SIMULATION LAB
M.Tech – E.P.S.
( 1 ) Y-BUS FORMATION
% THE Y-BUS FORMATION clear; clc; basemva=100; nbus=5; % lp lq r x ysh tap linedata =[ 1 2 0.02 0.06 0.03 1 1 3 0.08 0.24 0.025 1 2 3 0.06 0.18 0.02 1 2 4 0.06 0.18 0.02 1 2 5 0.04 0.12 0.015 1 3 4 0.01 0.03 0.01 1 4 5 0.08 0.24 0.025 1 ]; nline=length(linedata(:,1)); j=sqrt(-1); i=sqrt(-1); for k=1:nline lp(k)=linedata(k,1); lq(k)=linedata(k,2); r(k)=linedata(k,3); x(k)=linedata(k,4); ysh(k)=linedata(k,5); a(k)=linedata(k,6); z(k)= r(k)+j*x(k); y(k)=1/z(k); end ybus=zeros(nbus,nbus); yln =zeros(nbus,nbus); % PI METHOD FOR OFF-NOMINAL ADMITTANCE OF TRANSFORMER for k=1:nline ylp(k)=[1/(a(k)^2)-1/a(k)]*y(k); ylq(k)=[1-1/a(k)]*y(k); y(k)=y(k)/a(k); end for k=1:nline ybus(lp(k),lq(k))=ybus(lp(k),lq(k))-y(k); ybus(lq(k),lp(k))=ybus(lp(k),lq(k)); ybus(lp(k),lp(k))=ybus(lp(k),lp(k))+y(k)+ylp(k)+j*ysh(k); ybus(lq(k),lq(k))=ybus(lq(k),lq(k))+y(k)+ylq(k)+j*ysh(k); end ybus
J.N.T.U. College of Engineering, Anantapur
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SIMULATION LAB
M.Tech – E.P.S.
OUTPUT :-
Y-BUS = 6.2500 -18.695i
-5.000 + 15.000i
-1.250 + 3.750i
-5.0000 +15.000i
10.833-32.415i
-1.667 + 5.000i
-1.2500 + 3.750i
-1.667 + 5.000i
0
-1.667+ 5.000i
0
-2.500 + 7.500i
12.9167 -38.695i -10.000 +30.000i 0
0 -1.6667 + 5.000i
0 -2.500 + 7.500i
-10.000 +30.000i
0
12.9167 -38.695i
-1.250 + 3.750i
-1.250 + 3.750i
3.750 -11.210i
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SIMULATION LAB
M.Tech – E.P.S.
( 2 ) GAUSS-SEIDEL METHOD % THE Y-BUS FORMATION clear; clc; basemva=100; % n code v delta Pg Qg Pd Qd Qmin busdata = [ 1 0 1.04 0 0 0 0 0 0 2 1 1.04 0 100 0 50 0 20 3 2 1.00 0 0 0 100 -50 0 4 2 1.00 0 0 0 -30 10 0 0]; % lp lq r x ysh tap linedata =[ 1 2 0.05 0.15 0.0 1 1 3 0.1 0.3 0.0 1 2 3 0.15 0.45 0.0 1 2 4 0.1 0.3 0.0 1 3 4 0.05 0.15 0.0 1]; nline=length(linedata(:,1)); j=sqrt(-1); i=sqrt(-1); for k=1:nline lp(k)=linedata(k,1); lq(k)=linedata(k,2); r(k)=linedata(k,3); x(k)=linedata(k,4); ysh(k)=linedata(k,5); a(k)=linedata(k,6); nbus=length(busdata(:,2)); z(k)= r(k)+j*x(k); y(k)=1/z(k); end ybus=zeros(nbus,nbus); yln =zeros(nbus,nbus); % PI METHOD FOR OFF-NOMINAL ADMITTANCE OF TRANSFORMER for k=1:nline ylp(k)=[1/(a(k)^2)-1/a(k)]*y(k); ylq(k)=[1-1/a(k)]*y(k); y(k)=y(k)/a(k); end for k=1:nline ybus(lp(k),lq(k))=ybus(lp(k),lq(k))-y(k);
Qmax 0 100 0 0
Qsh 0 0 0
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SIMULATION LAB
M.Tech – E.P.S.
