# Chapter 5: Direct-Current Generators¶

## Example 5.1, Page 290¶

In :
#Variable declaration
P1=2;
P2=4.;
S=10.;#no. of slots

#Calculations&Results
S_p1=S/P1;#slots per pole
y1=int(S_p1);#coil pitch in slots
S_s1=180./S_p1;#slot span
C_p1=S_s1*y1;#coil pitch(electrical)
print 'coil pitch for 2-pole winding (electrical)=%.f degrees'%C_p1
S_p2=S/P2;#slots per pole
S_s2=180./S_p2;#slot span
y2=int(S_p2);#coil pitch in slots
C_p2=S_s2*y2;#coil pitch(electrical)
print 'coil pitch for 4-pole winding(electrical)=%.f degrees'%C_p2

coil pitch for 2-pole winding (electrical)=180 degrees
coil pitch for 4-pole winding(electrical)=144 degrees


## Example 5.2, Page 297¶

In :
#Variable declaration
C = 35.  #no. of segments
P = 6.   #no. of poles

#Calculations
yc1 = (C+1)/(P/2)
yc2 = (C-1)/(P/2)

#Result
print "The required windings are %d and %.2f"%(yc1,yc2)

The required windings are 12 and 11.33


## Example 5.3, Page 301¶

In :
import math

#Variable declaration
C=24.;#no. of coils
N_c=18.;#no. of turns per coil
P=2.;#no. of pole

#Calculations&Results
Z=2*C*N_c;#total armature conductors
a=2.;#no. of parallel paths
L=0.2;#effective length of machine(in meter)
A_p=(2*math.pi*r*L)/P;#actual pole area
A_e=A_p*0.8;#effective pole area
B=1.;#flux density per pole(in Tesla)
Phy=round(B*A_e,2);#effective flux per pole
K_a=round((Z*P)/(2*math.pi*a),2);#machine constant
E_a=K_a*Phy*W_m;
print '(a) induced emf in armature winding  (in Volts)=%.1f'%E_a
E_coil=E_a/(C/a);
print '(b) induced emf per coil  (in Volts)=%.2f'%E_coil
E_turn=E_coil/N_c;
print '(c) induced emf per turn  (in Volts)=%.2f'%E_turn
E_cond=E_turn/2;
print '(d) induced emf per conductor  (in Volts)=%.3f'%E_cond

(a) induced emf in armature winding  (in Volts)=1259.6
(b) induced emf per coil  (in Volts)=104.97
(c) induced emf per turn  (in Volts)=5.83
(d) induced emf per conductor  (in Volts)=2.916


## Example 5.4, Page 304¶

In :
#Variable declaration
K_a=137.51;#Refer to exa:5.3
Phy=0.05;#flux per pole (Refer to exa:5.3)
E_a=1259.6;#induced emf (Refer to exa:5.3)
I=25;#current in the machine (in Amperes)
a=2;#no. of parallel paths

#Calculations&Results
I_cond=I/a;
print '(a) current in each conductor (in Amperes)=%.1f'%I_cond
T_d=K_a*Phy*I;
print '(b) torque developed by machine (in Newton-meter)=%.2f'%T_d
P_d=E_a*I;
print '(c) Power developed (in Watts)=%.f'%P_d

(a) current in each conductor (in Amperes)=12.0
(b) torque developed by machine (in Newton-meter)=171.89
(c) Power developed (in Watts)=31490


## Example 5.5, Page 321¶

In :
import math

#Variable declaration
N_m=600.;#speed of rotor (in rpm)
R_a=0.01;#armature resistance (in ohms)
R_fw=30.;#feild winding resistance(in ohms)
V_f=120.;# voltage of external source (in volts)
N_f=500.;#no. of turns per pole
P_r=10000;#in watts
V_t=240.;#terminal voltage (in volts)
P_o=240*10**3;#rated power (in watts)

#Calculations&Results
I_a=I_L;#armature current
E_afl=V_t+(I_a*R_a);#refer to eqn:5.27
print '(a) induced emf at full load (in Volts)=%.f'%E_afl
P_d=E_afl*I_a;
print '(b) power developed (in watts)=%.f'%P_d
W_m=(2*math.pi*N_m)/60;#angular velocity (Refer to Eqn:5.5&5.6)
T_d=P_d/W_m;
print '(c) torque developed (in Newton-meter)=%.2f'%T_d
P_inm=P_d+P_r;#mechanical power input
T_s=P_inm/W_m;
print '(d) Applied torque (in Newton-meter)=%.2f'%T_s
#Refer fig:5.21 (magnetization curve)
I_f=2.5;#effective feild current
mmf=(2.5*N_f)+(0.25*I_a);#total  mmf
I_fa=mmf/N_f;#actual feild current
P_in=P_inm+(V_f*I_fa);#total power input
Eff=(P_o/P_in)*100;
print '(e) efficiency (%%)=%.1f'%Eff
R_f=V_f/I_fa;
R_fx=R_f-R_fw;
print '(f) external resistance in feild winding (in ohms)=%.f'%R_fx
VR=((266-V_t)/V_t)*100;#Refer to fig:5.21
print '(g) voltage regulation (%%)=%.2f'%VR

