Newton Raphson Matlab Code

NEWTON RAPHSON MATLAB CODE :clc clear all; data=[1 2 0.01008 1 3 0.00744 2 4 0.00744 3 4 0.01272

0.05040 0.05125; 0.03720 0.03875; 0.03720 0.03875; 0.06360 0.06375];

fb=data(:,1); tb=data(:,2); r=data(:,3); x=data(:,4); y2=data(:,5); z=r+(1i*x); y=1./z; nbus=max(max(fb),max(tb)); nbranch=length(fb); Y=zeros(nbus,nbus); % Ybus OFF Diagonal Elements for k=1:nbranch Y(fb(k),tb(k)) = Y(fb(k),tb(k))-y(k); Y(tb(k),fb(k)) = Y(fb(k),tb(k)); end % Ybus Diagonal Elements for m =1:nbus for n =1:nbranch if fb(n) == m Y(m,m) = Y(m,m) + y(n)+(1i*y2(n)); elseif tb(n) == m Y(m,m) = Y(m,m) + y(n)+(1i*y2(n)); end end end disp('Y-bus matrix of given system = ') disp(Y)

% bus no.| V | del| Pg | Qg | Pd | Qd busdata= [1 1.00 0 0 0 50 30.99; 2 1.00 0 0 0 170 105.35; 3 1.00 0 0 0 200 123.94; 4 1.02 0 318 0 80 49.58]; BMVA=100; busno=busdata(:,1); v=busdata(:,2); Vb=v; Del=busdata(:,3); Pg=busdata(:,4); Qg=busdata(:,5); Pd=busdata(:,6); Qd=busdata(:,7); Psch=(Pg-Pd)./BMVA; Qsch=(Qg-Qd)./BMVA; n=input('enter the no. of iteration = ' ); %to find the type of bus

%type-- 1-slack 2-PQ 3-PV type=zeros(nbus,1); type(1)=1; for c=2:nbus if Pg(c)==0 if Pd(c)~=0 if Qd(c)~=0 type(c)=2; end end end if Pg(c)~=0 type(c)=3; end end type; pq=find(type==2); npq=length(pq); pv=find(type==3); npv=length(pv); nou=(2*npq)+npv;

for iter=1:n V=Vb.*exp(1i*Del); Pcal=zeros(nbus,1); Qcal=zeros(nbus,1); for k=2:nbus soi=0; for j=1:nbus; if j~=k soi=soi+(V(j,1)*Y(k,j)); end soi; if type(k)==2 || type(k)==3 Pcal(k,1) = real(conj(V(k,1))*(soi + Y(k,k)*V(k,1))); end if type(k)==2 Qcal(k,1) = -imag(conj(V(k,1))*(soi + Y(k,k)*V(k,1))); end end end Pcal; Qcal; for x=1:npq y=pq(x); QschM(x,1)=Qsch(y); QcalM(x,1)=Qcal(y); end delP=Psch(2:nbus)-Pcal(2:nbus); delQ=QschM-QcalM; MM=[delP;delQ]; %Mismatch Matrix %to find J1 J1=zeros(nbus-1); for a=1:(nbus-1) m=a+1;

for b=1:(nbus-1) l=b+1; if m==l J1(a,b)=-Qcal(m)-imag(conj(V(m))*V(l)*Y(m,l)); else J1(a,b)=imag(conj(V(m)*V(l)*Y(m,l))); end end end J1; %to find J2 j2=zeros(nbus-1,nbus-1-npv); for a=1:(nbus-1) m=a+1; for b=1:(nbus-1-npv) l=pq(b); jjj=0; J2(a,b)=real(V(m)*V(l)*(Y(m,l)))/abs(V(l)); if l==m J2(a,b)=(2*J2(a,b))+real(soi); end end end J2; %to find J3 J3=zeros(nbus-1-npv,nbus-1); for a=1:(nbus-1-npv) m=pq(a); for b=1:nbus-1 l=b+1; if l==m for l=1:nbus J3(a,b)=J3(a,b)+real(conj(V(m))*V(l)*Y(m,l)); end J3(a,b)=J3(a,b)-real(conj(V(m))*V(m)*Y(m,m)); else J3(a,b)=-real(conj(V(m))*V(l)*Y(m,l)); end end end J3; %to find J4 J4=zeros(nbus-1-npv,nbus-1-npv); for a=1:(nbus-1-npv) m=pq(a); for b=1:(nbus-1-npv) l=pq(b); if l==m J4(a,b)=Qcal(m)-((abs(V(m)))^2)*imag(Y(m,m)); else J4(a,b)=(-imag(conj(V(m))*V(l)*Y(m,l)))/V(l); %(J1(m,l))/V(l); end end end J4; J=[J1,J2;J3,J4]; IM=(inv(J))*MM; delV=zeros(nbus,1);

%Improvement Matrix

delD=zeros(nbus,1); delD(2:nbus)=IM(1:(nbus-1)); for t=1:npq r=pq(t); delV(r)=IM((nbus-1)+t); end Vb=Vb+delV; Del=Del+(delD.*(180/pi)); fprintf('iteration no. = ') disp(iter) disp('jacobian matrix = ') disp(J) disp('Mismatch Matrix = ') disp(MM) disp('Improvement Matrix = ') disp(IM) disp('bus voltages = ') disp(Vb) disp('voltage angle del (in degree) = ') disp(Del) end

OUTPUT OF NR METHOD :Y-bus matrix of given system = 8.9852 -44.8360i -3.8156 +19.0781i -5.1696 +25.8478i 0.0000 + 0.0000i -3.8156 +19.0781i 8.9852 -44.8360i 0.0000 + 0.0000i -5.1696 +25.8478i -5.1696 +25.8478i 0.0000 + 0.0000i 8.1933 -40.8638i -3.0237 +15.1185i 0.0000 + 0.0000i -5.1696 +25.8478i -3.0237 +15.1185i 8.1933 -40.8638i

enter the no. of iteration = 2 iteration no. =

1

jacobian matrix = 45.4429

0 -26.3648 9.7771

0 41.2687 -15.4209

0

0 8.1933

-26.3648 -15.4209 42.5147 -5.2730 -3.0842 -9.0886

0 5.2730 44.2290

0 -8.2537 3.0842

bus voltages = 1.0000 0.9834 0.9710

0

0 40.4590

1.0200

voltage angle del (in degree) = 0 -0.9290 -1.7959 1.5162

iteration no. =

2

jacobian matrix = -14.9906

0 -18.7126 -57.2964

0 -24.7429 -15.2179

0

0 52.4889

-18.7126 -15.2179 42.5147 -18.9957 1.2937 -29.9292

0 12.6543 101.7131

0 -17.8524 -5.4912

bus voltages = 1.0000 0.7630 -0.0428 1.0200

voltage angle del (in degree) = 0 45.2801 -108.0489 -56.6632

0

0 101.7930