diff options
Diffstat (limited to 'Working_Examples/83/CH12')
29 files changed, 963 insertions, 0 deletions
diff --git a/Working_Examples/83/CH12/EX12.1/example_12_1.sce b/Working_Examples/83/CH12/EX12.1/example_12_1.sce new file mode 100755 index 0000000..dcc72ab --- /dev/null +++ b/Working_Examples/83/CH12/EX12.1/example_12_1.sce @@ -0,0 +1,26 @@ +//Chapter 12 +//Example 12.1 +//page 439 +//To find stored kinetic energy,rotor acceleration,change in torque angle and rotor speed +clear;clc; +G=100; //base machine rating +H=8.0; //inertia constant +P=4; //no of poles +//(a)To find stored energy in rotor at synchronous speed +stored_energy=G*H; +printf('\nStored energy = %d MJ',stored_energy); + +//(b)To find rotor acceleration when mechanical input is raised 80MW for an electrical load of 50MW +Pa=30; //nett power +f=50; //frequency +M=stored_energy/(180*f); +alpha=Pa/M; //rotor acceleration +printf('\n\nRotor acceleration = %0.1f elect deg/s^2 ',alpha); + +//(c)To calculate change in torque angle and rotor speed when the above acceleration is maintained for 10 cycles +change_angle=0.5*alpha*(10*20*10^(-3)); +printf('\n\nChange in torque angle = %0.2f elect degrees',change_angle); +change_angle=60*alpha/(2*360); +printf('\nChange in torque angle = %0.3f rpm/s',change_angle); +speed=(120*f/P)+(change_angle*0.2); +printf('\n\nRoor speed at the end of 10 cycles = %0.3f rpm',speed); diff --git a/Working_Examples/83/CH12/EX12.1/result_example_12_1.txt b/Working_Examples/83/CH12/EX12.1/result_example_12_1.txt new file mode 100755 index 0000000..b8ab028 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.1/result_example_12_1.txt @@ -0,0 +1,9 @@ + +Stored energy = 800 MJ + +Rotor acceleration = 337.5 elect deg/s^2 + +Change in torque angle = 33.75 elect degrees +Change in torque angle = 28.125 rpm/s + +Roor speed at the end of 10 cycles = 1505.625 rpm diff --git a/Working_Examples/83/CH12/EX12.10/example_12_10.sce b/Working_Examples/83/CH12/EX12.10/example_12_10.sce new file mode 100755 index 0000000..79310e8 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.10/example_12_10.sce @@ -0,0 +1,170 @@ +//Chapter 12 +//Example 12.10 +//page 482 +//To plot swing curves for sustained fault and fault cleared at 2.5 and 6.25 cycles +clear;clc; +P_delivered=18; +MVA_base=20; +Xd=0.35;E=1.1; +Xl=0.2; +V=1; + +H=2.52; +f=50; +M=H/(180*f); + +/////////Prefault////////////////////////// +X1=Xd+Xl/2; +delta=0:0.1:180; +Pe1=E*V*sind(delta)/X1; +P_initial=P_delivered/MVA_base;Pm=P_initial; +delta0=asind(P_initial/max(Pe1)); + + +//////during fault//////// +X2=1.25; //from delta to star conversion +Pe2=E*V*sind(delta)/X2; + +//////postfault:with faulted line switched off///////// +X3=Xd+Xl; +Pe3=E*V*sind(delta)/X3; + +Pa_0minus=0; +Pa_0plus=Pm-max(Pe2)*sind(delta0); +Pa_avg=(Pa_0minus+Pa_0plus)/2; + + +/////for a sustained fault/////////// +P_max=max(Pe2); +delta_delta=0; //initially +delta=21.64; //initially +delta_old=21.64; +delta_t=0.05; +z1=21.64 +n=10; +T=0; +printf('Point-by-point calculation of swing curve for sustained fault delta_t=0.05sec\n'); +printf('_______________________________________________________________________________________________\n'); +printf('t\t\tPmax\t\t sin(delta)\t\tPa\t\t y\t\tdelta\n'); +printf('_______________________________________________________________________________________________\n'); +printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',0.000,P_max,sind(delta),(0.9-P_max*sind(delta))/2,8.929*(0.9-P_max*sind(delta))/2,delta); +for i=1:n + t=i*delta_t; + if i==1 then + Pa=(0.9-P_max*sind(delta_old))/2; + else + Pa=0.9-P_max*sind(delta_old); + end + + y=(delta_t^2)*Pa/M; + delta_delta=delta_delta+y; + delta=delta+delta_delta; + z1=[z1,delta];T=[T,t]; + printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',t,P_max,sind(delta),0.9-P_max*sind(delta),8.929*(0.9-P_max*sind(delta)),delta); + delta_old=delta; +end + + +//////Fault cleared in 2.5 cycles(time to clear fault=0.05sec)///// + +P_max1=max(Pe2); +P_max2=max(Pe3); +delta_delta=0; //initially +delta=21.64; //initially +delta_old=21.64; +delta_t=0.05; +z2=21.64 +n=10; +T=0; +printf('\n\nComputations of swing curves for fault cleared at 2.5 cycles(0.05sec)\n'); +printf('______________________________________________________________________________________________\n'); +printf('t\t\tPmax\t\t sin(delta)\t\tPa\t\t y\t\tdelta\n'); +printf('______________________________________________________________________________________________\n'); +printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',0.000,P_max,sind(delta),(0.9-P_max*sind(delta))/2,8.929*(0.9-P_max*sind(delta))/2,delta); +for i=1:n + t=i*delta_t; + if i==1 then + Pa=(0.9-P_max*sind(delta_old))/2; + P_max=P_max1; + elseif i==2 then + Pa=((0.9-P_max2*sind(delta_old))+((0.9-P_max1*sind(delta_old))))/2; + P_max=P_max2; + else + Pa=0.9-P_max2*sind(delta_old); + P_max=P_max2; + end + + y=(delta_t^2)*Pa/M; + delta_delta=delta_delta+y; + delta=delta+delta_delta; + z2=[z2,delta];T=[T,t]; + + if i==1 then + delta_old=delta; + printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',t,P_max,sind(delta),((0.9-P_max2*sind(delta_old))+((0.9-P_max1*sind(delta_old))))/2,8.929*((0.9-P_max2*sind(delta_old))+((0.9-P_max1*sind(delta_old))))/2,delta); + else + printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',t,P_max,sind(delta),0.9-P_max*sind(delta),8.929*(0.9-P_max*sind(delta)),delta); + delta_old=delta; + end + +end + + + +//////Fault cleared in 6.25 cycles(time to clear fault=0.125sec)///// + +P_max1=max(Pe2); +P_max2=max(Pe3); +P_max=P_max1; +delta_delta=0; //initially +delta=21.64; //initially +delta_old=21.64; +delta_t=0.05; +z3=21.64 +n=10; +T=0; +printf('\n\nComputations of swing curves for fault cleared at 6.25 cycles(0.125sec)\n'); +printf('______________________________________________________________________________________________\n'); +printf('t\t\tPmax\t\t sin(delta)\t\tPa\t\t y\t\tdelta\n'); +printf('______________________________________________________________________________________________\n'); +printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',0.000,P_max,sind(delta),(0.9-P_max*sind(delta))/2,8.929*(0.9-P_max*sind(delta))/2,delta); +for i=1:n + t=i*delta_t; + if i==1 then + Pa=(0.9-P_max1*sind(delta_old))/2; + P_max=P_max1; + elseif i==2 then + Pa=(0.9-P_max1*sind(delta_old)); + P_max=P_max1; + elseif i==3 then + Pa=(0.9-P_max1*sind(delta_old)); + P_max=P_max2; + else + Pa=0.9-P_max2*sind(delta_old); + P_max=P_max2; + end + + y=(delta_t^2)*Pa/M; + delta_delta=delta_delta+y; + delta=delta+delta_delta; + z3=[z3,delta]; + T=[T,t]; + printf('%0.3f sec\t%0.3f\t\t %0.3f\t\t\t%0.3f\t\t%0.3f\t\t%0.3f\n',t,P_max,sind(delta),0.9-P_max*sind(delta),8.929*(0.9-P_max*sind(delta)),delta); + delta_old=delta; + +end + +plot(T,z1,T,z2,T,z3); +set(gca(),"grid",[1 1]); +legend('Sustained Fault','Fault cleared at 2.5 cycles','Fault cleared at 6.25 cycles',[,2]); + +title('Swing Curves for Example 12.10 for a sustained fault and for clearing in 2.5 and 6.25 cycles','fontsize',2.4); +xlabel('Time (in seconds)----->'); +ylabel('Torque Angle (delta,deg)----->'); +f=get("current_figure") +f.figure_position=[0,15] +f.figure_size=[645,1000] + + + + diff --git a/Working_Examples/83/CH12/EX12.10/result_example_12_10.txt b/Working_Examples/83/CH12/EX12.10/result_example_12_10.txt new file mode 100755 index 0000000..51afab7 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.10/result_example_12_10.txt @@ -0,0 +1,53 @@ + + +Point-by-point calculation of swing curve for sustained fault delta_t=0.05sec +_______________________________________________________________________________________________ +t Pmax sin(delta) Pa y delta +_______________________________________________________________________________________________ +0.000 sec 0.880 0.369 0.288 2.569 21.640 +0.050 sec 0.880 0.410 0.539 4.814 24.209 +0.100 sec 0.880 0.524 0.439 3.920 31.592 +0.150 sec 0.880 0.681 0.301 2.688 42.894 +0.200 sec 0.880 0.838 0.163 1.455 56.885 +0.250 sec 0.880 0.953 0.062 0.549 72.330 +0.300 sec 0.880 1.000 0.020 0.182 