(a) induced emf at full load (in Volts)=250
(b) power developed (in watts)=250000
(c) torque developed (in Newton-meter)=3978.87
(d) Applied torque (in Newton-meter)=4138.03
(e) efficiency (%)=92.2
(f) external resistance in feild winding (in ohms)=10
(g) voltage regulation (%)=10.83


## Example 5.6, Page 327¶

In :
#Variable declaration
R_fw=30;#in ohms
R_a=0.2;#in ohms
N_f=200;#turns/pole
P_r=1200;#in Watts
I_L=100;
D_mmf=0.5*I_L;#demagnetizing mmf
#Refer to fig:5.26 (magnetization curve)
I_f=3.5;#field current in Amperes

#Calculations&Results
R_f=V_nL/I_f;
R_fx=R_f-R_fw;
print 'R_fx (in ohms)=%.2f'%R_fx
#First iteration:
#Assume
E_a=170;
V_t1=E_a-103.5*R_a;
#Second iteration:
I_f2=V_t1/R_f;#actual field current
I_fe2=(N_f*I_f2-D_mmf)/N_f;
#Refer to fig:5.26
E_a2=165;
V_t2=E_a2-103.07*R_a;
#third iteration
I_f3=V_t2/R_f;#actual field current
I_fe=(N_f*I_f-D_mmf)/N_f;
#Refer to fig:
E_a3=163;
V_t3=E_a3-102.97*R_a;
V_t=V_t3;
print '(a) Terminal voltage (in Volts)=%.2f'%V_t
I_f=V_t/R_f;
E_a=E_a3;
VR=(V_nL-V_t)*100/V_t;
print '(b) Voltage Regulation (%%)=%.2f'%VR
P_o=V_t*I_L;#power output
P_cu=R_a*(I_L+I_f)**2+R_f*I_f**2;#copper loss
P_d=P_o+P_cu;#power developed
P_in=P_d+P_r;#power input
Eff=P_o*100/P_in;
print '(c) Efficiency (%%)=%.2f'%Eff

R_fx (in ohms)=18.57
(a) Terminal voltage (in Volts)=142.41
(b) Voltage Regulation (%)=19.38
(c) Efficiency (%)=79.22


## Example 5.7, Page 331¶

In :
#Variable declaration
V_o=240;#bus bar voltage (in Volts)
I_d=0;
I_s=300;#current in series winding (in Amperes)
R_s=0.03;#resistance of series feild winding(in ohms)
R_a=0.02;#resistance of armature winding(in ohms)
R_fe=0.25;#resistance of feeder (in ohms)
#Refer to eqn:5.33
I_a=I_s;

#Calculations
E_a=0.4*I_s;#induced emf
V_d=I_s*(R_s+R_a+R_fe);#voltage drop (in Volts)
V_t=V_o+E_a-V_d;

#Result
print ' voltage between far end of feeder and bus bar  (in Volts)=%.f'%V_t

 voltage between far end of feeder and bus bar  (in Volts)=270


## Example 5.8, Page 335¶

In :
#Variable declaration
Vt = 240  #V
Il = 100  #A
Is = 3   #shunt field current,A
Ra = 50*10**-3 #armature resistance,ohms
Rs = 10*10**-3 #series field resistance,ohms
Rd = 40*10**-3 #field diverter resistance,ohms
Pr = 2*10**3   #rotational loss,W
Rfe = 30*10**-3 #ohms

#Calculations
Po = Vt*Il   #W
If = 3     #A
Ia = Il+If  #A
Is = Rd/(Rd+Rs)*Il  #A
Id = Il-Is
Ea = Vt+(Il*Rfe)+(Is*Rs)+(Ia*Ra)  #V
Vf = Ea-(Ia*Ra)    #V
Rf = Vf/3  #ohms
#Copper losses
Pa = Ia**2*Ra   #armature loss
Pse = Is**2*Rs  #series filed loss
Psf = If**2*Rf  #shunt field loss
Pdr = Id**2*Rd  #diverter resistance loss
Pfr = Il**2*Rfe #feeder resistance loss
Pcu = Pa+Pse+Psf+Pdr+Pfr  #total copper loss
Pd = Po+Pcu  #power developed
Pin = Pd+Pr  #power input
N = Po/Pin*100

#Result
print "Efficiency = %.2f %%"%N

Efficiency = 86.82 %


## Example 5.9, Page 340¶

In :
import math

#Variable declaration
R_a=50*10**-3;#armature resistance (in ohms)
R_s=20*10**-3;#series field resistance
R_sh=40;#shunt field resistance
P_rot=2000;#rotational loss (in watts)
V=120;#voltage (in vollts)

#Calculations
I_f=V/R_sh;#shunt field current
#Refer toeqn 5.49
I_Lm=math.sqrt((P_rot+(R_a+R_s+R_sh)*(I_f**2))/(R_a+R_s));
P_o=I_Lm*V;#power output at max efficiency
P_cu=(((I_Lm**2)*(R_a+R_s))+((I_f**2)*R_sh));#total copper loss
P_d=P_o+P_cu;#Power developed at max efficiency
P_in=P_d+P_rot;
Eff=(P_o/P_in)*100;

#Result
print 'Max efficiency of generator(%%)=%.2f'%Eff

Max efficiency of generator(%)=82.36