% Load flow solution by Gauss-seidel Method nbus=length(busdata(:,1)); for n=1:nbus bus(n)=busdata(n,1); kb(n)=busdata(n,2); vm(n)=busdata(n,3); delta(n)=busdata(n,4); Pg(n)=busdata(n,5); Qg(n)=busdata(n,6); Pd(n)=busdata(n,7); Qd(n)=busdata(n,8); Qmin(n)=busdata(n,9); Qmax(n)=busdata(n,10); Qsh(n)=busdata(n,11); delta(n)=pi/180*delta(n); e(n)=vm(n)*cos(delta(n))+j*vm(n)*sin(delta(n)); P(n)=(Pg(n)-Pd(n))/basemva; Q(n)=(Qg(n)-Qd(n))/basemva; S(n)=P(n)+j*Q(n); dv(n)=0; end maxerror=0.1; iter=0; for n=1:nbus vc(n)=0+0*j; vnew(n)=0+0*j; end while (maxerror>0.00001 & iter<15) for m=1:nbus for n=1:nbus yv(n)=0+0*j; end if kb(m)==0 % Slackbus vc(m)=vm(m); e(m)=vc(m) ; end if kb(m)==2 %Load bus for k=1:nbus if k~=m yv(m)=yv(m)+ybus(m,k)*e(k); end end
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SIMULATION LAB
M.Tech – E.P.S.
if kb(m)==1 %Generator bus for k=1:nbus if k~=m yv(m)=yv(m)+ybus(m,k)*e(k); end end cos(m)=real(e(m))/abs(e(m)); sin(m)=imag(e(m))/abs(e(m)); e(m)=vm(m)*cos(m)+j*vm(m)*sin(m); Qnew(m)=-imag(conj(e(m))*(yv(m) ybus(m,m)*e(m)))*100; if(Qnew(m))Qmax(m) Q(m)=Qmax(m)/basemva; S(m)=P(m)+j*Q(m); e(m)=1+0*j; vc(m)=((conj(S(m))/conj(e(m)))-yv(m))/ybus(m,m); e(m)=e(m)+1.4*(vc(m)-e(m)); else Q(m)=Qnew(m)/basemva; S(m)=P(m)+j*Q(m); vc(m)=((conj(S(m))/conj(e(m)))-yv(m))/ybus(m,m); cos(m)=real(vc(m))/(abs(vc(m))); sin(m)=imag(vc(m))/(abs(vc(m))); vnew(m)=vm(m)*cos(m)+j*vm(m)*sin(m); e(m)=vnew(m); end end end maxerror=max(error); iter=iter+1; iter e end
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SIMULATION LAB
M.Tech – E.P.S.
% CALCULATION OF LINE POWER FLOWS ysh=zeros(nbus,nbus); yln=zeros(nbus,nbus); for k=1:nline yln(lp(k),lq(k))=yln(lp(k),lq(k))+y(k); yln(lq(k),lp(k))=yln(lp(k),lq(k)); ysh(lp(k),lq(k))=ysh(lp(k),lq(k))+j*ysh(k); ysh(lq(k),lp(k))=ysh(lp(k),lq(k)); end for i=1:nbus for k=1:nbus sln(i,k)=0+0*i; end end for m=1:nbus for n=1:nbus sln(m,n)=((e(m)*(conj(e(m))-conj(e(n)))*conj(yln,n))) +(e(m)*conj(e(m))*conj(ysh(m,n))))*basemva; end end
sln
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SIMULATION LAB
M.Tech – E.P.S.