88.324 +0.350 sec 0.880 0.968 0.048 0.429 104.500 +0.400 sec 0.880 0.856 0.147 1.308 121.105 +0.450 sec 0.880 0.656 0.323 2.883 139.019 +0.500 sec 0.880 0.345 0.596 5.325 159.815 + + +Computations of swing curves for fault cleared at 2.5 cycles(0.05sec) +______________________________________________________________________________________________ +t Pmax sin(delta) Pa y delta +______________________________________________________________________________________________ +0.000 sec 0.880 0.369 0.288 2.569 21.640 +0.050 sec 0.880 0.410 0.310 2.764 24.209 +0.100 sec 2.000 0.493 -0.086 -0.769 29.542 +0.150 sec 2.000 0.561 -0.221 -1.977 34.105 +0.200 sec 2.000 0.598 -0.295 -2.634 36.692 +0.250 sec 2.000 0.597 -0.294 -2.622 36.644 +0.300 sec 2.000 0.559 -0.218 -1.943 33.975 +0.350 sec 2.000 0.490 -0.081 -0.720 29.361 +0.400 sec 2.000 0.407 0.086 0.765 24.028 +0.450 sec 2.000 0.333 0.234 2.087 19.460 +0.500 sec 2.000 0.292 0.316 2.822 16.978 + + +Computations of swing curves for fault cleared at 6.25 cycles(0.125sec) +______________________________________________________________________________________________ +t Pmax sin(delta) Pa y delta +______________________________________________________________________________________________ +0.000 sec 0.880 0.369 0.288 2.569 21.640 +0.050 sec 0.880 0.410 0.539 4.814 24.209 +0.100 sec 0.880 0.524 0.439 3.920 31.592 +0.150 sec 2.000 0.681 -0.461 -4.119 42.894 +0.200 sec 2.000 0.767 -0.634 -5.660 50.078 +0.250 sec 2.000 0.784 -0.667 -5.960 51.603 +0.300 sec 2.000 0.733 -0.567 -5.060 47.168 +0.350 sec 2.000 0.611 -0.322 -2.878 37.673 +0.400 sec 2.000 0.427 0.045 0.404 25.301 +0.450 sec 2.000 0.231 0.439 3.918 13.332 +0.500 sec 2.000 0.092 0.716 6.392 5.282 +WARNING : The size of the figure may not be as wide as you want. + diff --git a/Working_Examples/83/CH12/EX12.10/result_example_12_10_img.jpeg b/Working_Examples/83/CH12/EX12.10/result_example_12_10_img.jpeg Binary files differnew file mode 100755 index 0000000..f6279f5 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.10/result_example_12_10_img.jpeg 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]; + + + + + + + + + + + + + + + diff --git a/Working_Examples/83/CH12/EX12.11/result_example_12_11.txt b/Working_Examples/83/CH12/EX12.11/result_example_12_11.txt new file mode 100755 index 0000000..7e66326 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.11/result_example_12_11.txt @@ -0,0 +1,38 @@ + + + + Augmented prefault bus admittance matrix (in PU) is given by + + Ybus= + + 11.284152 - 65.612163i 0 0 - 4.244997 + 24.257126i - 7.0391553 + 41.355037i + 0 - 11.235955i 0 11.235955i 0 + 0 0 - 7.1428571i 0 7.1428571i + - 4.244997 + 24.257126i 11.235955i 0 6.659713 - 44.617911i - 1.4488088 + 8.8538313i + - 7.0391553 + 41.355037i 0 7.1428571i - 1.4488088 + 8.8538313i 8.9769945 - 57.297216i + + + + Bus admittance matrix during fault (in PU) is given by + + Ybus_during_fault= + + 5.7986033 - 35.768947i 0 - 0.0681253 + 5.1661269i + 0 - 11.235955i 0 + - 0.0681253 + 5.1661269i 0 0.1361683 - 6.2737394i + + + + Bus admittance matrix postfault (in PU) is given by + + Ybus_post_fault= + + 1.3931179 - 14.011919i - 0.2213865 + 7.628982i - 0.0901365 + 6.0974822i + - 0.2213865 + 7.628982i 0.5005328 - 7.7897867i 0 + - 0.0901365 + 6.0974822i 0 0.1590837 - 6.1167759i + + + +WARNING : The size of the figure may not be as wide as you want. + + diff --git a/Working_Examples/83/CH12/EX12.11/result_example_12_11_img.jpeg b/Working_Examples/83/CH12/EX12.11/result_example_12_11_img.jpeg Binary files differnew file mode 100755 index 0000000..5660f18 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.11/result_example_12_11_img.jpeg diff --git a/Working_Examples/83/CH12/EX12.12/example_12_12.sce b/Working_Examples/83/CH12/EX12.12/example_12_12.sce new file mode 100755 index 0000000..647cf0a --- /dev/null +++ b/Working_Examples/83/CH12/EX12.12/example_12_12.sce @@ -0,0 +1,97 @@ +//Chapter 12 +//Example 12.12 +//page 500 +//To plot swing curves for single pole and three pole switching +clear;clc; + +Xg0=0.1;Xg1=0.3;Xg2=0.15;E=1.2;H=4.167; +Xt=0.1; +Xl0=1.0;Xl1=0.3;Xl2=0.3;V=1; + +//transfer reactance during LG fault(fault not cleared) by star delta transformation is given by +X12_fault=1.45; + +//transfer reactance after LG faulted line open is given by +X12_fault_open=1.22; + +//transfer reactance when all the lines are healthy is given by +X12_healthy=0.8; + +//power angle equations +delta=0:0.1:180; + +//Prefault condition +Pe1=(E*V)*sind(delta)/X12_healthy; +//for an initial load of 1PU +delta0=asind(1/1.5); + +//during fault +Pe2=(E*V)*sind(delta)/X12_fault; + +//during single pole switching +Pe3=(E*V)*sind(delta)/X12_fault_open; + +//during three pole switching +Pe4=0; + +//after reclosure +Pe5=Pe1; + +Pm=1.0; + +//xdot function defining the swing equations of machine during single poling +function xdot=mac_1_pole(t,x,tc,tr) + xdot(1)=x(2); + if (t<=tc) then + xdot(2)=180*50*(Pm-(0.827*sind(x(1))))/12; //swing equation before clearing the faulted line + elseif (t>tc)&(t<tr) then + xdot(2)=180*50*(Pm-(0.985*sind(x(1))))/12;//swing equation during single pole switching + elseif (t>=tr) then + xdot(2)=180*50*(Pm-(1.5*sind(x(1))))/12; //after reclosure + end +endfunction + +//xdot function defining the swing equations of machine during three poling +function xdot=mac_3_pole(t,x,tc,tr) + xdot(1)=x(2); + if (t>tc)&(t<tr) then + xdot(2)=180*50*(Pm-0)/4.167;//swing equation during three pole switching + elseif (t<=tc) then + xdot(2)=180*50*(Pm-(0.827*sind(x(1))))/4.167; //swing equation before clearing the faulted line + elseif (t>=tr) then + xdot(2)=180*50*(Pm-(1.5*sind(x(1))))/4.167; //after reclosure + end +endfunction + +//to find the solution of swing equation to draw the swing curves + +//to draw the swing curves for three pole switching with reclosure +subplot(2,1,1) +x_1_0=[41.8,0]';t0=0; T=0:0.001:0.65;T=T'; +tc=0.075;tr=0.325; +sol1=ode(x_1_0,t0,T,mac_3_pole); +plot(T,sol1(1,:)'); +set(gca(),"grid",[1 1]); +title('Swing Curve for three pole switching at '+string(tc)+' s'+' and reclosure at '+string(tr)+' s','fontsize',3); +xset("font size",3) +xstring(0.2,300,'MACHINE UNSTABLE'); +xlabel('Time (in seconds)----->'); +ylabel('Torque Angle (delta,deg)----->'); + +//to draw the swing curves for single pole switching with reclosure +subplot(2,1,2) +x_1_0=[41.8,0]';t0=0; T=0:0.001:2.2;T=T'; +tc=0.075;tr=0.325; +sol2=ode(x_1_0,t0,T,mac_1_pole); +plot(T,sol2(1,:)'); +set(gca(),"grid",[1 1]); +title('Swing Curve for single pole switching at '+string(tc)+' s'+' and reclosure at '+string(tr)+' s','fontsize',3); +xset("font size",3) +xstring(1.2,50,'MACHINE STABLE'); +xlabel('Time (in seconds)----->'); +ylabel('Torque Angle (delta,deg)----->'); + +f=get("current_figure"); +f.figure_position=[0,15]; +f.figure_size=[560,1000]; + diff --git a/Working_Examples/83/CH12/EX12.12/result_12_12.jpeg b/Working_Examples/83/CH12/EX12.12/result_12_12.jpeg Binary files differnew file mode 100755 index 0000000..8614513 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.12/result_12_12.jpeg diff --git a/Working_Examples/83/CH12/EX12.2/example_12_2.sce b/Working_Examples/83/CH12/EX12.2/example_12_2.sce new file mode 100755 index 0000000..198bc31 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.2/example_12_2.sce @@ -0,0 +1,45 @@ +//Chapter 12 +//Example 12.1 +//page 448 +//To calculate steady state power limit +clear;clc; + +Xdg=1*%i; //generator's +Xdm=1*%i; //motor's +Xt=0.1*%i; //transformers +Xl=0.25*%i; //transmission line's +Xc=-1*%i; //static capacitor's +Xi=1*%i; //inductive reactor +Eg=1.2; //generator's internal voltage +Em=1; //motor's internal voltage + +//case(i) steady state power limit without reactor +P1=(abs(Eg)*abs(Em))/(abs(Xdg+Xt+Xl+Xt+Xdm)); +printf('\n\n Steady state power limit without reactor = %0.5f pu',P1); + +//case(ii) steady state power limit with capacitive reactor +//three arms of star connected reactances are +Xa=Xdg+Xt+Xl; //from generator side +Xb=Xdm+Xt; //from load side +Xc=Xc; //from reactor side + +//converting star to delta +//reactance