电力系统稳定性分析matlab程序

1、电力系统稳定性分析作业一1 euler.m ,reuler.m, kunta.m分别为（1）中的欧拉法，改进欧拉法，龙格库塔法的主程序；doty.m,doty2.m,doty3.m均为（1）中子函数程序。Runge-Kutta.m为（2）和（3）的运行程序。下表为三种方法的部分运行结果功角数据：时间00.010.020.030.040.050.060.070.08欧拉35.161535.161535.282835.523635.882036.356036.943437.642238.4500改进35.161535.222235.402335.699936.113036.639437.27703

2、8.023438.8763龙格35.161535.221935.401635.698936.111636.637637.274738.020738.8731时间0090.100.110.120.130.140.150.160.17欧拉39.364640.383541.504342.636643.777344.923046.070937.642238.4500改进39.833240891842.005143.125644.250145.375746.499547.618748.7305龙格39.829540.887542.000243.120044.244045.369046.492347.61

3、1048.7224（1）欧拉法在matlaB中输入命令t,x,y,z=euler('doty','doty2','doty3',0,5,0.1,0.01)可得t-w曲线，t-曲线分别如下图所示。具体功角，角速度数据分别见文件1.mat 和2.mat（2）欧拉改进法在matlab命令窗口输入t,x,y,z=reuler('doty','doty2','doty3',0,5,0.1,0.01)t-w曲线，t-曲线分别如下图所示。具体功角，角速度数据分别见文件3.mat 和4.mat（3）龙格库塔法在ma

4、tlab命令窗口输入t,x,y,z=kunta('doty','doty2','doty3',0,5,0.1,0.01)t-w曲线，t-曲线分别如下图所示。具体功角，角速度数据分别见文件5.mat 和6.mat2 运行Runge-Kutta,将参数阻尼D设置为0.05，不断更改参数切除时间t的值，当t=0.2728和t=0.2730时，运行程序分别得到如下两图： 则当阻尼D=0.05 时，临界切除时间 CCT=0.2729类似可以求得：阻尼D=0.2时，临界切除时间为CCT=0.5729由以上数据我们可以看出：阻尼增大时，临界切除时间也增大了。即

5、伴随阻尼的增大，功角和角速度振荡衰减更明显，系统更容易回到平衡状态，系统的稳定性更好。3接地阻抗X=0.05时，临界切除时间CCT=0.2462接地阻抗X=0.1时，临界切除时间CCT=0.3112由以上数据我们可以看出：接地阻抗增大时，系统临界切除时间也增大了，系统稳定性变好。附注：以下为详细的程序清单。【Euler.m】欧拉法主程序functiont,x,y,z=euler(fun1,fun2,fun3,t0,xfinal,tm,h)n=(xfinal-t0)/h;n1=(tm-t0)/h; global Kw p0 pp2 d1 w pp1 f=50;Tj=11;p0=1.0;d1=0.

6、05;xd=0.29;xt1=0.13;xt2=0.11;xx=0.07149;xl=0.58;E0=1.4239;V0=1.0;w=2*pi*f;Kw=w2/Tj;x1=xd+xt1+0.5*xl+xt2;x2=x1+(xd+xt1)*(0.5*xl+xt2)/xx;x3=x1+0.5*xl;pp1=E0*V0/x2;pp2=E0*V0/x3;t(1)=t0;x(1)=asin(p0*x1/E0/V0);y(1)=2*pi*f;z(1)=x(1)*180/pi;for ii=1:n1 t(ii+1)=t(ii)+h; x(ii+1)=x(ii)+h*feval(fun1,y(ii); y(i

7、i+1)=y(ii)+h*feval(fun2,x(ii),y(ii); z(ii+1)=x(ii+1)*180/pi;endfor ii=n1+1:n t(ii+1)=t(ii)+h; x(ii+1)=x(ii)+h*feval(fun1,y(ii); y(ii+1)=y(ii)+h*feval(fun3,x(ii),y(ii); z(ii+1)=x(ii+1)*180/pi;end【reuler.m】改进欧拉法主程序：function t,x,y,z=reuler(fun1,fun2,fun3,t0,xfinal,tm,h)n=(xfinal-t0)/h;n1=(tm-t0)/h;glob

