# Chapter 26: D.C. Generators¶

## Example Number 26.3, Page Number:912¶

In :
#variable declaration
i=450#A
v=230#v
rs=50#ohm
ra=.03#ohm

#calculations
ish=v/rs
ia=i+ish
va=ia*ra
E=v+va

#result
print "e.m.f. generated in the armature= ",E," V"

e.m.f. generated in the armature=  243.62  V


## Example Number 26.4, Page Number:913¶

In :
#variable declaration
i=50#A
v=500#v
rs=250#ohm
ra=.05#ohm
rseries=0.03#ohm
b=1#V

#calculations
ish=v/rs
ia=i+ish
vs=ia*rseries
va=ia*ra
vb=ish*b
E=v+va+vs+vb

#result
print "generated voltage in the armature= ",E," V"

generated voltage in the armature=  506.16  V


## Example Number 26.5, Page Number:913¶

In :
#variable declaration
i=30#A
v=220#v
rs=200#ohm
ra=.05#ohm
rseries=0.30#ohm
b=1#V

#calculations
vs=i*rseries
vshunt=v+vs
ish=vshunt/v
ia=i+ish
vb=b*2
E=v+vs+vb+(ia*ra)

#result
print "generated voltage in the armature= ",E," V"

generated voltage in the armature=  232.552045455  V


## Example Number 26.6, Page Number:913¶

In :
#variable declaration
v=230.0#v
i=150.0#A
rs=92.0#ohm
rseries=0.015#ohm
rd=0.03#ohm(divertor)
ra=0.032#ohm

#calculations
ish=v/rs
ia=i+ish
sdr=(rd*rseries)/(rd+rseries)
tr=ra+sdr
vd=ia*tr
Eg=v+vd
tp=Eg*ia
pl=(ia*ia*ra)+(ia*ia*sdr)+(v*ish)+(v*i)

#resuts
print "i) Induced e.m.f.= ",Eg," V"
print "ii)Total power generated= ",tp," W"
print "iii)Distribution of the total power:"
print " power lost in armature=                ", ia*ia*ra
print "power lost in series field and divider= ", ia*ia*sdr
print "power dissipated in shunt winding=      ", v*ish
print "power delivered to load=                ", v*i
print "                                         ------------"
print "Total=                                  ", pl

i) Induced e.m.f.=  236.405  V
ii)Total power generated=  36051.7625  W
iii)Distribution of the total power:
power lost in armature=                 744.2
power lost in series field and divider=  232.5625
power dissipated in shunt winding=       575.0
------------
Total=                                   36051.7625


## Example Number 26.7, Page Number:914¶

In :
#variable declaration
p=300000.0#w
v=600.0#v
sr=75.0#ohm
abr=0.03#ohm
cr=0.011#ohm
rseries=0.012#ohm
dr=0.036#ohm

#calculatons
io=p/v#output current
ish=v/sr
ia=io+ish
sdr=(rseries*dr)/(rseries+dr)
tr=abr+cr+sdr
vd=ia*tr
va=v+vd
pg=va*ia
W=pg/1000

#result
print "Voltage generatedby the armature= ",va," V"
print "Power generated by the armature= ",W, "kW"

Voltage generatedby the armature=  625.4  V
Power generated by the armature=  317.7032 kW


## Example Number 26.8, Page Number:915¶

In :
import math
#variable declaration
phi=7*math.pow(10,-3)
z=51*20
a=p=4
n=1500#r.p.m

#calculations
Eg=(phi*z*n*p)/(a*60)

#result
print "Voltage generated= ",Eg," V"

Voltage generated=  178.5  V


## Example Number 26.9, Page Number:916¶

In :
#variable declaration
p=a=8
phi=0.05#Wb
n=1200#rpm
N=500#armature conductor

#calculations
E=phi*(n/60)*(p/a)*N

#result
print "e.m.f generated= ",E," V"

e.m.f generated=  500.0  V


## Example Number 26.10, Page Number:916¶

In :
#variable declaration
v=127#v
vt=120#v(terminal voltage)
r=15#ohms
i1=8.47#A
ra=0.02#ohms
fi=8#A

#calculations
Eg=v+(i1*ra)
ia=(Eg-vt)/ra
il=ia-fi

#result

Load current  350.47  A


## Example Number 26.11(a), Page Number:917¶

In :
#variable declaration
p=8
z=778
n=500
ra=0.24
rl=12.5
r=250
v=250
a=2
#calculations
il=v/rl
si=v/r
ai=il+si
emf=v+(ai*ra)
phi=(emf*60*a)/(p*z*n)