between generator side to load side is +Xab=(Xa*Xb+Xb*Xc+Xc*Xa)/Xc; +//power limit is +P2=(abs(Eg)*abs(Em))/(abs(Xab)); +printf('\n\n Steady state power limit with capacitive reactor = %0.5f pu',P2); + +//case(iii) steady state power limit with inductive reactor +//three arms of star connected reactances are +Xa=Xdg+Xt+Xl; //from generator side +Xb=Xdm+Xt; //from load side +Xc=Xi; //from reactor side + +//converting star to delta +//reactance between generator side to load side is +Xab=(Xa*Xb+Xb*Xc+Xc*Xa)/Xc; +//power limit is +P3=(abs(Eg)*abs(Em))/(abs(Xab)); +printf('\n\n Steady state power limit with inductive reactor = %0.5f pu',P3); + diff --git a/Working_Examples/83/CH12/EX12.2/result_example_12_2.txt b/Working_Examples/83/CH12/EX12.2/result_example_12_2.txt new file mode 100755 index 0000000..20581cd --- /dev/null +++ b/Working_Examples/83/CH12/EX12.2/result_example_12_2.txt @@ -0,0 +1,7 @@ + + + Steady state power limit without reactor = 0.48980 pu + + Steady state power limit with capacitive reactor = 1.24352 pu + + Steady state power limit with inductive reactor = 0.30496 pu diff --git a/Working_Examples/83/CH12/EX12.3/example_12_3.sce b/Working_Examples/83/CH12/EX12.3/example_12_3.sce new file mode 100755 index 0000000..e01d48d --- /dev/null +++ b/Working_Examples/83/CH12/EX12.3/example_12_3.sce @@ -0,0 +1,62 @@ +//Chapter 12 +//Example 12.3 +//page 450 +//To calculate maximum power transferred +clear;clc; + +Vt=1.0; //generator terminal voltage +V=1.0 ; //infinite bus voltage +Pe=1.0 ; //power delivered +Xd=0.25*%i ; //generator's transient reactance +Xl=0.5*%i ; //transmission line's reactance +Xt=0.1*%i; //transformer's reactance + +//to calculate alpha +alpha=asind(Pe*abs(Xt+Xl/2)/(abs(Vt)*abs(V))); +printf('\n\nAlpha=%0.1f deg',alpha); + +//current to infinite bus +I=(Vt*(cosd(alpha)+%i*sind(alpha))-V)/(Xt+Xl/2); +printf('\nCurrent to infinte bus=%d+j%0.3f pu',real(I),imag(I)); + +//votage behind transient reactance +E=Vt+I*(Xd+Xt+Xl/2); +printf('\nVoltage behind transient reactance= E''= %0.3f+j%0.1f pu = %0.3f @%0.1f deg pu\n\n',real(E),imag(E),abs(E),atand(imag(E)/real(E))); + +delta=0:0.001:180; + +//case(a) Maximum power when system is healthy +X12=Xd+Xt+Xl/2; +Pmax=abs(V)*abs(E)/abs(X12); +Pe1=Pmax*sind(delta); +printf('Maximum power that can be transferred under the following condition is') +printf('\n\n(a)System Healthy:'); +printf('\nPmax=%0.2f pu',Pmax); +printf('\nPe=%0.2f sin(delta) pu',Pmax); + +//case(b) One line short in the middle +//converting bus3 to delta40 +Xa=Xd+Xt; //generator side +Xb=Xl; //healthy transmission line side +Xc=Xl/2; //unhealthy line side +X12=(Xa*Xb+Xb*Xc+Xc*Xa)/(Xc); +Pmax=abs(V)*abs(E)/abs(X12); +Pe2=Pmax*sind(delta); +printf('\n\n(b)One line shorted in the middle:'); +printf('\nPmax=%0.4f pu',Pmax); +printf('\nPe=%0.4f sin(delta) pu',Pmax); + +//case(c) One line open +X12=Xd+Xt+Xl; +Pmax=abs(V)*abs(E)/abs(X12); +Pe3=Pmax*sind(delta); +printf('\n\n(c)One line open :'); +printf('\nPmax=%0.4f pu',Pmax); +printf('\nPe=%0.4f sin(delta) pu',Pmax); + +//plotting Power angle curves +plot(delta,Pe1,delta,Pe2,delta,Pe3); +legend(['1.79sin(delta)';'0.694sin(delta)';'1.265sin(delta)']); +title("Power angle curves"); +xlabel("Delta"); +ylabel("Pe");
\ No newline at end of file diff --git a/Working_Examples/83/CH12/EX12.3/result_example_12_3.txt b/Working_Examples/83/CH12/EX12.3/result_example_12_3.txt new file mode 100755 index 0000000..7ba9b55 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.3/result_example_12_3.txt @@ -0,0 +1,20 @@ + + +Alpha=20.5 deg +Current to infinte bus=1+j0.181 pu +Voltage behind transient reactance= E'= 0.892+j0.6 pu = 1.075 @33.9 deg pu + +Maximum power that can be transferred under the following condition is + +(a)System Healthy: +Pmax=1.79 pu +Pe=1.79 sin(delta) pu + +(b)One line shorted in the middle: +Pmax=0.6933 pu +Pe=0.6933 sin(delta) pu + +(c)One line open : +Pmax=1.2643 pu +Pe=1.2643 sin(delta) pu + diff --git a/Working_Examples/83/CH12/EX12.3/result_example_12_3_img.jpeg