CHAPTER 8 - DC MACHINES: OPERATION AND TESTING

Example E2 - Pg 160

In [1]:
#Caption: Find the (a)current (b)voltage required
#Exa:8.2
import math 
r=1.#Resistance of series motor(in ohms)
V=230.#Voltage of series motor(in volts)
n_1=300.#Speed of motor(in r.p.m)
i_1=15.#Current taken by motor(in A)
n_2=375.#Speed of motor(in r.p.m)
i_2=math.sqrt(((i_1**2.)*(n_2**2.))/(n_1**2.))
print '%s %.2f' %('(a)Current(in A)=',i_2)
V_2=(((V-(i_1*r))*(i_2*n_2))/(i_1*n_1))+(i_2*r)
print '%s %.2f' %('(b)Voltage(in volts)=',V_2)

(a)Current(in A)= 18.75
(b)Voltage(in volts)= 354.69

Example E3 - Pg 161

In [2]:
#Caption: Find the resistance required #Exa:8.3
import math
I_1=40.#Current taken by series motor(in A)
V=663.#Supplied voltage(in volts)
n_1=100.#Initial speed(in%)
n_2=80.#final speed(in%)
I_2=math.sqrt(((I_1**2.)*(n_2**2.))/(n_1**2.))
a=(I_1*(n_1/100.))/(I_2*(n_2/100.))
R=((a*V)-V)/(a*I_2)
print '%s %.2f' %('Resistance required(in ohms) is=',R)

Resistance required(in ohms) is= 7.46

Example E5 - Pg 166

In [3]:
#Caption: Find (a)Speed at full load torque (b)Speed at double full load torque (c)Stalling torque
#Exa:8.5
import math
V=250.#Voltage of motor(in volts)
R_a=0.5#Armature resistance(in ohms)
n=400.#Speed of motor at full load(in r.p.m)
i=30.#Current taken by motor(in A)
R=1.#Series resistance with armature(in ohms)
E_b1=V-(i*R_a)
E_b2=V-((R_a+R)*i)
N=n*(E_b2/E_b1)
print '%s %.f' %('(a)Speed at full load torque(in r.p.m)=',N)
I=2*i
E_b=V-(I*(R+R_a))
N_1=n*(E_b/E_b1)
print '%s %.f' %('(b)Speed at double full load torque(in r.p.m)=',N_1)
I_ft=V/(R+R_a)
T_stalling=I_ft/i
print '%s %.2f %s' %('(c)Stalling torque=',T_stalling,'times the full load torque')

(a)Speed at full load torque(in r.p.m)= 349
(b)Speed at double full load torque(in r.p.m)= 272
(c)Stalling torque= 5.56 times the full load torque

Example E6 - Pg 170

In [4]:
#Caption: Find (a)Input to generator from prime mover on full load (b)Efficiency on full load (c)Load current at which generator efficiency is maximum
#Exa:8.6
import math
V=230.#Voltage of generator(in volts)
I=150.#Full load current(in A)
R_a=0.1#Armature resistance(in ohms)
R_f=230.#Field resistance(in ohms)
P_s=1500.#Stray losses(in watt)
I_f=V/R_f
I_a=I_f+I
W_ac=(I_a**2.)*R_a
W_fc=(I_f**2.)*R_f
P_c=W_fc+P_s
L_t=W_ac+P_c
P_o=V*I
P_i=P_o+L_t
print '%s %.f' %('(a)Input to generator from prime mover on full load(in watt)=',P_i)
Eff=(P_o/P_i)*100
print '%s %.1f' %('(b)Efficiency on full load(in %)=',Eff)
I_l=math.sqrt(P_c/R_a)
print '%s %.1f' %('(c)Load current at which generator efficiency is maximum(in A)=',I_l)

(a)Input to generator from prime mover on full load(in watt)= 38510
(b)Efficiency on full load(in %)= 89.6
(c)Load current at which generator efficiency is maximum(in A)= 131.5