OUTPUT :-
(a) P.V.BUS WITHOUT VIOLATION OF Q-LIMITS :( i ) BUS VOLTAGES :ITER.
E1
1
1.0400
2
E2
E3
E4
1.0395 + 0.0335i
1.0444 - 0.1251i
1.0599 - 0.0545i
1.0400
1.1067 - 0.0030i
1.0733 - 0.1206i
1.0965 - 0.0483i
3
1.0400
1.1281 + 0.0005i
1.0960 - 0.1134i
1.1126 - 0.0438i
4
1.0400
1.1400 + 0.0040i
1.1033 - 0.1095i
1.1183 - 0.0409i
5
1.0400
1.1440 + 0.0061i
1.1062 - 0.1075i
1.1205 - 0.0395i
6
1.0400
1.1456 + 0.0072i
1.1073 - 0.1066i
1.1214 - 0.0388i
7
1.0400
1.1462 + 0.0077i
1.1078 - 0.1062i
1.1218 - 0.0385i
8
1.0400
1.1465 + 0.0079i
1.1080 - 0.1060i
1.1219 - 0.0383i
9
1.0400
1.1466 + 0.0080i
1.1081 - 0.1060i
1.1220 - 0.0383i
10
1.0400
1.1466 + 0.0080i
1.1081 - 0.1059i
1.1220 - 0.0383i
11
1.0400
1.1466 + 0.0081i
1.1081 - 0.1059i
1.1220 - 0.0383i
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SIMULATION LAB
M.Tech – E.P.S.
(b) P.V.BUS WITH VIOLATION OF Q-LIMITS :( i ) BUS VOLTAGES :ITER.
E1
E2
E3
E4
1
1.0400
1.0783 + 0.0477i
1.0543 - 0.1215i
1.0872 - 0.0444i
2
1.0400
1.1254 - 0.0002i
1.0955 - 0.1125i
1.1145 - 0.0445i
3
1.0400
1.1463 + 0.0021i
1.1066 - 0.1109i
1.1236 - 0.0429i
4
1.0400
1.1526 + 0.0031i
1.1110 - 0.1089i
1.1269 - 0.0416i
5
1.0400
1.1550 + 0.0041i
1.1126 - 0.1079i
1.1282 - 0.0408i
6
1.0400
1.1559 + 0.0047i
1.1132 - 0.1075i
1.1287 - 0.0405i
7
1.0400
1.1562 + 0.0049i
1.1135 - 0.1072i
1.1289 - 0.0403i
8
1.0400
1.1564 + 0.0050i
1.1136 - 0.1072i
1.1289 - 0.0402i
9
1.0400
1.1564 + 0.0051i
1.1137 - 0.1071i
1.1290 - 0.0402i
10
1.0400
1.1564 + 0.0051i
1.1137 - 0.1071i
1.1290 - 0.0402i
11
1.0400
1.1565 + 0.0051i
1.1137 - 0.1071i
1.1290 - 0.0402i
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SIMULATION LAB
M.Tech – E.P.S.