b/Working_Examples/83/CH12/EX12.3/result_example_12_3_img.jpeg Binary files differnew file mode 100755 index 0000000..22682b4 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.3/result_example_12_3_img.jpeg diff --git a/Working_Examples/83/CH12/EX12.4/example_12_4.sce b/Working_Examples/83/CH12/EX12.4/example_12_4.sce new file mode 100755 index 0000000..bcd57a0 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.4/example_12_4.sce @@ -0,0 +1,20 @@ +//Chapter 12 +//Example 12.4 +//page 453 +//To calculate acceleration and rotor angle +clear;clc; + +delta0=33.9; //initial rotor angle +H=4; //inertia constant +f=50; //frequency +Pm=1; //mechanical power input +t=0.05; //time interval +angular_acceleration=(Pm-0.694*sind(delta0))*180*f/H; +delta_change=0.5*angular_acceleration*t^2; +delta_new=delta0+delta_change; +new_angular_acceleration=(Pm-0.694*sind(delta_new))*180*f/H; + +printf('\n\nInitial rotor angular acceleration = %d elect deg/s^2',angular_acceleration); +printf('\nDelta_change=%0.1f deg',delta_change); +printf('\nNew delta =delta1=%0.1f deg',delta_new); +printf('\nAngular acceleration at the end of 0.05s =%d elect deg/s^2\n\n',new_angular_acceleration); diff --git a/Working_Examples/83/CH12/EX12.4/result_example_12_4.txt b/Working_Examples/83/CH12/EX12.4/result_example_12_4.txt new file mode 100755 index 0000000..e05c3a4 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.4/result_example_12_4.txt @@ -0,0 +1,7 @@ + + +Initial rotor angular acceleration = 1379 elect deg/s^2 +Delta_change=1.7 deg +New delta =delta1=35.6 deg +Angular acceleration at the end of 0.05s =1340 elect deg/s^2 + diff --git a/Working_Examples/83/CH12/EX12.5/example_12_5.sce b/Working_Examples/83/CH12/EX12.5/example_12_5.sce new file mode 100755 index 0000000..ed53369 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.5/example_12_5.sce @@ -0,0 +1,35 @@ +//Chapter 12 +//Example 12.5 +//page 456 +//To calculate frequency of natural oscilations +clear;clc; + +E=1.2; //no load voltage +V=1; //infinite bus voltage +Xg=1.2; // synchronous generator reactance +Xtl=0.6 //transformer anf transmission line reactance +H=4; //inertia constant + +//case(i) 50% loading +delta0=asind(0.5); +synchronizing_coefficien=(abs(E)*abs(V)*cosd(delta0))/(Xg+Xtl); +M=H/(%pi*50); +p=%i*sqrt(synchronizing_coefficien/M); +f=abs(p)/(2*%pi); +printf('\n\ncase(i) For 50%% loading'); +printf('\nDelta_0=%d deg',delta0); +printf('\nsynchronizing_coefficient=%0.3f MW(pu)/elect rad',synchronizing_coefficien); +printf('\nM=%0.4f s^2/elect rad',M); +printf('\nFrequency of oscillations=%0.2f rad/sec = %0.3f Hz\n',abs(p),f); + +//case(i) 80% loading +delta0=asind(0.8); +synchronizing_coefficien=(abs(E)*abs(V)*cosd(delta0))/(Xg+Xtl); +M=H/(%pi*50); +p=%i*sqrt(synchronizing_coefficien/M); +f=abs(p)/(2*%pi); +printf('\n\ncase(ii) For 80%% loading'); +printf('\nDelta_0=%d deg',delta0); +printf('\nSynchronizing_coefficient=%0.3f MW(pu)/elect rad',synchronizing_coefficien); +printf('\nM=%0.4f s^2/elect rad',M); +printf('\nFrequency of oscillations=%0.2f rad/sec = %0.3f Hz\n',abs(p),f);
\ No newline at end of file diff --git a/Working_Examples/83/CH12/EX12.5/result_example_12_5.txt b/Working_Examples/83/CH12/EX12.5/result_example_12_5.txt new file mode 100755 index 0000000..d48c344 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.5/result_example_12_5.txt @@ -0,0 +1,15 @@ + + + +case(i) For 50% loading +Delta_0=30 deg +synchronizing_coefficient=0.577 MW(pu)/elect rad +M=0.0255 s^2/elect rad +Frequency of oscillations=4.76 rad/sec = 0.758 Hz + + +case(ii) For 80% loading +Delta_0=53 deg +Synchronizing_coefficient=0.400 MW(pu)/elect rad +M=0.0255 s^2/elect rad +Frequency of oscillations=3.96 rad/sec = 0.631 Hz diff --git a/Working_Examples/83/CH12/EX12.6/example_12_6.sce b/Working_Examples/83/CH12/EX12.6/example_12_6.sce new file mode 100755 index 0000000..1507d88 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.6/example_12_6.sce @@ -0,0 +1,23 @@ +//Chapter 12 +//Example 12.6 +//page 457 +//To find steady state power limit +clear;clc; + +V=1.0; //infinite bus volatge +Vt=1.2; //terminal volatge +Xd=0.5*%i; //synchronous generator reactance +X=%i; //series reactance +//by solving the expressions given in the textbook +theta=acosd(0.5/1.8); +printf('\n\ntheta=%0.3f deg',theta); +Vt=Vt*(cosd(theta)+%i*sind(theta)); +printf('\nVt=%0.3f+j%0.3f pu',real(Vt),imag(Vt)); +I=(Vt-V)/X; +printf('\nI=%0.3f+j%0.3f pu',real(I),imag(I)); +E=Vt+Xd*I; +printf('\nE=%0.3f @ %d deg pu',abs(E),atand(imag(E)/real(E))); +Pmax=(abs(E)*abs(V))/abs(X+Xd); +printf('\n\nSteady state power limit is given by:\tPmax=%0.3f pu',Pmax); +E=1.2;Pmax=(abs(E)*abs(V))/abs(X+Xd); +printf('\n\nIf the generator emf is held fixed at a value 1.2pu,steady state power limit would be :\t Pmax=%0.2f pu\n\n',Pmax);
\ No newline at end of file diff --git a/Working_Examples/83/CH12/EX12.6/result_example_12_6.txt b/Working_Examples/83/CH12/EX12.6/result_example_12_6.txt new file mode 100755 index 0000000..b7933b1 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.6/result_example_12_6.txt @@ -0,0 +1,10 @@ + +theta=73.872 deg +Vt=0.333+j1.153 pu +I=1.153+j0.667 pu +E=1.729 @ -90 deg pu + +Steady state power limit is given by: Pmax=1.153 pu + +If the generator emf is held fixed at a value 1.2pu,steady state power limit would be : Pmax=0.80 pu + diff --git a/Working_Examples/83/CH12/EX12.7/example_12_7.sce b/Working_Examples/83/CH12/EX12.7/example_12_7.sce new file mode 100755 index 0000000..5e2663f --- /dev/null +++ b/Working_Examples/83/CH12/EX12.7/example_12_7.sce @@ -0,0 +1,45 @@ +//Chapter 12 +//Example 12.7 +//page 475 +//To calculate critcal clearing angle +clear;clc; + +Xd=0.25; //direct axis transient reactance of the generator +Xl1=0.5; Xl2=0.4; //reactances of transmission line +E=1.2; //voltage behind transient reactance +Xinf=0.05; //reactnce before infinite bus +V=1; //infinite bus voltage +Pm=1; //mechanical input to the generator +delta=0:1:180; + +//Normal operation (prefault) +X1=Xd+(Xl1*Xl2/(Xl1+Xl2))+Xinf; //equivalent reactance between sending ened and receiving end +//Power angle equation before the fault is +Pe1=(E*V/X1)*sind(delta); +//prefault operating power =1.0pu +delta0=asin(1/max(Pe1)); +printf('Normal Operation (prefault):\n'); +printf('X1=%0.3f PU\n',X1); +printf('Pe1=%0.1fsin(delta)\n\n',max(Pe1)); + +//during fault there will be no power transfer +Pe2=0; +printf('During Fault:\n'); +printf('Pe2=%d\n\n',Pe2); + +//Post fault operation(fault cleared by opening the faulted line) +X3=Xd+Xl1+Xinf; +Pe3=(E*V/X3)*sind(delta); +delta_max=%pi-asin(Pm/max(Pe3)); +//from A1 and A2, we solve A1=A2 +deff('[y]=fx(delta_cr)',"y=1.5*cos(delta_cr)+delta_cr-1.293-Pm*(delta_cr-delta0)"); +delta_cr=fsolve(0.45,fx); +printf('Post fault operation(fault cleared by opening the faulted line):\n'); +printf('X3=%0.1fPU\n',X3); +printf('Pe3=%0.1fsin(delta)\n',max(Pe3)); +printf('Delta_cr=%0.4f rad =%0.2f deg',delta_cr,delta_cr*180/%pi); +plot(delta,Pe1,delta,Pe3,delta,Pm*ones(1,length(delta))); +legend('Pe1=2.3sin(delta)','Pe3=1.5sin(delta)','Pm=1'); +title('Power angle Diagram for example 12.7'); +xlabel('delta (in degrees)----->'); +ylabel('Electrical output (Pe)----->');
\ No newline at end of file diff --git a/Working_Examples/83/CH12/EX12.7/result_example_12_7.txt b/Working_Examples/83/CH12/EX12.7/result_example_12_7.txt new file mode 100755 index 0000000..63fb998 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.7/result_example_12_7.txt @@ -0,0 +1,12 @@ + +Normal Operation (prefault): +X1=0.522 PU +Pe1=2.3sin(delta) + +During Fault: +Pe2=0 + +Post fault operation(fault cleared by opening the faulted line): +X3=0.8PU +Pe3=1.5sin(delta) +Delta_cr=0.9742 rad =55.82 deg diff --git a/Working_Examples/83/CH12/EX12.7/result_example_12_7_img.jpeg b/Working_Examples/83/CH12/EX12.7/result_example_12_7_img.jpeg Binary files differnew file mode 100755 index 0000000..42d4b8e --- /dev/null +++ b/Working_Examples/83/CH12/EX12.7/result_example_12_7_img.jpeg diff --git a/Working_Examples/83/CH12/EX12.8/example_12_8.sce b/Working_Examples/83/CH12/EX12.8/example_12_8.sce