AIM:
To determine the power flow analysis using Newton – Raphson method.
SOFTWARE REQUIRED:
MATLAB
THEORY:
The Newton Raphson method of load flow analysis is an iterative method which
approximates the set of non-linear simultaneous equations to a set of linear simultaneous equations
using Taylor’s series expansion and the terms are limited to first order approximation.
The load flow equations for Newton Raphson method are
non-linear equations in terms of
real and imaginary part of bus voltages.
EXERCISE:
1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a
total shunt admittance of j0.02 pu. The specified quantities at the buses are given below :
2. Verify the result using MATLAB.
PROGRAM:
RESULT:
Thus the power flow analysis using Newton – Raphson method determined.
To determine the power flow analysis using Newton – Raphson method.
SOFTWARE REQUIRED:
MATLAB
THEORY:
The Newton Raphson method of load flow analysis is an iterative method which
approximates the set of non-linear simultaneous equations to a set of linear simultaneous equations
using Taylor’s series expansion and the terms are limited to first order approximation.
The load flow equations for Newton Raphson method are
non-linear equations in terms of
real and imaginary part of bus voltages.
EXERCISE:
total shunt admittance of j0.02 pu. The specified quantities at the buses are given below :
PROGRAM:
%NEWTON RAPHSON METHOD
clc;
gbus = [1 2.0 1.0 0.0 0.0
2 0.0 0.0 0.5 1.0
3 1.5 0.6 0.0 0.0];
ybus = [5.882-j*23.528 -2.941+j*11.764 -2.941+j*11.764
-2.941+j*11.764 5.882-j*23.528 -2.941+j*11.764
-2.941+j*11.764 -2.941+j*11.764 5.882-j*23.528];
t= 0.001
v1=1.04+j*0;
v2=1+j*0;
v3=1.04+j*0;
del3=angle(v3);
del1=angle(v1);
del2=angle(v2);
%abs(ybus(2,1))
%abs(v2)
for i=1:10
p2=(abs(v2)*abs(v1)*abs(ybus(2,1))*cos((angle(ybus(2,1)))+del1-
del2))+abs(v2)*
abs(v2)*abs(ybus(2,2))*cos((angle(ybus(2,2))))+(abs(v2)*abs(v3)*
abs(ybus(2,3))*cos((angle(ybus(2,3))+del3-del2));
q2=-(abs(v2)*abs(v1)*abs(ybus(2,1))*sin((angle(ybus(2,1)))+del1-del2))-
abs(v2)*abs(v2)*abs(ybus(2,2))*sin((angle(ybus(2,2))))-(abs(v2)*abs(v3)*
abs(ybus(2,3))*sin((angle(ybus(2,3)))+del3-del2));
p3=(abs(v3)*abs(v1)*abs(ybus(3,1))*cos((angle(ybus(3,1)))+del1-
del3))+abs(v3)*abs(v3)*abs(ybus(3,3))*cos((angle(ybus(3,3))))+(abs(v2)*abs(v3)*
abs(ybus(3,2))*cos((angle(ybus(3,2)))+del2-del3));
delp20=gbus(2,4)-gbus(2,2)-p2;
delp30=gbus(3,4)-gbus(3,2)-p3;
delq20=gbus(2,5)-gbus(2,3)-q2;
J(1,1)=(abs(v2)*abs(v1)*abs(ybus(2,1))*sin((angle(ybus(2,1)))+del1-
del2))+(abs(v2)*abs(v3)*abs(ybus(2,3))*sin((angle(ybus(2,3)))+del3-
del2));
J(1,2)=-(abs(v2)*abs(v3)*abs(ybus(2,3))*sin((angle(ybus(2,3)))+del3-
del2));
J(1,3)=(abs(v1)*abs(ybus(2,1))*cos((angle(ybus(2,1)))+del1-del2))+2*(abs(v2)*abs(ybus(2,2))*cos((angle(ybus(2,2))))+(abs(v3)*abs(ybus(2,3)
)*
cos((angle(ybus(2,3)))+del3-del2));
J(2,1)=-(abs(v3)*abs(v2)*abs(ybus(3,2))*sin((angle(ybus(3,2)))+del2-
del3));
J(2,2)=(abs(v3)*abs(v1)*abs(ybus(3,1))*sin((angle(ybus(3,1)))+del1-
del3))+(abs(v3)*abs(v2)*abs(ybus(3,2))*sin((angle(ybus(3,2)))+del2-
del3));
J(2,3)=(abs(v3)*abs(ybus(3,2))*cos((angle(ybus(3,2)))+del2-del3));
J(3,1)=(abs(v2)*abs(v1)*abs(ybus(2,1))*cos((angle(ybus(2,1)))+del1-
del2))-(abs(v2)*abs(v3)*abs(ybus(2,3))*cos((angle(ybus(2,3)))+del2-
del3));
J(3,2)=(abs(v2)*abs(v3)*abs(ybus(2,3))*cos((angle(ybus(2,3)))+del2-
del3));
J(3,3)=-(abs(v2)*abs(ybus(2,1))*sin((angle(ybus(2,1)))+del1-
del2))-2*(abs(v2)*abs(ybus(2,2))*sin((angle(ybus(2,2))))-
(abs(v3)*abs(ybus(2,3))*
sin((angle(ybus(2,3)))+del3-del2));
end
J
inv(J);
A=[del2;del3;abs(v2)];
delA0=[delp20;delp30;delq20];
delA1=inv(J)*delA0;
delA1;
b0=abs(v2);
A1=[del2;del3;b0]+delA1;
A1-delA0;
if((A1-delA0)<=t)
break;
del2=A1(1,1);
del3=A1(2,1);
abs(v2)=A1(3,1);
end
A1
RESULT:
Thus the power flow analysis using Newton – Raphson method determined.
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