# Chapter10-The Synchronous Generator¶

## Ex9-pg407¶

In :
## Example10_9_pg407.sce
## To find the field excitation required
## Theory of Alternating Current Machinery by Alexander Langsdorf
## First Edition 1999, Thirty Second reprint
## Tata McGraw Hill Publishing Company
## Example in Page 407

import math

## Given data
va = 2500e+3; ## Volt Ampere rating of machine, VA
vll = 6600.; ## Line to Line voltage in volts
N = 3000.; ## Number of turns
f = 50.; ## Frequency in Hz
slots = 60.;
n = 4.;
poles =2.;
r = 0.073;
x = 0.87;
pf1 = 0.8;
pf2 = 1.;
pf3 = 0.;
phase = 3.;

## Calculations

## For 80% power factor

phi = math.acos(pf1);
V = vll / math.sqrt(3.);
I = round(va / (phase*V)) ;
IR_a = I*r;
IX_a = I*x;
V_vec = complex(V*math.cos(phi) ,V*math.sin(phi));
E = V_vec + complex(I*r , I*x);
E_mag = math.sqrt((E.real)**2+ (E.imag)**2)
conductors = slots * n;
turns = conductors/2;
N_p = turns / (poles * phase);
q = slots / (poles * phase);
gama = 360 / slots;
gama = gama*math.pi/2;
k_b1 = (math.sin(q*gama/2))/(q*math.sin(gama/2));
k_p1 = 1;
A = (2.*math.sqrt(2)/math.pi)*phase*k_b1*k_p1*N_p*I;
cos_alpha = ((E.real)/E_mag);
sin_alpha = ((E.imag)/E_mag);
alpha = math.acos(cos_alpha);
F_r_mag = 17500.;
F_r = complex(F_r_mag*math.cos(alpha + math.pi/2.) , F_r_mag*math.sin(alpha + math.pi/2));
F = F_r - A;
F_mag = math.sqrt((F.real)**2+ (F.imag)**2)
print('The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4450 volts;');
oc_volt = 4450.;
regulation80 = ((oc_volt - V)/V)*100.;
print'%s %.2f %s'%("\n\nThe regulation for 80%% power factor is  ", regulation80,"%");

## For power factor 1.0

phi = math.acos(pf2);
V_vec = complex(V*math.cos(phi) ,V*math.sin(phi));
E = V_vec + complex(I*r , I*x);
E_mag = math.sqrt((E.real)**2+ (E.imag)**2)
cos_alpha = ((E.real)/E_mag);
sin_alpha = ((E.imag)/E_mag);
alpha = math.acos(cos_alpha);
F_r_mag = 16500.;
F_r =complex(F_r_mag*math.cos(alpha + math.pi/2.) , F_r_mag*math.sin(alpha + math.pi/2));
F = F_r - A;
F_mag = math.sqrt((F.real)**2 + (F.imag)**2);
print('The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4150 volts;');
oc_volt = 4150.;
regulation100 = ((oc_volt - V)/V)*100.;
print'%s %.2f %s'%("\n\nThe regulation for 100%% power factor is  ", regulation100,"%");

## For power factor 0

phi = math.acos(pf3);
E = V + I*(x);
F_r_mag = 18000.;
F_r = F_r_mag + 11300.;
print'%s %.2f %s'%("\nThe value F_R corresponding to Fig 10-12 is ",F_r," Volts\n");
print('The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4500 volts;');
oc_volt = 4500.;
regulation0 = ((oc_volt - V)/V)*100.;
print'%s %.2f %s'%("\n\nThe regulation for 0%% power factor is  ", regulation0,"%");

## Result
##  The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4450 volts;
##
## The regulation for 80% power factor is 16.8 %
## The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4150 volts;
##
## The regulation for 100% power factor is 8.9 %
## The value F_R corresponding to Fig 10-12 is 29300 Volts
##
## The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4500 volts;
##
## The regulation for 0% power factor is 18.1 %

