电力系统稳定性分析matlab程序

1、电力系统稳定性分析作业一1euler.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00.010020.030.040.050.060.070.08欧35.16135.16135.28235.52335.88236.35636.94337.64238.450拉558600420改35.16135.22235.40235.69936.11336.63937.27738.02338.876进

2、523904043龙35.16135.22135.40135.69836.11136.63737.27438.02038.873格596966771时间0.090.100.110.120.130140.150.16017欧39.36440.383541.50442.63643.77744.92346.07037.64238.450拉63630920改39.83340.891842.00543.12544.25045.37546.49947.61848.730进21617575龙39.82940.887542.00043.12044.24445.36946.49247.61148.722格520

3、00304（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-d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-6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matlab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-6曲

4、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.mat6&31560553134022635o3W531553145313.531叫2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

5、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;globalKwp0pp2d1wpp1f=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=

6、2*pi*f;Kw=wA2/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;forii=1:n1t(ii+1)=t(ii)+h;x(ii+1)=x(ii)+h*feval(fun1,y(ii);y(ii+1)=y(ii)+h*feval(fun2,x(ii),y(ii);z(ii+1)=x(ii+1)*180/pi;endforii=n1

7、+1:nt(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：functiont,x,y,z=reuler(fun1,fun2,fun3,t0,xfinal,tm,h)n=(xfinal-t0)/h;n1=(tm-t0)/h;globalKwp0pp2d1wpp1f=50;Tj=11;p0=1.0;d1=0.05;xd=0.29;xt1=0.13;xt2=0.11;xx=0.07149

8、;xl=0.58;E0=1.4239;V0=1.0;w=2*pi*f;Kw=wA2/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;forii=1:n1t(ii+1)=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=f

9、eval(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);endforii=n1+1:nt(ii+1)=t(ii)+h;k1=feval(fun1,y(ii);g1=feval(fun3,x(ii),y(ii);x0=x(ii)+h*k1;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/

10、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;globalKwp0pp2d1wpp1f=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=wA2/

11、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;forii=1:n1t(ii+1)=t(ii)+h;k1=feval(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

12、,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)+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);endforii=n1+1:nt(ii+1)=t(ii)+h;k1=feval(fun1,y(

13、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(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(

14、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】functionfun1=doty(y)globalwfun1=(y-w);【doty2.m】functionfun2=doty2(x,y)globalwp0pp1d1Kwfun2=Kw*(p0-pp1*sin(x)-d1*(y-w)/y【doty3.m】functionfun3=doty3(x,y)globalKwp0pp2d1wfun3=Kw*(p0-

15、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：functionjj%初始值symsE0xdTjxt1xt2xlDxzU0P0Q0;E0=1.4239;xd=0.29;Tj=11;xt1=0.13;xt2=0.11;xl=0.58;U0=1;P0=1;Q0=0.2;h=0.0001;%2参数调试xdet=0.07149;D=0.05;%D=0t=0.2730;%xdet=0.07149;D=0.05%xdet=0.07149;D=0.2%xdet=0.05;D=0.05%xdet=0.1;D=0.05%xdet=0.07149;.05;修改t可得到t=CCT

16、=0.2729修改t可得到t=CCT=0.5729修改t可得至吐=CCT=0.2462修改t可得至吐=CCT=0.3111det_c_lim=det3(2729)det_c_lim=det3(5729)det_c_lim=det3(2462)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=wnA2/Tj;Xdnum1=xd+xt1+0.5*xl+xt2;Peli1=E0*U0/Xdnum1;Xdn

17、um2=Xdnum1+(xd+xt1)*(0.5*xl+xt2)/xdet;Peli2=E0*U0/Xdnum2;Xdnum3=Xdnum1+0.5*xl;Peli3=E0*U0/Xdnum3;%四阶龙格库塔当t0.1s后清除故障fori=T+1:50000K1det(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);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-Peli3*sin(det_c0*2*pi/360)/w_c0;det_c1=det3(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-Peli3*sin(det_c1*2*pi/360)/w_c1;det_c2=det3(i)+h*K3det(i);w_c2=w3(i)+h*K3w(