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Diffstat (limited to 'Working_Examples/83/CH12/EX12.11/example_12_11.sce')
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diff --git a/Working_Examples/83/CH12/EX12.11/example_12_11.sce b/Working_Examples/83/CH12/EX12.11/example_12_11.sce new file mode 100755 index 0000000..33c64db --- /dev/null +++ b/Working_Examples/83/CH12/EX12.11/example_12_11.sce @@ -0,0 +1,173 @@ +//Chapter 12 +//Example 12.11 +//page 488 +//To plot swing curves for fault cleared at 0.275s and 0.08s of a multimachine system +clear;clc; + +xd1=%i*0.067;xd2=%i*0.1; + +//primitive admittances of the lines +y45=1/(0.018+%i*0.11); B45=%i*0.113; +y51=1/(0.004+%i*0.0235); B51=%i*0.098; +y41=1/(0.007+%i*0.04); B41=%i*0.041; +z24=(%i*0.022); +z35=(%i*0.04); + +//Bus data and prefault load-flow values in PU +V1=1.0; P1=-3.8083; Q1=-0.2799; Pl1=0; Ql2=0; +V2=1.0194+%i*0.1475; P2=3.25; Q2=0.6986; Pl2=0; Ql2=0; +V3=1.0121+%i*0.1271; P3=2.10; Q3=0.3110; Pl3=0; Ql3=0; +V4=1.0146+%i*0.0767; P4=0; Q4=1.0; Pl4=1.0; Ql4=0.44; +V5=1.0102+%i*0.0439; P5=0; Q5=0; Pl5=0.5; Ql5=0.16; + + +// To find voltage behind transient reactances before the occurance of fault + +I2=(P2-%i*Q2)/(V2'); +E2=V2+I2*xd1; +E1=V1; +I3=(P3-%i*Q3)/(V3'); +E3=V3+I3*xd2; + +//converting loads into their admittances +Yl4=(Pl4-%i*Ql4)/(V4*V4'); +Yl5=(Pl5-%i*Ql5)/(V5*V5'); + +//forming augmented Bus admittance matrix before the occurance of fault +Y11=y41+y51;Y12=0;Y13=0;Y14=-y41;Y15=-y51; +Y21=Y12;Y22=1/(xd1+z24);Y23=0;Y24=-(1/(z24+xd1));Y25=0; +Y31=0;Y32=0;Y33=1/(z35+xd2);Y34=0;Y35=-1/(z35+xd2); +Y41=Y14;Y42=Y24;Y43=Y34;Y44=y41+Yl4+y45+B45+B41-Y24;Y45=-y45; +Y51=Y15;Y52=Y25;Y53=Y35;Y54=Y45;Y55=Yl5+y45+y51+B45+B51-Y35; + +Ybus=[Y11 Y12 Y13 Y14 Y15; + Y21 Y22 Y23 Y24 Y25; + Y31 Y32 Y33 Y34 Y35; + Y41 Y42 Y43 Y44 Y45; + Y51 Y52 Y53 Y54 Y55]; + +printf('\n Augmented prefault bus admittance matrix (in PU) is given by\n\n Ybus=\n'); +disp(Ybus); +///////to find the Ybus during fault +Ybus_1=Ybus([1:3,5],[1:3,5]); +n=4 +for k=1:n-1 + for j=1:n-1 + Ybus_during_fault(k,j)=Ybus_1(k,j)-(Ybus_1(k,n)*Ybus_1(n,j))/Ybus_1(n,n); + end +end +printf('\n\n\n Bus admittance matrix during fault (in PU) is given by\n\n Ybus_during_fault=\n'); +disp(Ybus_during_fault); + +//to find Ybus after the fault has been cleared +Y45=0;Y54=0;Y44=Y44-y45-B45;Y55=Y55-y45-B45; +Ybus_2=[Y11 Y12 Y13 Y14 Y15; + Y21 Y22 Y23 Y24 Y25; + Y31 Y32 Y33 Y34 Y35; + Y41 Y42 Y43 Y44 Y45; + Y51 Y52 Y53 Y54 Y55]; + +//eliminating node 5 from Ybus_2 +n=5 +for k=1:n-1 + for j=1:n-1 + Ybus_3(k,j)=Ybus_2(k,j)-(Ybus_2(k,n)*Ybus_2(n,j))/Ybus_2(n,n); + end +end + +//eliminating node 4 to get post fault Ybus +n=4 +for k=1:n-1 + for j=1:n-1 + Ybus_post_fault(k,j)=Ybus_3(k,j)-(Ybus_3(k,n)*Ybus_3(n,j))/Ybus_3(n,n); + end +end +printf('\n\n\n Bus admittance