( 3 ) F.D.L.F. METHOD clear; clc; basemva=100; % n code v del pg qg pd qd qmin qmax busdata=[1 0 1.06 0 0 0 0 0 0 0 2 2 1.0 0 40 30 20 10 0 0 3 2 1.0 0 0 0 45 15 0 0 4 2 1.0 0 0 0 40 5 0 0 5 2 1.0 0 0 0 60 10 0 0 % lp lq r x ysh tap linedata=[1 2 0.02 0.06 0.030 1 1 3 0.08 0.24 0.025 1 2 3 0.06 0.18 0.020 1 2 4 0.06 0.18 0.020 1 2 5 0.04 0.12 0.015 1 3 4 0.01 0.03 0.01 1 4 5 0.08 0.24 0.025 1 ]; %Ybus formulation by inspection method nline=length(linedata(:,1)); for k=1:nline lp(k)=linedata(k,1); lq(k)=linedata(k,2); r(k)=linedata(k,3); x(k)=linedata(k,4); ysh(k)=linedata(k,5); a(k)=linedata(k,6); nbus=length(busdata(:,2)); z(k)=r(k)+j*x(k); y(k)=1/z(k);
qsh 0 0 0 0 0 ];
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SIMULATION LAB
for n=1:nbus bus(n)=busdata(n,1); kb(n)=busdata(n,2); vm(n)=busdata(n,3); delta(n)=busdata(n,4); pg(n)=busdata(n,5); qg(n)=busdata(n,6); pd(n)=busdata(n,7); qd(n)=busdata(n,8); qmin(n)=busdata(n,9); qmax(n)=busdata(n,10); qsh(n)=busdata(n,11); delta(n)=pi/180*delta(n); v(n)=vm(n)*cos(delta(n))+j*vm(n)*sin(delta(n)); p(n)=(pg(n)-pd(n))/basemva; q(n)=(qg(n)-qd(n))/basemva; s(n)=p(n)+j*q(n); end ym=abs(ybus); t=angle(ybus); ii=0; for n=1:nbus if(kb(n)==1|kb(n)==2) if (kb(n)==1|kb(n)==2) ii=ii+1; jj=0; for m=1:nbus if(kb(m)==1|kb(m)==2) if (kb(m)==1|kb(m)==2) jj=jj+1; B1(ii,jj)=imag(ybus(n,m)); end end end
M.Tech – E.P.S.
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SIMULATION LAB
M.Tech – E.P.S.
B1inv=inv(B1); B2inv=inv(B2); maxerror=0.1; iter=0; while maxerror>0.00001&iter<15 iter=iter+1; id=0; iv=0; for n=1:nbus J11=0; J33=0; for m=1:nline if(lp(m)==n|lq(m)==n) if (lp(m)==n|lq(m)==n) if(lp(m)==n) if (lp(m)==n) l=lq(m); end if(lq(m)==n) if (lq(m)==n) l=lp(m); end J11=J11+vm(n)*vm(l)*ym(n,l)*sin(t(n,l)-delta(n) +delta(l)); J33=J33+vm(n)*vm(l)*ym(n,l)*cos(t(n,l)-delta(n) +delta(l)); end end pk=vm(n)^2*ym(n,n)*cos(t(n,n))+J33; qk=-vm(n)^2*ym(n,n)*sin(t(n,n))-J11; if(kb(n)==0) if (kb(n)==0) p(n)=pk; q(n)=qk; end
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SIMULATION LAB
M.Tech – E.P.S.
end end end if(kb(n)~=0) if (kb(n)~=0) id=id+1; dp(id)=p(n)-pk; dpv(id)=(p(n)-pk)/vm(n); iv=iv+1; dq(iv)=q(n)-qk; dqv(iv)=(q(n)-qk)/vm(n); end end f=dpv'; dd=-B1inv*dpv'; dv=-B2inv*dqv'; id=0; iv=0; for n=1:nbus if(kb(n)~=0) if (kb(n)~=0) id=id+1; delta(n)=delta(n)+dd(id); iv=iv+1; vm(n)=vm(n)+dv(iv);
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SIMULATION LAB
M.Tech – E.P.S.
OUTPUT :-
ITER
E0
E1
E2
E3
E4
1
1.0600
1.0691 - 0.0404i
1.0566 - 0.0920i
1.0575 - 0.0988i
1.0558 - 0.1166i
2
1.0600
1.0493 - 0.0591i
1.0191 - 0.0982i
1.0175 - 0.1043i
1.0089 - 0.1186i
3
1.0600
1.0427 - 0.0519i
1.0162 - 0.0881i
1.0150 - 0.0938i
1.0077 - 0.1072i
4
1.0600
1.0461 - 0.0502i
1.0208 - 0.0883i
1.0197 - 0.0942i
1.0129 - 0.1083i
5
1.0600
1.0466 - 0.0513i
1.0207 - 0.0894i
1.0195 - 0.0953i
1.0124 - 0.1093i
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SIMULATION LAB
M.Tech – E.P.S.
