電力系統(tǒng)分析大作業(yè)一、設(shè)計(jì)題目本次設(shè)計(jì)題目選自課本第五章例5-8,美國(guó)西部聯(lián)合電網(wǎng)WSCC系統(tǒng)的簡(jiǎn)化三機(jī)九節(jié)點(diǎn)系統(tǒng)，例題中已經(jīng)給出了潮流結(jié)果，計(jì)算結(jié)果可以與之對(duì)照。取ε=0.00001。二、計(jì)算環(huán)節(jié)第一步，為了方便編程，修改節(jié)點(diǎn)的序號(hào)，將平衡節(jié)點(diǎn)放在最后。如下圖：992132745683第二步，這樣得出的系統(tǒng)參數(shù)如下表所示：第三步，形成節(jié)點(diǎn)導(dǎo)納矩陣。第四步，設(shè)定初值：；，。第五步，計(jì)算失配功率=0，=-1.25，=-0.9，=0，=-1，=0，=1.63，=0.85；=0.8614，=-0.2590，=-0.0420，=0.6275，=-0.1710，=0.7101。顯然，。第六步，形成雅克比矩陣（階數(shù)為14×14）第七步，解修正方程，得到：-0.0371，-0.0668，-0.0628，0.0732，0.0191，0.0422，0.1726，0.0908；0.0334，0.0084，0.0223，0.0372，0.0266，0.0400。從而-0.0371，-0.0668，-0.0628，0.0732，0.0191，0.0422，0.1726，0.0908；1.0334，1.0084，1.0223，1.0372，1.0266，1.0400。然后轉(zhuǎn)入下一次迭代。經(jīng)三次迭代后。迭代過(guò)程中失配功率的變化情況如下表：k0123Δ=P10-0.01060.00010.Δ=P2-1.250.03790.00050.Δ=P3-0.90.04390.00050.Δ=P40-0.0421-0.0012-0.Δ=P5-10.0610.00090.Δ=P60-0.0269-0.0007-0.Δ=P71.63-0.0579-0.0004-0.Δ=P80.85-0.0336-0.0002-0.Δ=Q10.8614-0.0501-0.0004-0.Δ=Q2-0.259-0.0714-0.0012-0.Δ=Q3-0.042-0.0424-0.0006-0.Δ=Q40.6275-0.1875-0.0021-0.Δ=Q5-0.171-0.0241-0.0004-0.Δ=Q60.7101-0.0828-0.0007-0.max1.630.0610.00090.迭代過(guò)程中節(jié)點(diǎn)電壓變化情況如下表：kU1U2U3U4U5U6011111111.03341.00841.02231.03721.02661.040021.02590.99581.01281.02591.01601.032431.02580.99561.01271.02581.01591.0324迭代收斂后各節(jié)點(diǎn)的電壓和功率：kUθPQ11.0258-2.21680.00000.000020.9956-3.9888-1.2500-0.500031.0127-3.6874-0.9000-0.300041.02583.71970.00000.000051.01590.7275-1.0000-0.350061.03241.96670.00000.000071.02509.28001.63000.066581.02504.66480.8500-0.108691.04000.00000.71640.2705同課本上給出的潮流相比較，結(jié)果完全一致，證明計(jì)算過(guò)程與程序編寫對(duì)的。最后得出迭代收斂后各支路的功率和功率損耗：ijPijQijIijPjiQjiIjiPLQL120.40940.22890.4572-0.4068-0.38690.56390.0026-0.1579130.30700.01030.2995-0.3054-0.16540.34300.0017-0.155124-0.8432-0.11310.85450.8662-0.08380.84840.0230-0.196936-0.5946-0.13460.60200.6082-0.18070.61460.0135-0.3153450.7638-0.00800.7447-0.7590-0.10700.75460.0048-0.115056-0.2410-0.24300.33680.24180.03120.23620.0009-0.2118910.71640.27050.7363-0.7164-0.23920.73630.00000.0312741.63000.06651.5916-1.63000.09181.59160.00000.1583860.8500-0.10860.8360-0.85000.14960.83600.00000.0410三、源程序及注釋由于計(jì)算流程比較簡(jiǎn)樸，所以編寫程序過(guò)程中沒(méi)有采用模塊化的形式，直接按順序一步步進(jìn)行。