The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4450 volts;

The regulation for 80%% power factor is   16.78 %
The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4150 volts;

The regulation for 100%% power factor is   8.91 %

The value F_R corresponding to Fig 10-12 is  29300.00  Volts

The open-circuit voltage corresponding to this excitation, determined from Fig. 10-12, is 4500 volts;

The regulation for 0%% power factor is   18.09 %


## Ex10-pg413¶

In :
## Example10_10_pg413.sce
## Regulation by emf method
## Theory of Alternating Current Machinery by Alexander Langsdorf
## First Edition 1999, Thirty Second reprint
## Tata McGraw Hill Publishing Company
## Example in Page 413

import math

## Given data
va = 2500e+3; ##Volt-Ampere rating of the transformer, VA
vll = 6600.; ## Line to Line voltage in volts
r = 0.073; ## Resistance in Ohms
pf1 = 0.8;
phase = 3.;
vref = 3640.; ## Reference for voltage in volts
iref = 340.; ## Reference for current in Amperes

## Calculations
z_s = vref/iref;
x_s = math.sqrt(z_s**2 - r**2);
print('By Referring to Fig. 10-19');
phi = math.acos(pf1);
V = vll / math.sqrt(3.);
I = round(va / (phase*V)) ;
V_vec = complex(V*math.cos(phi) ,V*math.sin(phi));
E = V_vec + complex(I*r , I*x_s);
E_mag = math.sqrt((E.real)**2+ (E.imag)**2)

Regulation = ((E_mag - V)/V)*100;

print'%s %.2f %s'%(" Regulation is found to be ",Regulation," %%");

## Result
## By Referring to Fig. 10-19
## Regulation is found to be 45.73 %

By Referring to Fig. 10-19
Regulation is found to be  45.73  %%


## Ex12-pg416¶

In :
## Example10_12_pg416.sce
## Regulation by mmf method
## Theory of Alternating Current Machinery by Alexander Langsdorf
## First Edition 1999, Thirty Second reprint
## Tata McGraw Hill Publishing Company
## Example in Page 416

import math

## Given data
va = 2500e+3; ## Volt Ampere rating of the transformer, VA
vll = 6600.; ## Line to Line voltage, Volts
r = 0.073; ## Resistance in Ohms
x = 0.87; ## Reactance in Ohms
pf1 = 0.8;
phase = 3.;

## Calculations

phi = math.acos(pf1);
V = vll / math.sqrt(3.);
I = round(va / (phase*V)) ;
IR_a = I*r;
IX_a = I*x;
V_vec = complex(V*math.cos(phi) ,math.sin(phi));
E = V_vec + IR_a;
E_mag = math.sqrt((E.real)**2+ (E.imag)**2)
F_r1_mag = 16500.;
cos_alpha = ((E.real)/E_mag);
sin_alpha = ((E.imag)/E_mag);
alpha = math.acos(cos_alpha);
F_r1 = complex(F_r1_mag*math.cos(math.pi/2 + alpha) , F_r1_mag*math.sin(math.pi/2. + alpha));
A_plus_Ax = 10000.;
F = F_r1 - (A_plus_Ax);
F_mag = math.sqrt((F.real)**2+ (F.imag)**2)
print'%s %.2f %s'%("\n Magnitude of F is ",F_mag," amp-turns per pole");
print('This magnitude of F corresponds to Open-circuit voltage of 4330 Volts');
oc_volt = 4330.;
regulation = ((oc_volt - V)/V)*100;
print'%s %.2f %s'%("\nRegulation is found to be ", regulation,"");

## Result
##  Magnitude of F is 23866.02 amp-turns per pole
## This magnitude of F corresponds to Open-circuit voltage of 4330 Volts
##
## Regulation is found to be 13.6 %

 Magnitude of F is  19295.46  amp-turns per pole
This magnitude of F corresponds to Open-circuit voltage of 4330 Volts

Regulation is found to be  13.63