#result
print "armature current= ",ai," A"
print "induced e.m.f.= ",emf," V"
print "flux per pole= ",round(phi*1000,2)," mWb"

armature current=  21.0  A
induced e.m.f.=  255.04  V
flux per pole=  9.83  mWb


## Example Number 26.11(b), Page Number:916¶

In :
#variable declaration
p=a=4
P=5000.0#w
P2=2500.0#W
v=250.0#v
ra=0.2#ohm
r=250.0#ohm
z=120
N=1000#rpm

#calculations
gc=P/v
li=P2/v
ti=gc+li
fc=1
ai=ti+fc
ard=ai*ra
emf=v+ard+2
phi=(emf*60*a)/(p*z*N)
ac_perparralelpath=ai/p

#result
print "Flux per pole= ",phi*1000," mWb"
print "Armature current per parallel path= ",ac_perparralelpath," A"

Flux per pole=  129.1  mWb
Armature current per parallel path=  7.75  A


## Example Number 26.12, Page Number:918¶

In :
#variable declaration
i=200.0#A
v=125.0#V
n1=1000#rpm
n2=800#rpm
ra=0.04#ohm
bd=2.0#V(brush drop)

#calculations
R=v/i
E1=v+(i*ra)+bd
E2=(E1*n2)/n1
il=(E2-bd)/0.675

#result
print "Load current when speed drops to 800 r.p.m.= ",round(il,2)," A"

Load current when speed drops to 800 r.p.m.=  157.04  A


## Example Number 26.13, Page Number:918¶

In :
import math
#variable declaration
p=4
n=900 #rpm
V=220#V
E=240#V
ra=0.2#ohm
phi=10#mWb
N=8

#calculations
ia=(E-V)/ra
Z=(E*600*2)/(phi*math.pow(10,-3)*n*p)
#since there ae 8 turns in a coil,it means there are 16 active conductor
number_of_coils=Z/16

#result
print "armature current= ",ia," A"
print "number of coils= ",number_of_coils

armature current=  100.0  A
number of coils=  500.0


## Example Number 26.14, Page Number:919¶

In :
#variable declaration
V=120.0#V
ra=0.06#ohm
rs=25#ohm
rsw=0.04#ohm(series winding)
il=100.0#A
#i)Long shunt
ish=V/rs
ia=il+ish
vd=ia*rsw
vda=ia*ra
E=V+vd+vda

print "Induced e.m.f. when the machine is connected to long shunt= ",E," V"
print "Armature current when the machine is connected to long shunt=",ia," A"

#i)Short shunt
vds=il*rsw
vs=V+vds
ish=vs/rs
ia=il+ish
vd=ia*rsw
vda=ia*ra
E=V+vd+vda

print "Induced e.m.f. when the machine is connected to short shunt= ",E," V"
print "Armature current when the machine is connected to short shunt=",ia," A"

Induced e.m.f. when the machine is connected to long shunt=  130.48  V
Armature current when the machine is connected to long shunt= 104.8  A
Induced e.m.f. when the machine is connected to short shunt=  130.496  V
Armature current when the machine is connected to short shunt= 104.96  A


## Example Number 26.15, Page Number:920¶

In :
#variable declaration
p=25000.0#W
V=500.0#V
ra=0.03#ohm
rs=200.0#ohm
rseries=0.04#ohm
vb=1.0#V
n=1200#rpm
phi=0.02#Wb

#calculations
i=p/V
ish=V/rs
ia=i+ish
p=4
vds=ia*rseries
vda=ia*ra
vdb=vb*2
E=V+vds+vda+vdb
Z=(E*60*4)/(phi*n*p)

#result
print "The e.m.f. generated= ",E," V"
print "The number of conductors=",Z

The e.m.f. generated=  505.675  V
The number of conductors= 1264.1875


## Example Number 26.16, Page Number:920¶

In :
#variable declaration
p=4
n=750#rpm
e=240.0#V
z=792
phi=0.0145#Wb

#calculations
phi_working=(e*60*2)/(n*z*p)
lambda_=phi/phi_working

#results
print "Leakage coefficient= ",round(lambda_,1)

