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Diffstat (limited to 'Working_Examples/83/CH6/EX6.6/example_6_6.sce')
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diff --git a/Working_Examples/83/CH6/EX6.6/example_6_6.sce b/Working_Examples/83/CH6/EX6.6/example_6_6.sce new file mode 100755 index 0000000..0058084 --- /dev/null +++ b/Working_Examples/83/CH6/EX6.6/example_6_6.sce @@ -0,0 +1,114 @@ +//Chapter 6 +//Example 6.6 +//page 218 +//To find load flow solution using the NR method +clear;clc; + +///////////////////////////////////////////////////////////////////////// +//Pd Qd Pg Qg V Bus Type///// +///////////////////////////////////////////////////////////////////////// +Pd1=2.0; Qd1=1.0; Pg1=0; Qg1=0; V1=1.04; //1 slack bus +Pd2=0; Qd2=0; Pg2=0.5; Qg2=1; V2=1; //2 PQ bus +Pd3=1.5; Qd3=0.6; Pg3=0.0; Qg3=0; V3=1.04; //3 PV bus +///////////////////////////////////////////////////////////////////////// +[V1_mag,V1_ang]=polar(V1); +[V2_mag,V2_ang]=polar(V2); +[V3_mag,V3_ang]=polar(V3); +y_series=1/(0.02+%i*0.08); +y_self=2*y_series; +y_off=-1*y_series; +Ybus=[y_self y_off y_off;y_off y_self y_off;y_off y_off y_self]; + +[y_bus_mag_21,y_bus_ang_21]=polar(Ybus(2,1)); +[y_bus_mag_22,y_bus_ang_22]=polar(Ybus(2,2)); +[y_bus_mag_23,y_bus_ang_23]=polar(Ybus(2,3)); +[y_bus_mag_31,y_bus_ang_31]=polar(Ybus(3,1)); +[y_bus_mag_32,y_bus_ang_32]=polar(Ybus(3,2)); +[y_bus_mag_33,y_bus_ang_33]=polar(Ybus(3,3)); +[y_bus_mag_11,y_bus_ang_11]=polar(Ybus(1,1)); + +//direct computer solution has been found as below by running for 3 iterations + +n=3; +for i=1:n +//from eq.6.27 and 6.28 +P2=V2_mag*V1_mag*y_bus_mag_21*cos(y_bus_ang_21+V1_ang-V2_ang)+(V2_mag^2)*y_bus_mag_22*cos(y_bus_ang_22)+V2_mag*V3_mag*y_bus_mag_23*cos(y_bus_ang_23+V3_ang-V2_ang); + +P3=V3_mag*V1_mag*y_bus_mag_31*cos(y_bus_ang_31+V1_ang-V3_ang)+(V3_mag^2)*y_bus_mag_33*cos(y_bus_ang_33)+V2_mag*V3_mag*y_bus_mag_32*cos(y_bus_ang_32+V2_ang-V3_ang); + +Q2=-V2_mag*V1_mag*y_bus_mag_21*sin(y_bus_ang_21+V1_ang-V2_ang)-(V2_mag^2)*y_bus_mag_22*sin(y_bus_ang_22)-V2_mag*V3_mag*y_bus_mag_23*sin(y_bus_ang_23+V3_ang-V2_ang); + +P2=real(P2); +P3=real(P3); +Q2=real(Q2); + +delta_P2=(Pg2-Pd2)-(P2); +delta_P3=(Pg3-Pd3)-(P3); +delta_P2=(Pg2-Pd2)-(P2); +delta_Q2=(Qg2-Qd2)-(Q2); + +//forming jacobian matrix by differentiating expressions of P2,P3,Q2 +j11=V2_mag*V1_mag*y_bus_mag_21*sin(y_bus_ang_21+V1_ang-V2_ang)+V2_mag*V3_mag*y_bus_mag_23*sin(y_bus_ang_23+V3_ang-V2_ang); +j12=-V2_mag*V3_mag*y_bus_mag_23*sin(y_bus_ang_23+V3_ang-V2_ang); +j13=V1_mag*y_bus_mag_21*cos(y_bus_ang_21+V1_ang-V2_ang)+(V2_mag*2)*y_bus_mag_22*cos(y_bus_ang_22)+V3_mag*y_bus_mag_23*cos(y_bus_ang_23+V3_ang-V2_ang); + +j21=-V2_mag*V3_mag*y_bus_mag_32*sin(y_bus_ang_32+V2_ang-V3_ang); +j22=V3_mag*V1_mag*y_bus_mag_31*sin(y_bus_ang_31+V1_ang-V3_ang)+V2_mag*V3_mag*y_bus_mag_32*sin(y_bus_ang_32+V2_ang-V3_ang); +j23=V3_mag*y_bus_mag_32*cos(y_bus_ang_32+V2_ang-V3_ang); + +j31=V2_mag*V1_mag*y_bus_mag_21*cos(y_bus_ang_21+V1_ang-V2_ang)+V2_mag*V3_mag*y_bus_mag_23*cos(y_bus_ang_23+V3_ang-V2_ang); +j32=-V2_mag*V3_mag*y_bus_mag_23*cos(y_bus_ang_23+V3_ang-V2_ang); +j33=-V1_mag*y_bus_mag_21*sin(y_bus_ang_21+V1_ang-V2_ang)-(V2_mag*2)*y_bus_mag_22*sin(y_bus_ang_22)-V3_mag*y_bus_mag_23*sin(y_bus_ang_23+V3_ang-V2_ang); + +J=[j11 j12 j13;j21 j22 j23;j31 j32 j33]; +J=real(J); + +//power residuals +PR=[delta_P2;delta_P3;delta_Q2]; + +//changes in variables +ch_var=inv(J)*PR; + +V2_ang=V2_ang+ch_var(1,1); +V3_ang=V3_ang+ch_var(2,1); +V2_mag=V2_mag+ch_var(3,1); + +P1=(V1_mag^2)*y_bus_mag_11*cos(y_bus_ang_11)+V1_mag*V2_mag*y_bus_mag_21*cos(y_bus_ang_21+V2_ang-V1_ang)+V1_mag*V3_mag*y_bus_mag_31*cos(y_bus_ang_31+V3_ang-V1_ang); +Q1=-V1_mag^2*y_bus_mag_11*sin(y_bus_ang_11)-V1_mag*V2_mag*y_bus_mag_21*sin(y_bus_ang_21+V2_ang-V1_ang)-V1_mag*V3_mag*y_bus_mag_31*sin(y_bus_ang_31+V3_ang-V1_ang); + +Q3=-V3_mag*V1_mag*y_bus_mag_31*sin(y_bus_ang_31+V1_ang-V3_ang)-(V3_mag^2)*y_bus_mag_33*sin(y_bus_ang_33)-V2_mag*V3_mag*y_bus_mag_32*sin(y_bus_ang_32+V2_ang-V3_ang); +Qg3=Q3+Qd3; + +end + +S1=real(P1)+%i*real(Q1); +S2=P2+%i*Q2; +S3=P3+%i*Q3; + +printf('\nThe final results are given below:\n'); +printf('V2=%0.3f @ %0.3f rad\n',V2_mag,V2_ang); +printf('V3=%0.3f @ %0.3f rad\n',V3_mag,V3_ang); +printf('Qg3=%0.2f pu(with in limits)\n',Qg3); +printf('\nS1=');disp(S1);printf('pu'); +printf('\n\nS2=');disp(S2);printf("pu"); +printf('\n\nS3=');disp(S3);printf("pu"); +printf('\n\nTransmission losses=%0.3f pu\n',(real(P1)+P2+P3)); + +//Line Flows + +//V_mag=[V1_mag V2_mag V3_mag]; +//V_ang=[V1_ang V2_ang V3_ang]; +v1=V1_mag*(cos(V1_ang)+%i*sin(V1_ang)); +v2=V2_mag*(cos(V2_ang)+%i*sin(V2_ang)); +v3=V3_mag*(cos(V3_ang)+%i*sin(V3_ang)); +V=[v1 v2 v3]; +for i=1:3 + for j=1:3 + s(i,j)=conj(V(i))*(V(i)-V(j))*(2.941-%i*11.764)+conj(V(i))*V(i)*(%i*0.01); + s(j,i)=conj(V(j))*(V(j)-V(i))*(2.941-%i*11.764)+conj(V(j))*V(j)*(%i*0.01); + end +end +P=real(s); +Q=-imag(s); +printf('\nLine Flows\nThe following matrix shows the real part of line flows(in pu)');disp(P); +printf('\nThe following matrix shows the imaginary part of line flows(in pu)');disp(Q);
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