8、al Kw p0 pp2 d1 w pp1 f=50;Tj=11;p0=1.0;d1=0.05;xd=0.29;xt1=0.13;xt2=0.11;xx=0.07149;xl=0.58;E0=1.4239;V0=1.0;w=2*pi*f;Kw=w2/Tj;x1=xd+xt1+0.5*xl+xt2;x2=x1+(xd+xt1)*(0.5*xl+xt2)/xx;x3=x1+0.5*xl;pp1=E0*V0/x2;pp2=E0*V0/x3;t(1)=t0;x(1)=asin(p0*x1/E0/V0);y(1)=2*pi*f;z(1)=x(1)*180/pi; for ii=1:n1 t(ii+1)=

9、t(ii)+h; k1=feval(fun1,y(ii); g1=feval(fun2,x(ii),y(ii); x0=x(ii)+h*k1; y0=y(ii)+h*g1; k2=feval(fun1,y0); g2=feval(fun2,x0,y0); x(ii+1)=x(ii)+h/2*(k1+k2); z(ii+1)=x(ii+1)*180/pi; y(ii+1)=y(ii)+h/2*(g1+g2);endfor ii=n1+1:n t(ii+1)=t(ii)+h; k1=feval(fun1,y(ii); g1=feval(fun3,x(ii),y(ii); x0=x(ii)+h*k1

10、; y0=y(ii)+h*g1; k2=feval(fun1,y0); g2=feval(fun3,x0,y0); x(ii+1)=x(ii)+h/2*(k1+k2); z(ii+1)=x(ii+1)*180/pi; y(ii+1)=y(ii)+h/2*(g1+g2);endsubplot(1,2,1)plot(t,y)subplot(1,2,2)plot(t,z);【kunta.m】龙格库塔法主程序functiont,x,y,z=kunta(fun1,fun2,fun3,t0,xfinal,tm,h)n=(xfinal-t0)/h;n1=(tm-t0)/h;global Kw p0 pp2

11、d1 w pp1 f=50;Tj=11;p0=1.0;d1=0.05;xd=0.29;xt1=0.13;xt2=0.11;xx=0.07149;xl=0.58;E0=1.4239;V0=1.0;w=2*pi*f;Kw=w2/Tj;x1=xd+xt1+0.5*xl+xt2;x2=x1+(xd+xt1)*(0.5*xl+xt2)/xx;x3=x1+0.5*xl;pp1=E0*V0/x2;pp2=E0*V0/x3;t(1)=t0;x(1)=asin(p0*x1/E0/V0);y(1)=2*pi*f;z(1)=x(1)*180/pi; for ii=1:n1 t(ii+1)=t(ii)+h; k1=f

12、eval(fun1,y(ii); g1=feval(fun2,x(ii),y(ii); x11=x(ii)+0.5*h*k1; y11=y(ii)+0.5*h*g1; k2=feval(fun1,y11); g2=feval(fun2,x11,y11); x22=x(ii)+0.5*h*k2; y22=y(ii)+0.5*h*g2; k3=feval(fun1,y22); g3=feval(fun2,x22,y22); x33=x(ii)+h*k2; y33=y(ii)+h*g2; k4=feval(fun1,y33); g4=feval(fun2,x33,y33); x(ii+1)=x(ii

13、)+h/6*(k1+2*k2+2*k3+k4); z(ii+1)=x(ii+1)*180/pi; y(ii+1)=y(ii)+h/6*(g1+2*g2+2*g3+g4);endfor ii=n1+1:n t(ii+1)=t(ii)+h; k1=feval(fun1,y(ii); g1=feval(fun3,x(ii),y(ii); x11=x(ii)+0.5*h*k1; y11=y(ii)+0.5*h*g1; k2=feval(fun1,y11); g2=feval(fun3,x11,y11); x22=x(ii)+0.5*h*k2; y22=y(ii)+0.5*h*g2; k3=feval(