( 4 ) F.D.L.F. METHOD FOR DISTRIBUTION SYSTEM clear; clc; rxratio=1.5; % n v delta pd busdata=[ 1 1.05 0 0.000 2 1.00 0 0.278 3 1.00 0 0.442 4 1.00 0 0.195 5 1.00 0 0.149 6 1.00 0 0.26 % lp lq z linedata=[ 1 2 0.052 2 3 0.035 2 4 0.0645 4 5 0.0117 4 6 0.075 ]; nline=length(linedata(:,1)); nbus=length(busdata(:,1)); j=sqrt(-1); for k=1:nline
qd ysh 0.000 0 0.069 0 0.084 0 0.066 0 0.05 0 0.016 0.5 ];
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SIMULATION LAB
invG=inv(G(2:nbus,2:nbus)); %reading the bus data for k=1:nbus bus(k)=busdata(k,1); vm(k)=busdata(k,2); delta(k)=busdata(k,3); pd(k)=busdata(k,4); qd(k)=busdata(k,5); delta=pi/180*delta; end maxerror=1; iter=0; while(maxerror>0.0001 while (maxerror>0.0001 & iter<30) iter=iter+1; %initialisation of isp,ical for k=1:nbus-1 isp(k)=0; ik(k)=0; end %calculation of specified e.c.i. for k=1:nbus-1 isp(k)=[conj(pd(k+1)+j*qd(k+1))/vm(k+1)]; end
M.Tech – E.P.S.
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SIMULATION LAB
for i=1:nbus-1 delir(i,1)=real(id(i)); delii(i,1)=imag(id(i)); end dele=invG*delir; %change in bus voltage(real part) delf=invG*delii; %change in bus voltage(imag part) %calculation of modified bus voltages for i=1:nbus-1 e(i)=real(vm(i+1))+dele(i); f(i)=imag(vm(i+1))+delf(i); vm(i+1)=e(i)+j*f(i); end maxerror=max(max(abs(dele)),max(abs(delf))); Em=abs(vm); ang=angle(vm); iter Em ang end
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SIMULATION LAB
M.Tech – E.P.S.
OUTPUT :-
VOLTAGE MAGNITUDES :ITER
E0
1
1.0500 500
E1
0.9684 684
E2
0.9496 496
E3
0.9235
E4
0.9214
E5
0.9048
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SIMULATION LAB
M.Tech – E.P.S.
PHASE ANGLES OF BUS VOLTAGES :ITER
δ0
δ1
δ2
δ3
δ4
δ5
1
0
-0.0483
-0.0455
-0.0816
-0.0810
-0.1318
2
0
-0.0715
-0.0829
-0.1368
-0.1381
-0.1965
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SIMULATION LAB
M.Tech – E.P.S.
( 5 ) TRANSIENT STABILITY ANALYSIS BY “POINT BY POINT METHOD” clear; clc; t=0; tf=0; tfinal=0.5; tc=0.125; %(FOR FAULT CLEARED AT 2.5 CYCLES:tc=0.05, 6.25CYCLES:tc=0.125, SUSTAINED FAULT:tc=0.5to1.0) tstep=0.05; M=2.52/(180*50); i=2; delta=21.64*pi/180;
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SIMULATION LAB
pause time(i)=t; ang(i)=deltadeg i=i+1; end axis ([0 0.6 0 160]) plot(time,ang,'ko-' plot(time,ang,'ko-') ) grid
M.Tech – E.P.S.
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SIMULATION LAB
OUTPUT :-
M.Tech – E.P.S.
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SIMULATION LAB
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