new file mode 100755 index 0000000..68b4863 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.8/example_12_8.sce @@ -0,0 +1,50 @@ +//Chapter 12 +//Example 12.8 +//page 477 +//To calculate critcal clearing angle +clear;clc; + +Xd=0.25; //direct axis transient reactance of the generator +Xl1=0.28; Xl2_1=0.14;Xl2_2=0.14; //reactances of transmission line +E=1.2; //voltage behind transient reactance +Xinf=0.17; //reactnce before infinite bus +V=1; //infinite bus voltage +Pm=1; //mechanical input to the generator +Xtr=0.15; //transformer reactance +delta=0:1:180; + +//prefault operation +X1=Xd+Xinf+(Xtr+Xl1+Xtr)/2; //transfer reactance between generator and infinte bus +Pe1=E*V*sind(delta)/X1; +delta0=asin(1/max(Pe1)); +printf('Normal Operation (prefault):\n'); +printf('X1=%0.3f PU\n',X1); +printf('Pe1=%0.2fsin(delta)\n',max(Pe1)); +printf('delta0=%0.3fPU\n\n',delta0); +//during fault there will be no power transfer +//using star delta transformation given in the textbook +X2=2.424; +Pe2=E*V*sind(delta)/X2; +printf('During Fault:\n'); +printf('X2=%0.3f PU\n',X2); +printf('Pe2=%0.3fsin(delta)\n\n',max(Pe2)); + +//Post fault operation(faulty line switched off) +X3=Xd+Xinf+(Xtr+Xl1+Xtr); +Pe3=E*V*sind(delta)/X3; +delta_max=%pi-asin(Pm/max(Pe3)); +//from A1 and A2, we solve A1=A2 +deff('[y]=fx(delta_cr)',"y=-delta0+max(Pe2)*cos(delta_cr)-0.399-0.661-max(Pe3)*cos(delta_cr)+delta_max"); +delta_cr=fsolve(0.45,fx); +printf('Post fault operation(faulty line switched off):\n'); +printf('X3=%0.1fPU\n',X3); +printf('Pe3=%0.1fsin(delta)\n',max(Pe3)); +printf('Delta_cr=%0.4f rad =%0.2f deg',delta_cr,delta_cr*180/%pi); +plot(delta,Pe1,delta,Pe2,delta,Pe3,delta,Pm); +legend('Pe1=1.69sin(delta)','Pe2=0.495sin(delta)','Pe3=1.2sin(delta)','Pm=1'); +title('Power angle Diagram for example 12.8'); +xlabel('delta (in degrees)----->'); +ylabel('Electrical output (Pe)----->'); +f=get("current_figure") +f.figure_position=[0,15] +f.figure_size=[750,750] diff --git a/Working_Examples/83/CH12/EX12.8/result_example_12_8.jpeg b/Working_Examples/83/CH12/EX12.8/result_example_12_8.jpeg Binary files differnew file mode 100755 index 0000000..424f5aa --- /dev/null +++ b/Working_Examples/83/CH12/EX12.8/result_example_12_8.jpeg diff --git a/Working_Examples/83/CH12/EX12.8/result_example_12_8.txt b/Working_Examples/83/CH12/EX12.8/result_example_12_8.txt new file mode 100755 index 0000000..47c5db1 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.8/result_example_12_8.txt @@ -0,0 +1,16 @@ + + +Normal Operation (prefault): +X1=0.710 PU +Pe1=1.69sin(delta) +delta0=0.633PU + +During Fault: +X2=2.424 PU +Pe2=0.495sin(delta) + +Post fault operation(faulty line switched off): +X3=1.0PU +Pe3=1.2sin(delta) +Delta_cr=0.8536 rad =48.91 deg + diff --git a/Working_Examples/83/CH12/EX12.9/example_12_9.sce b/Working_Examples/83/CH12/EX12.9/example_12_9.sce new file mode 100755 index 0000000..8fe1976 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.9/example_12_9.sce @@ -0,0 +1,19 @@ +//Chapter 12 +//Example 12.9 +//page 479 +//To calculate critcal clearing angle +clear;clc; +Pmax1=2; // prefault(2 lines) +Pmax2=0.5; //deuring fault +Pmax3=1.5; //post fault(1 line) +Pm=1; //initial loading + +delta0=asin(Pm/Pmax1); +delta_max=%pi-asin(Pm/Pmax3); + +//to find critical angle,using eq.12.67 +delta_cr=acos((Pm*(delta_max-delta0)-Pmax2*cos(delta0)+Pmax3*cos(delta_max))/(Pmax3-Pmax2)); +printf('Pmax1=%0.1f PU\t Pmax2=%0.2f PU\t Pmax3=%0.2f PU\n\n',Pmax1,Pmax2,Pmax3); +printf('Delta0=%0.3f rad\n\n',delta0); +printf('Delta_max=%0.3f rad\n\n',delta_max); +printf('Delta_cr=%0.3f rad =%0.2f deg\n\n',delta_cr,delta_cr*180/%pi); diff --git a/Working_Examples/83/CH12/EX12.9/result_example_12_9.txt b/Working_Examples/83/CH12/EX12.9/result_example_12_9.txt new file mode 100755 index 0000000..bad40c5 --- /dev/null +++ b/Working_Examples/83/CH12/EX12.9/result_example_12_9.txt @@ -0,0 +1,11 @@ + + +Pmax1=2.0 PU Pmax2=0.50 PU Pmax3=1.50 PU + +Delta0=0.524 rad + +Delta_max=2.412 rad + +Delta_cr=1.227 rad =70.29 deg + + |
