = 2672.75 rpm

Example 4.6 Page 219

In [6]:
# Given data
lm=6*10**-3 #magnet length in m
g=2*10**-3 #in m
Tph=200 #turns
Br=0.3 #in T
l=50*10**-3 #in m
n=25*10**-3 #in m
I=10*10**-3 #in A
N=200 #turns
mo=4*pi*10**-7 #permittivity
#Calculations
Am=(2/3)*pi*(n-g-lm/2)*l #in m**2
Ag=((2/3)*pi*(n-g/2)+2*g)*(l+2*g) #in m**2    
Cfi=Am/Ag #unitless
#For normal BLDG motor, HC=606 KA/M
HC=606 #in  KA/M
Hm=N*I/l #KA/M
Bm=Br*(1-Hm/HC) #in T
Mrec=(Br-Bm)*10**-3/(4*pi*10**-7*40) 
Pmo=mo*Mrec*Am/lm #in m-Wb/AT
Pmo=Pmo*10**-3 #in Wb/AT
Kc=1.05 #given constant
g_dash=Kc*g #in m
Rg=g_dash/mo/Am 
Bg=Cfi*Br/(1+Pmo*Rg) #in T
Torque=2*Tph*Bg*l*n*I #in N-m
print "Torque per phase = %0.3e N-m "%Torque 

Torque per phase = 1.072e-03 N-m

Example 4.7 Page 220

In [7]:
from math import sin, pi, sqrt
# Given data
P=16 #no.of poles
slots=144 #no. of slotes
conductors=10 #per slot
fi=0.03 #in mb/pole
N=375#in rpm

#Calculations
f=P*N/120 #in Hz
print "Frequency = %0.2f Hz "%f 
kc=1 #for full pitcheed coil
n=slots/P #slots per pole
Beta=180/n #in degree
m=n/3 #slots per pole per phase
kd=sin(pi/180*3*Beta/2)/(m*sin(Beta/2*pi/180)) #Distribution factor
Z=conductors*slots #total no. of conductors
Zph=Z/3 # no. of armature per phase conductions
Tph=Zph/2 #turns/ph
Eph=4.44*kc*kd*f*fi*Tph #in volts
print "Phase Voltage = %0.f V" %Eph
VL=sqrt(3)*Eph #in volt
print "Line Voltage = %0.f V" %VL

Frequency = 50.00 Hz 
Phase Voltage = 1534 V
Line Voltage = 2657 V

Example 4.8 Page 221

In [8]:
from math import cos
# Given data
P=4 #no.of poles
phase=3 #no. of phase
slots=36 #no. of stator slotes
turns=20 #turns per coil
conductors=10 #per slot
fi_m=1.8 #in m wb
N=3000#in rpm

#Calculations
f=P*N/120 #in Hz
Tph=turns*phase*P #no. of turns per phase
m=slots/(phase*P) #slots per pole per phase
n=slots/P #slots per pole
Beta=180/n #in degree
kd1=sin(pi/180*3*Beta/2)/(m*sin(pi/180*Beta/2)) #Distribution factor
alfa=2*Beta #in degree(Short Pitched by 2slots)
kp1=cos(pi/180*alfa/2) #unitless
ks1=1 #coefficient
kn1=kd1*kp1*ks1 #winding factor
Eq=4.44*f*fi_m*10**-3*kn1*Tph #in volts
print "Open circuit Phase emf = %0.f V" %Eq

Open circuit Phase emf = 173 V