Leakage coefficient=  1.2


## Example Number 26.17, Page Number:920¶

In :
#variable declaration
p=a=4
phi=0.07#Wb
t=220
rt=0.004#ohm
n=900#rpm
ia=50.0#A

#calculations
z=2*t
E=(phi*z*n*p)/(60*a)
rtotal=t*rt
r_eachpath=rtotal/p
ra=r_eachpath/a
vda=ia*ra
V=E-vda

#result
print "Terminal Voltage= ",V, " V"

Terminal Voltage=  459.25  V


## Example Number 26.18, Page Number:920¶

In :
#variable declaration
p=a=4
phi=0.07#Wb
t=220
rturn=0.004#ohm
rs=100.0#ohm
rsc=0.02#ohm
n=900#rpm
ia=50.0#A

#calculations
z=2*t
E=(phi*z*n*p)/(60*a)
ra=0.055#ohm
ra=ra+rsc
va=ia*ra
v=E-va
ish=v/rs
i=ia-ish
output=v*i

#result
print "Output= ",round(output/1000,3)," kW"

Output=  20.813  kW


## Example Number 26.19, Page Number:921¶

In :
#variable declaration
n1=1200#rpm
ia=200#A
v=125#V
n2=1000#rpm
ra=0.04#ohm
vb=2#V

#calculations
E1=v+vb+(ia*ra)
E2=E1*n2/n1*0.8

#results
print "Generated e.m.f. when field current is reduced to 80%=",E2," V"

Generated e.m.f. when field current is reduced to 80%= 90.0  V


## Example Number 26.20(a), Page Number:921¶

In :
#variable declaration
p=4
rs=100.0#ohm
ra=1.0#ohm
z=378
phi=0.02#Wb
rl=10.0#ohm
n=1000#rpm
a=2

#calculations
E=(phi*z*n*p)/(60*a)
V=(100.0/111.0)*E
il=V/rl
P=il*V

#result
print "Power absorbed by the load is= ",P," W"

Power absorbed by the load is=  5154.12710007  W


## Example Number 26.20(b), Page Number:921¶

In :
#variable declaration
p=a=4
z=300
phi=0.1#Wb
n=1000#rpm
ra=0.2#rpm
rf=125#ohm
il=90#A

#calculations
E=(phi*z*n*p)/(60*a)
ifield=E/rf
ia=ifield+il
V=E-(ia*ra)

#result
print "Terminal voltage= ",V," V"

Terminal voltage=  481.2  V


## Example Number 26.21(a), Page Number:922¶

In :
#variable declaration
p=6
n=1200#rpm
e=250.0#V
d=350.0#mm
air_gap=3.0#mm
al=260.0#mm
fringing=0.8
coils=96
t=3

#calculations
z=t*coils*2
a=p*2
phi=(e*60*a)/(n*z*p)
di=d+air_gap
pole_arc=(3.14*di*fringing)/6
B=phi/(pole_arc*0.000001*al)

#result
print "flux per pole= ",phi," Wb"
print "effective pole arc lenght= ",pole_arc*0.001," m"
print "flux density= ",B," T"

flux per pole=  0.0434027777778  Wb
effective pole arc lenght=  0.147789333333  m
flux density=  1.12953862717  T


## Example Number 26.21(b), Page Number:922¶

In :
import math
#variable declaration
p=a=4
z=1200
e=250.0#v
n=500#rpm
b=35.0#cm
ratio=0.7
lpole=20.0#cm

#calculations
pole_pitch=(b*3.14)/p
polearc=ratio*pole_pitch
pole_area=polearc*lpole
phi=(e*60*a)/(n*z*p)
mean_flux=phi/(pole_area*math.pow(10,-4))

#result
print "Mean flux density= ",mean_flux," Wb/m2"

Mean flux density=  0.649941505265  Wb/m2


## Example Number 26.21(d), Page Number:923¶

In :
#variable declaration
i=200.0#A
v=100.0#V
ra=0.04#ohm
rseries=0.03#ohm
rs=60.0#ohm

#calculations
va=v+(i*rseries)
ish=va/rs
ia=i+ish
e=va+(ia*ra)

#long shunt
ishunt=v/rs
vd=ia*(ra+rseries)
e2=v+vd

#result
print "emf generated(short shunt)",e," V"
print "emf generated(long shunt)",e2," V"

#result
print

emf generated(short shunt) 114.070666667  V
emf generated(long shunt) 114.123666667  V