matrix postfault (in PU) is given by\n\n Ybus_post_fault=\n'); +disp(Ybus_post_fault); +printf('\n\n\n'); +//During fault power angle equation +delta3=0:0.1:180; +Pe2f=0; +Pe3f=(abs(E3'))^2*real(Ybus_during_fault(3,3))+abs(E1')*abs(E3')*abs(Ybus_during_fault(3,1))*cosd(delta3-atand(imag(Ybus_during_fault(1,3))/real(Ybus_during_fault(1,3)))); + +//Postfault power angle equations +delta2=0:0.1:180; +Pe2pf=(abs(E2'))^2*real(Ybus_post_fault(2,2))+abs(E1')*abs(E2')*abs(Ybus_post_fault(2,1))*cosd(delta2-atand(imag(Ybus_post_fault(1,2))/real(Ybus_post_fault(1,2)))); +Pe3pf=(abs(E3'))^2*real(Ybus_post_fault(3,3))+abs(E1')*abs(E3')*abs(Ybus_post_fault(3,1))*cosd(delta3-atand(imag(Ybus_post_fault(1,3))/real(Ybus_post_fault(1,3)))); + +//mechanical inputs which are assumed to be constant are given by +Pm2=max(real(E2*I2')); +Pm3=max(real(E3*I3')); + +//xdot function defining the swing equations of each of the machines +function xdot=mac2(t,x,tc) + xdot(1)=x(2); + if t>tc then + xdot(2)=180*50*(Pm2-(0.6012+8.365*sind(x(1)-1.662)))/12;//swing equation after clearing the fault + else + xdot(2)=180*50*(Pm2-(0))/12; //swing equation before clearing the fault + end + +endfunction + +function xdot=mac3(t,x,tc) + xdot(1)=x(2); + if t>tc then + xdot(2)=180*50*(Pm3-(0.1823+6.5282*sind(x(1)-0.8466)))/9;//swing equation after clearing the fault + else + xdot(2)=180*50*(Pm3-(0.1561+5.531*sind(x(1)-0.755)))/9; //swing equation before clearing the fault + end + +endfunction + +//to find the solution of swing equation to draw the swing curves + +//to draw the swing curves for machines 2 and 3 for example12.11 for clearing at 0.275 sec +subplot(2,1,1) +x_1_0=[19.354398,0]';t0=0; T=0:0.01:1;T=T'; +x_2_0=[18.2459,0]';tc=0.275; +sol1=ode(x_1_0,t0,T,mac2); +sol2=ode(x_2_0,t0,T,mac3); + +plot(T(1:20),sol1(1,1:20)',T,sol2(1,:)'); +set(gca(),"grid",[1 1]); +legend('Machine 2','Machine 3',[,1]); +title('Swing Curves for machines 2 and 3 of Example 12.11 for a clearing at '+string(tc)+' s'); +xstring(0.55,59,'Machine 1 is reference (infinte bus)'); +xlabel('Time (in seconds)----->'); +ylabel('Torque Angle (delta,deg)----->'); + + +//to draw the swing curves for machines 2 and 3 for example12.11 for clearing at 0.08 sec +subplot(2,1,2) +x_1_0=[19.354398,0]';t0=0; T=0:0.01:1;T=T'; +x_2_0=[18.2459,0]';tc=0.08; +sol1=ode(x_1_0,t0,T,mac2); +sol2=ode(x_2_0,t0,T,mac3); + +plot(T,sol1(1,:)',T,sol2(1,:)'); +set(gca(),"grid",[1 1]); +legend('Machine 2','Machine 3',[,4]); +title('Swing Curves for machines 2 and 3 of Example 12.11 for a clearing at '+string(tc)+' s'); +xstring(0.44,43,'Machine 1 is reference (infinte bus)'); +xlabel('Time (in seconds)----->'); +ylabel('Torque Angle (delta,deg)----->'); + +f=get("current_figure"); +f.figure_position=[0,15]; +f.figure_size=[565,1000]; + + + + + + + + + + + + + + + |