14、fun1,y22); g3=feval(fun3,x22,y22); x33=x(ii)+h*k2; y33=y(ii)+h*g2; k4=feval(fun1,y33); g4=feval(fun3,x33,y33); x(ii+1)=x(ii)+h/6*(k1+2*k2+2*k3+k4); z(ii+1)=x(ii+1)*180/pi; y(ii+1)=y(ii)+h/6*(g1+2*g2+2*g3+g4);endsubplot(1,2,1)plot(t,y)subplot(1,2,2)plot(t,z);以下为子程序【doty.m】function fun1=doty(y)global

15、wfun1=(y-w);【doty2.m】function fun2=doty2(x,y)global w p0 pp1 d1 Kwfun2=Kw*(p0-pp1*sin(x)-d1*(y-w)/y【doty3.m】function fun3=doty3(x,y)global Kw p0 pp2 d1 wfun3=Kw*(p0-pp2*sin(x)-d1*(y-w)/y;以下为四阶龙格库塔法求临界切除时间程序：function jj % 初始值syms E0 xd Tj xt1 xt2 xl D xz U0 P0 Q0;E0=1.4239;xd=0.29;Tj=11;xt1=0.13;xt2=

16、0.11;xl=0.58;U0=1;P0=1;Q0=0.2; h=0.0001; %²参数调试xdet=0.07149; %xdet=0.07149;D=0.05; %D=0.05;t=0.2730;%xdet=0.07149; D=0.05 修改t可得到t= CCT=0.2729 det_c_lim=det3(2729)%xdet=0.07149; D=0.2 修改t可得到t= CCT=0.5729 det_c_lim=det3(5729)%xdet=0.05; D=0.05 修改t可得到t= CCT=0.2462 det_c_lim=det3(2462)%xdet=0.1; D=

17、0.05 修改t可得到t= CCT=0.3111 det_c_lim=det3(3111) %初始公式wn=2*pi*50; w1(1)=wn;w2(1)=wn;w3(1)=wn; T=t*10000;det1(1)=35.1615;det2(1)=35.1615;det3(1)=35.1615; Kw=wn2/Tj; Xdnum1=xd+xt1+0.5*xl+xt2; Peli1=E0*U0/Xdnum1; Xdnum2=Xdnum1+(xd+xt1)*(0.5*xl+xt2)/xdet; Peli2=E0*U0/Xdnum2; Xdnum3=Xdnum1+0.5*xl; Peli3=E0*

18、U0/Xdnum3; %四阶龙格库塔当t<0.1s时，故障for i=1:T K1det(i)=(w3(i)-wn)*180/pi; Pd=D*(w3(i)-wn); K1w(i)=Kw*(P0-Pd-Peli2*sin(det3(i)*2*pi/360)/w3(i); det_c0=det3(i)+0.5*h*K1det(i); w_c0=w3(i)+0.5*h*K1w(i); K2det(i)=(w_c0-wn)*180/pi; Pd=D*(w_c0-wn); K2w(i)=Kw*(P0-Pd-Peli2*sin(det_c0*2*pi/360)/w_c0; det_c1=det3(

19、i)+0.5*h*K2det(i); w_c1=w3(i)+0.5*h*K2w(i); K3det(i)=(w_c1-wn)*180/pi; Pd=D*(w_c1-wn); K3w(i)=Kw*(P0-Pd-Peli2*sin(det_c1*2*pi/360)/w_c1; det_c2=det3(i)+h*K3det(i); w_c2=w3(i)+h*K3w(i); K4det(i)=(w_c2-wn)*180/pi; Pd=D*(w_c2-wn); K4w(i)=Kw*(P0-Pd-Peli2*sin(det_c2*2*pi/360)/w_c2; det3(i+1)=det3(i)+h*(K1det(i)+ 2*K2det(i)+ 2*K3det(i)+ K4det(i)/6; w3(i+1)=w3(i)+h*(K1w(i)+2*K2w(i)+2*K3w(i)+K4w(i)/6;end% t>0.1s后清除故障for i=T+1:50000 K1det(i)=(w3(i)-wn)*180/pi; Pd=D*(w3(i)-wn); K1w(i)=Kw*(P0-Pd-Peli3*sin(det3(i)*2*pi/360)/w3(i);