## Example Number 26.22, Page Number:923¶

In :
#variable declaration
n=1000#rpm
w=20000.0#W
v=220.0#v
ra=0.04#ohm
rs=110.0#ohm
rseries=0.05#ohm
efficiency=.85

#calculations
il=w/v
i_f=v/rs
ia=il+i_f
ip=w/efficiency#input power
total_loss=ip-w
copper_loss=(ia*ia*(ra+rseries))+(i_f*i_f*rs)
ironloss=total_loss-copper_loss
omega=2*3.14*n/60
T=ip/omega

#omega
print "Copper loss= ",copper_loss," W"
print "Iron and friction loss= ",ironloss," W"
print "Torque developed by the prime mover= ",T,"Nw-m"

Copper loss=  1216.88892562  W
Iron and friction loss=  2312.52283909  W
Torque developed by the prime mover=  224.803297115 Nw-m


## Example Number 26.23, Page Number:928¶

In :
#variable declartaion
power=10000.0#W
v=250.0#V
p=a=6
n=1000.0#rpm
z=534
cu_loss=0.64*1000#W
vbd=1.0#V

#calculations
ia=power/v
ra=cu_loss/(ia*ia)
E=v+(ia*ra)+vbd
phi=(E*60*a)/(n*z*p)

#result
print "flux per pole= ",phi*1000," mWb"

flux per pole=  30.0  mWb


## Example Number 26.24(a), Page Number:928¶

In :
#variable declaration
i=195#A
pd=250#V
ra=0.02#ohm
rsh=50#ohm
p=250#W
strayloss=950#W
#calculations
ish=pd/rsh
ia=i+ish
vda=ia*ra
E=pd+vda
cu_loss=(ia*ia*ra)+(pd*ish)
output_prime=(pd*i)+strayloss+cu_loss
power_a=output_prime-strayloss
neu_m=(power_a/output_prime)
neu_e=(pd*i)/((pd*i)+cu_loss)
neu_c=(pd*i)/output_prime

#result
print "a)e.m.f. generated= ",E," V"
print " b)Cu losses= ",cu_loss," W"
print " c)output of prime mover= ",output_prime," W"
print " d)mechanical efficiency= ",neu_m*100," %"
print "   electrical efficiency= ",neu_e*100," %"
print "   commercial efficiency= ",neu_c*100," %"

a)e.m.f. generated=  254.0  V
b)Cu losses=  2050.0  W
c)output of prime mover=  51750.0  W
d)mechanical efficiency=  98.1642512077  %
electrical efficiency=  95.9645669291  %
commercial efficiency=  94.2028985507  %


## Example Number 26.24(b), Page Number:929¶

In :
#variable declaration
v=500.0#V
i=5.0#A
ra=0.15#ohm
rf=200.0#ohm
il=40.0#A

#calculations
output=v*il
total_loss=(v*i*0.5)+((il+i*0.5)*(il+i*0.5)*ra)+(v*i*0.5)
efficiency=output/(output+total_loss)

#result
print "Efficiency= ",efficiency*100," %"

Efficiency=  87.8312542029  %


## Example Number 26.25, Page Number:929¶

In :
import math
#variable declaration
i=196#A
v=220#V
stray_loss=720#W
rsh=55#ohm
e=0.88

#calculations
output=v*i
inpute=output/e
total_loss=inpute-output
ish=v/rsh
ia=i+ish
cu_loss=v*ish
constant_loss=cu_loss+stray_loss
culoss_a=total_loss-constant_loss
ra=culoss_a/(ia*ia)
I=math.sqrt(constant_loss/ra)

#result
print "Load curent corresponding to maximum efficiency",I," A"

Load curent corresponding to maximum efficiency 122.283568103  A


## Example Number 26.26, Page Number:929¶

In :
#variable declaration
n=1000#rpm
p=22*1000#w
v=220#V
ra=0.05#ohm
rsh=110#ohm
rseries=0.06#ohm
efficiency=.88

#calculations
ish=v/rsh
I=p/v
ia=ish+I
vdseries=ia*rseries
cu_loss=(ia*ia*ra)+(ia*ia*rseries)+(rsh*ish*ish)
total_loss=(p/efficiency)-p
strayloss=total_loss-cu_loss
T=(p/efficiency*60)/(2*3.14*n)

#result
print "a)cu losses= ",cu_loss," W"
print "b)iron and friction loss= ",strayloss," W"
print "c)Torque exerted by the prime mover= ",T," N-m"

a)cu losses=  1584.44  W
b)iron and friction loss=  1415.56  W
c)Torque exerted by the prime mover=  238.853503185  N-m