Example E7 - Pg 170

In [5]:
#Caption: Calculate (a)Efficiency on full load (b)Efficiency on 40A input (c)Efficiency on 25A input (d)Full load speed regulation 
#Exa:8.7
V=230.#Voltage of motor(in volts)
i_l=50.#Full load current(in A)
r_a=0.25#Armature resistance(in ohms)
r_f=230.#Field resistance(in ohms)
i_o=3.#No load current(in A)
i_1=40.#Input current(in A)
i_2=25.#Input current(in A)
P_c=V*i_o
P_i1=V*i_l
i_f=V/r_f
i_a1=i_l-i_f
L_fl=((i_a1**2.)*r_a)+P_c
Eff_1=((P_i1-L_fl)/P_i1)*100.
print '%s %.2f' %('(a)Efficiency on full load(in%)=',Eff_1)
P_i2=V*i_1
i_a2=i_1-i_f
L=((i_a2**2.)*r_a)+P_c
Eff_2=((P_i2-L)/P_i2)*100.
print '%s %.2f' %('(b)Efficiency on 40A input(in%)=',Eff_2)
P_i3=V*i_2
i_a3=i_2-i_f
L_1=((i_a3**2.*r_a)+P_c)
Eff_3=((P_i3-L_1)/P_i3)*100.
print '%s %.1f' %('(c)Efficiency on 25A input(in%)=',Eff_3)
I_ao=i_o-i_f
E_bo=V-(I_ao*r_a)
E_bl=V-(r_a*i_a1)
Re=((E_bo-E_bl)/E_bo)*100.
print '%s %.1f' %('(d)Full load speed regulation(in%)=',Re)

(a)Efficiency on full load(in%)= 88.78
(b)Efficiency on 40A input(in%)= 88.37
(c)Efficiency on 25A input(in%)= 85.5
(d)Full load speed regulation(in%)= 5.1

Example E10 - Pg 179

In [6]:
#Caption: Calculate efficiency of (a)motor and (b)generator
#Exa:8.10
import math
V=230.#Line voltage for both shunt machines(in volts)
I=70.#Line current excluding field currents of both machines(in A)
i_a=400.#Armature current(in A)
i_f1=4.#Field current of first machine(in A)
i_f2=3.#Field current of second machine(in A)
r_a=0.03#Resistance of armature of each mchine(in ohms)
P_acm=(i_a**2.)*r_a
P_i=V*I
I_g=i_a-I
P_acg=(I_g**2.)*r_a
P_f=(P_i-P_acm-P_acg)/2.
P_m=(V*i_a)+(V*i_f2)
P_fc=V*i_f2
L_t=P_fc+P_acm+P_f
P_o=P_m-L_t
n_m=(P_o/P_m)*100.
print '%s %.1f' %('(a)Efficiency of motor(in%)=',n_m)
P_og=V*I_g
P_fcu=V*i_f1
L_t1=P_f+P_fcu+P_acg
P_ig=P_og+L_t1
n_g=(P_og/P_ig)*100.
print '%s %.1f' %('(b)Efficiency of generator(in%)=',n_g)

(a)Efficiency of motor(in%)= 89.7
(b)Efficiency of generator(in%)= 90.2

Example E11 - Pg 180

In [7]:
#Caption: Calculate efficiency of motor
#Exa:8.11
import math
W=25.#Effective load on break drum(in kgf)
d=50.#Diameter of drum(in cm)
n=750.#Speed of the motor(in r.p.m)
I=25.#Current taken by motor(in A)
V=230.#Voltage of motor(in volts)
P_o=(2.*math.pi*n*W*9.81*(d/2.))/(60.*100.)
P_i=V*I
Eff=(P_o/P_i)*100.
print '%s %.2f' %('Efficiency of motor(in %)=',Eff)

Efficiency of motor(in %)= 83.75

Example E12 - Pg 180

In [8]:
#Caption:Find efficiency of motor
#Exa:8.12
import math
V=500.#Voltage of shunt motor(in volts)
I=10.#.Current taken by motor on no load(inA)
I_f=3.#Field Current(inA)
r_a=0.1#Armature resistance(in ohms)
P_i=100000.#Input power to motor(in watt)
P_nl=V*I
I_ao=I-I_f
P_acn=(I_ao**2.)*r_a
P_fcn=I_f*V
P_c=(P_nl)-P_acn-P_fcn
I_l=P_i/V
I_al=I_l-I_f
P_acl=(I_al**2.)*r_a
P_fcl=V*I_f
L_t=P_acl+P_fcl+P_c
Eff=((P_i-L_t)/P_i)*100.
print '%s %.2f' %('Efficiency of motor(in%) is=',Eff)

Efficiency of motor(in%) is= 91.12