# Chapter 45 Load Frquency Control,Load sheeding and Static relay¶

## Example 45_1 pgno:944¶

In :
from math import sqrt
v=460;
i=200;
r=1.73*v*i/1e3;
r=round(r*10)/10;
p=120;
c=p/r;#the difference in result is due to erroneous calculation in textbook.
s=sqrt(1-(c**2))
rr=r*s;
print"the power factor=\nthe rating=kVA\n the kVAr of system=kVA",c,r,rr
print"the difference in result is due to erroneous calculation in textbook."

the power factor=
the rating=kVA
the kVAr of system=kVA 0.753768844221 159.2 104.616633477
the difference in result is due to erroneous calculation in textbook.


## Example 45_2 pgno:944¶

In :
from math import sin,cos,acos,sqrt
r1=75;
c1=.8;
p1=r1*c1;
rr1=r1*(sin(acos(c1)));
r2=150;
c2=.8;
p2=r2*c2;
rr2=r2*(sin(acos(c2)));
r3=50;
c3=1;
p3=r3*c3;
rr3=r3*(sin(acos(c3)));
rr=-rr1+rr2+rr3;
p=p1+p2+p3;
r=sqrt(p**2+rr**2);
r=round(r)
j=p/r;
print"the power factor of the substation=",round(j,2)

the power factor of the substation= 0.98


## Example 45_3 pgno:945¶

In :
from math import sin,cos,acos,sqrt
c1=.8;
p1=120;
r1=p1/c1;
rr1=r1*(sin(acos(c1)));
c2=.9;
r2=p1/c2;
rr2=r2*(sin(acos(c2)));
rr2=round(rr2);
rr=rr1-rr2;
print"the kVAr of capacitors = kVA",rr

the kVAr of capacitors = kVA 32.0


## Example 45_4 pgno:946¶

In :
k=100.;
s=400.;
pf=1-((k/s)**2);
print"the power factor is ",pf
print"the difference in result is due to erroneous calculation in textbook."

the power factor is  0.9375
the difference in result is due to erroneous calculation in textbook.


## Example 45_5 pgno:946¶

In :
k=12.
m=72.;
pf=1-((k/m)**2);
print"the power factor is (lag)",round(pf,2)

the power factor is (lag) 0.97


## Example 45_6 pgno:946¶

In :
from math import sin,cos,acos,sqrt,tan,atan

n1=.89;
h1=150;
c1=.9;
h2=200;
n2=.9;
c2=.8;
h3=500;
n3=.93;
c3=.707;
p4=100;
p1=h1*.746/n1;
p2=h2*.746/n2;
p3=h3*.746/n3;
rr1=p1*(tan(acos(c1)));
rr2=p2*(tan(acos(c2)));
rr3=p3*(tan(acos(c3)));
rr4=0;
rr=rr1+rr2-rr3+rr4;
p=p1+p2+p3+p4;
c=rr/p;
j=cos(atan(c));
j=round(j*1000)/1000;
print"the Power Factor of the combined sub-station= leading",j

the Power Factor of the combined sub-station= leading 0.965