disp('【節(jié)點(diǎn)數(shù):】');[n1]=xlsread('input.xls','A3:A3')%節(jié)點(diǎn)數(shù)disp('【支路數(shù):】');[n]=xlsread('input.xls','B3:B3')%支路數(shù)disp('【精度:】');Accuracy=xlsread('input.xls','B4:B4')%精度[branch]=xlsread('input.xls','E4:K12');[node]=xlsread('input.xls','M4:S12');Data_B1=branch;%支路參數(shù)Data_B2=node;%節(jié)點(diǎn)參數(shù)T1=zeros(n,2);T2=zeros(n1,3);i=sqrt(-1);formatshortforj=1:nT1(j,1)=Data_B1(j,3)+Data_B1(j,4)*1i;T1(j,2)=Data_B1(j,5)*1i;endforj=1:n1T2(j,1)=Data_B2(j,1)+Data_B2(j,2)*1i;T2(j,2)=Data_B2(j,3)+Data_B2(j,4)*1i;endB1=zeros(n,6);B2=zeros(n1,5);forj=1:nB1(j,1)=Data_B1(j,1);B1(j,2)=Data_B1(j,2);B1(j,3)=T1(j,1);B1(j,4)=T1(j,2);B1(j,5)=Data_B1(j,6);B1(j,6)=Data_B1(j,7);endforj=1:n1B2(j,1)=T2(j,1);B2(j,2)=T2(j,2);B2(j,3)=Data_B2(j,5);B2(j,4)=Data_B2(j,6);B2(j,5)=Data_B2(j,7);enddisp('【支路參數(shù)矩陣:】');B1%顯示支路參數(shù)矩陣disp('【節(jié)點(diǎn)參數(shù)矩陣:】');B2%顯示節(jié)點(diǎn)參數(shù)矩陣%以上為從excel中導(dǎo)入初值的程序Y=zeros(n1);fori=1:nifB1(i,6)==0%不含變壓器的支路p=B1(i,1);q=B1(i,2);Y(p,q)=Y(p,q)-1/B1(i,3);Y(q,p)=Y(p,q);Y(p,p)=Y(p,p)+1/B1(i,3)+0.5*B1(i,4);Y(q,q)=Y(q,q)+1/B1(i,3)+0.5*B1(i,4);else%具有變壓器的支路p=B1(i,1);q=B1(i,2);Y(p,q)=Y(p,q)-1/(B1(i,3)*B1(i,5));Y(q,p)=Y(p,q);Y(p,p)=Y(p,p)+1/B1(i,3);Y(q,q)=Y(q,q)+1/(B1(i,5)^2*B1(i,3));endenddisp('【導(dǎo)納矩陣:】');Y%顯示導(dǎo)納矩陣m=0;fori=1:n1ifB2(i,5)==2m=m+1;endendm%PQ節(jié)點(diǎn)個(gè)數(shù)l=0;fori=1:n1ifB2(i,5)==1l=l+1;endendl%PV節(jié)點(diǎn)個(gè)數(shù)Mismatch_power=zeros(l+m*2,1);fori=1:n1-1Pj=0;forj=1:n1Pj=Pj+(B2(i,3)*B2(j,3)*(real(Y(i,j))*cos(B2(i,4)-B2(j,4))+imag(Y(i,j))*sin(B2(i,4)-B2(j,4))));endMismatch_power(i,1)=real(B2(i,1))-real(B2(i,2))-Pj;endfork=n1:(l+m*2)Qj=0;forj=1:n1Qj=Qj+B2((k-n1+1),3)*B2(j,3)*(real(Y((k-n1+1),j))*sin(B2((k-n1+1),4)-B2(j,4))-imag(Y((k-n1+1),j))*cos(B2((k-n1+1),4)-B2(j,4)));endMismatch_power(k,1)=imag(B2((k-n1+1),1))-imag(B2((k-n1+1),2))-Qj;end%Mismatch_power%計(jì)算失配功率times=0;while(max(Mismatch_power)>Accuracy)fori=1:(n1-1)Pj=0;forj=1:n1Pj=Pj+B2(i,3)*B2(j,3)*(real(Y(i,j))*cos(B2(i,4)