## Example Number 26.27, Page Number:930¶

In :
#variable declaration
p=4
i=20#A
r=10#ohm
ra=0.5#ohm
rsh=50#ohm
vdb=1#V(voltage drop per brush)

#calculations
v=i*r
ish=v/rsh
ia=i+ish
E=v+(ia*ra)+(2*vdb)
totalpower=E*ia
output=v*i
efficiency=output/totalpower

#result
print "induced e.m.f.= ",E," V"
print "efficiency= ",efficiency*100," %"

induced e.m.f.=  214.0  V
efficiency=  77.8816199377  %


## Example Number 26.28, Page Number:930¶

In :
#variable declaration
v=240#V
i=100#A
ra=0.1#ohm
rseries=0.02#ohm
ri=0.025#ohm
rsh=100#ohm
ironloss=1000#W
frictionloss=500#W

#calculations
output=v*i
totalra=ra+rseries+ri
ish=v/rsh
ia=i+ish
copperloss=ia*ia*totalra
shculoss=ish*v
total_loss=copperloss+ironloss+frictionloss+shculoss
efficiency=output/(output+total_loss)

#result
print "F.L. efficiency of the machine= ",efficiency*100," %"

F.L. efficiency of the machine=  87.3089843128  %


## Example Number 26.29, Page Number:930¶

In :
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
A=Symbol('A')
B=Symbol('B')
ironloss=8#kW
r=0.25#reduction in speed
n_ironloss=5#kW

#calculations
ans=solve([ironloss-(A*1+B*1**2),n_ironloss-(A*(1-r)+B*(1-r)**2)],[A,B])
wh=ans[A]
we=ans[B]
wh2=ans[A]*0.5
we2=ans[B]*0.5**2

#result
print "i)full speed:"
print "Wh=",round(wh,3),"kW"
print "We=",round(we,3),"kW"
print "ii)half speed:"
print "Wh=",round(wh2,3),"kW"
print "We=",round(we2,3),"kW"

i)full speed:
Wh= 2.667 kW
We= 5.333 kW
ii)half speed:
Wh= 1.333 kW
We= 1.333 kW


## Example Number 26.30, Page Number:931¶

In :
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
N=Symbol('N')
n=1000.0#rpm
wh=250.0#w
we=100.0#w

#calculations
A=wh/(n/60)
B=we/((n/60)**2)
new_loss=(wh+we)/2
ans=solve([new_loss-A*N-B*(N**2)],[N])

#result
print "Speed at which total loss will be halved=",ans,"r.p.s"

Speed at which total loss will be halved= (9.50045787200216,) r.p.s


## Example Number 26.31, Page Number:931¶

In :
#variable declaration
output=10.0*1000#W
v=240.0#V
ra=0.6#ohm
rsh=160.0#ohm
mechcoreloss=500.0#W
culoss=360.0#W

#calculations
ish=v/rsh
i=output/v
ia=ish+i
culossa=ia*ia*ra
totalloss=culoss+mechcoreloss+culossa
inputp=output+totalloss
efficiency=output/inputp

#result
print "Power required= ",inputp*0.001," kW"
print "efficinecy= ",efficiency*100," %"

Power required=  11.9780166667  kW
efficinecy=  83.486275552  %


## Example Number 26.32, Page Number:932¶

In :
#variable declaration
p=110*1000#W
v=220#V
ra=0.01#ohm
rse=0.002#ohm
rsh=110#ohm

#calculations
il=p/v
ish=v/rsh
ia=il+ish
E=v+ia*(ra+rse)

#result
print "induced emf= ",E," V"

induced emf=  226.024  V


## Example Number 26.33 Page Number:932¶

In :
#variable declaration
p=4
E=216.0#V
n=600.0#rpm
slots=144
con=6
n2=500.0#rpm

#calculations
z=con*slots
a=p
phi=(E*60*a)/(n*z*p)
a=2
armatureE=(phi*z*n2*p)/(60*a)

#result
print "the armature emf= ",armatureE," V"

the armature emf=  360.0  V


## Example Number 26.34 Page Number:933¶

In :
#variable declaration
p=4
r=0.15#ohm

#calculations
ar=p*r

#result
print "armature resistance=",ar

armature resistance= 0.6

In [ ]: