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constant:

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v(i)=v(i)+acc*(vt-v(i));c endc % P-V busc q5=0; for i=1:5 q5=q5+ybus(5,i)*v(i); end q5=-imag(conj(v(5))*q5); tmp1=(p(5)-j*q5)/conj(v(5)); tmp2=0; for k=1:4 tmp2=tmp2+ybus(5,k)*v(k); endc vt=(tmp1-tmp2)/ybus(5,5); v(5)=abs(v(5))*vt/abs(vt);c % Calculate P and Qc for i=1:5 sm=0; for k=1:5 sm=sm+ybus(i,k)*v(k); end s(i)=conj(v(i))*sm; endc % The mismatchc delp=p-real(s)'; delq=q+imag(s)'; delpq=[delp(2:5);delq(2:4)]; del=max(abs(delpq)); indx=indx+1; if indx==1 pause endc endc 'GS LOAD 'FINAL

FLOW VOLTAGE

'FINAL ANGLES 'THE REAL POWERS IN 0.24])*100,pausec



CONVERGES IN MAGNITUDES IN EACH

ITERATIONS',indx,pause ARE',abs(v)',pause

DEGREE ARE',angle(v)'/d2r,pause BUS IN MW ARE',(real(s)+[0 0 0 0

'THE REACTIVE POWERS IN EACH BUS IN MVar ARE',(-imag(s)+[0 0 0 0 0.11])*100c

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   $ $   ( % Program nwtraph % THIS IS A NEWTON-RAPHSON PROGRAM % We have to solve three nonlinear equations given by % % g1=x1^2-x2^2+x3^2-11=0 % g2=x1*x2+x2^2-3x3-3=0 % g3=x1-x1*x3+x2*x3-6=0 % % Let us assume the initial conditions of x1=x2=x3=1 % % The Jacobian matrix is % % J=[2x1 -2x2 2x3 % x2 x1+2x2 -3 % 1-x3 x3 -x1+x2];c clear allc x=[1;1;1];c % The Newton-Raphson iterations starts herec del=1; indx=0; while del>1e-6c g=[x(1)^2-x(2)^2+x(3)^2-11;x(1)*x(2)+x(2)^2-3*x(3)3;x(1)-x(1)*x(3)+x(2)*x(3)-6]; J=[2*x(1) -2*x(2) 2*x(3);x(2) x(1)+2*x(2) -3;1-x(3) x(3) -x(1)+x(2)]; delx=-inv(J)*g; x=x+delx;c del=max(abs(g)); indx=indx+1;c endc 'NEWTON-RAPHSON SOLUTION ITERATIONS',indx,pausec

CONVERGES

IN



'FINAL VALUES OF x ARE',xc

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 c c c cc (c % Program % THIS IS THE NEWTON-RAPHSON POWER FLOW PROGRAMc clear allc d2r=pi/180;w=100*pi;c % The Ybus matrix isc [ybus,ych]=ybus;c g=real(ybus);b=imag(ybus);c % The given parameters and initial conditions arec

loadflow_nr

p=[0;-0.96;-0.35;-0.16;0.24]; q=[0;-0.62;-0.14;-0.08;-0.35]; mv=[1.05;1;1;1;1.02]; th=[0;0;0;0;0];c del=1;indx=0;c % The Newton-Raphson iterations starts herec while del>1e-6 for i=1:5 temp=0; for k=1:5 temp=temp+mv(i)*mv(k)*(g(i,k)-j*b(i,k))*exp(j*(th(i)-th(k))); end pcal(i)=real(temp);qcal(i)=imag(temp); endc % The mismatchesc delp=p-pcal'; delq=q-qcal';c % The Jacobian matrixc for i=1:4 ii=i+1; for k=1:4 kk=k+1; j11(i,k)=mv(ii)*mv(kk)*(g(ii,kk)*sin(th(ii)-th(kk))b(ii,kk)*cos(th(ii)-th(kk))); end j11(i,i)=-qcal(ii)-b(ii,ii)*mv(ii)^2; endc for i=1:4 ii=i+1; for k=1:4 kk=k+1; j211(i,k)=-mv(ii)*mv(kk)*(g(ii,kk)*cos(th(ii)-th(kk))b(ii,kk)*sin(th(ii)-th(kk))); end j211(i,i)=pcal(ii)-g(ii,ii)*mv(ii)^2; end j21=j211(1:3,1:4); j12=-j211(1:4,1:3); for i=1:3 j12(i,i)=pcal(i+1)+g(i+1,i+1)*mv(i+1)^2; end j22=j11(1:3,1:3); for i=1:3 j22(i,i)=qcal(i+1)-b(i+1,i+1)*mv(i+1)^2; end

jacob=[j11 j12;j21 j22];c delpq=[delp(2:5);delq(2:4)];c corr=inv(jacob)*delpq;c th=th+[0;corr(1:4)];c mv=mv+[0;mv(2:4).*corr(5:7);0];c del=max(abs(delpq));c indx=indx+1;c endc preal=(pcal+[0 0 0 0 0.24])*100;c preac=(qcal+[0 0 0 0 0.11])*100;c % Power flow calculationsc for i=1:5 v(i)=mv(i)*exp(j*th(i)); endc for i=1:4 for k=i+1:5 if (ybus(i,k)==0) s(i,k)=0;s(k,i)=0; c(i,k)=0;c(k,i)=0; q(i,k)=0;q(k,i)=0; cur(i,k)=0;cur(k,i)=0; else cu=-(v(i)-v(k))*ybus(i,k); s(i,k)=-v(i)*cu'*100; s(k,i)=v(k)*cu'*100; c(i,k)=100*abs(ych(i,k))*abs(v(i))^2; c(k,i)=100*abs(ych(k,i))*abs(v(k))^2; cur(i,k)=cu;cur(k,i)=-cur(i,k); end end endc pwr=real(s); qwr=imag(s);c q=qwr-c;c % Power lossc

ilin=abs(cur);c

c

for i=1:4 for k=i+1:5 if (ybus(i,k)==0) pl(i,k)=0;pl(k,i)=0; ql(i,k)=0;ql(k,i)=0; else z=-1/ybus(i,k); r=real(z); x=imag(z); pl(i,k)=100*r*ilin(i,k)^2;pl(k,i)=pl(i,k); )=100*x*ilin(i,k)^2;ql(k,i)=ql(i,k); end end endc

 c

ql(i,k