-B2(j,4))+imag(Y(i,j))*sin(B2(i,4)-B2(j,4)));endMismatch_power(i,1)=real(B2(i,1))-real(B2(i,2))-Pj;endfork=n1:(l+m*2)Qj=0;forj=1:n1Qj=Qj+B2((k-n1+1),3)*B2(j,3)*(real(Y((k-n1+1),j))*sin(B2((k-n1+1),4)-B2(j,4))-imag(Y((k-n1+1),j))*cos(B2((k-n1+1),4)-B2(j,4)));endMismatch_power(k,1)=imag(B2((k-n1+1),1))-imag(B2((k-n1+1),2))-Qj;enddisp('【當(dāng)前迭代次數(shù):】');timesdisp('【失配功率:】');Mismatch_powerJacobian=zeros(l+m*2);%雅克比矩陣7*7%————————————————————————————————————Hfori=1:(n1-1)forj=1:(n1-1)ifi==jP_H=0;fork=1:n1P_H=P_H+B2(i,3)*B2(k,3)*(real(Y(i,k))*sin(B2(i,4)-B2(k,4))-imag(Y(i,k))*cos(B2(i,4)-B2(k,4)));endJacobian(i,i)=P_H-B2(i,3)*B2(i,3)*(0-imag(Y(i,i)));elseJacobian(i,j)=0-B2(i,3)*B2(j,3)*(real(Y(i,j))*sin(B2(i,4)-B2(j,4))-imag(Y(i,j))*cos(B2(i,4)-B2(j,4)));endendend%————————————————————————————————————Nfori=1:(n1-1)forj=1:mifi==jP_N=0;fork=1:n1P_N=P_N+B2(k,3)*(real(Y(i,k))*cos(B2(i,4)-B2(k,4))+imag(Y(i,k))*sin(B2(i,4)-B2(k,4)));endJacobian(i,n1-1+i)=0-B2(i,3)*real(Y(i,i))-P_N;elseJacobian(i,n1-1+j)=0-B2(i,3)*(real(Y(i,j))*cos(B2(i,4)-B2(j,4))+imag(Y(i,j))*sin(B2(i,4)-B2(j,4)));endendend%————————————————————————————————————Kfori=1:mforj=1:(n1-1)ifi==jP_K=0;fork=1:n1P_K=P_K+B2(i,3)*B2(k,3)*(real(Y(i,k))*cos(B2(i,4)-B2(k,4))+imag(Y(i,k))*sin(B2(i,4)-B2(k,4)));endJacobian(n1-1+i,i)=0+B2(i,3)*B2(i,3)*real(Y(i,i))-P_K;elseJacobian(n1-1+i,j)=B2(i,3)*B2(j,3)*(real(Y(i,j))*cos(B2(i,4)-B2(j,4))+imag(Y(i,j))*sin(B2(i,4)-B2(j,4)));endendend%————————————————————————————————————Lfori=1:mforj=1:mifi==jP_L=0;fork=1:n1P_L=P_L+B2(k,3)*(real(Y(i,k))*sin(B2(i,4)-B2(k,4))-imag(Y(i,k))*cos(B2(i,4)-B2(k,4)));endJacobian(n1-1+i,n1-1+i)=0-P_L+B2(i,3)*imag(Y(i,i));elseJacobian(n1-1+i,n1-1+j)=0-B2(i,3)*(real(Y(i,j))*sin(B2(i,4)-B2(j,4))-imag(Y(i,j))*cos(B2(i,4)-B2(j,4)));endendendS=zeros(l+m*2,1);%初始化電壓角度變化量S=inv(Jacobian)*(0-Mismatch_power);%求解修正方程S=(Jacobian)\(0-Mismatch_power);%求解修正方程fori=1:(n1-1)%角度初值加變化量B2(i,4)=B2(i,4)+S(i,1);endfori=1:m%電壓初值加變化量B2(i,3)=B2(i,3)+S(n1-1+i,1);enddisp('【雅克比矩陣:】');Jacobian%顯示雅克比矩陣%S=inv(Jacobian)times=times+1;endtimes=times-1;disp('【共計(jì)迭代次數(shù):】');times%顯示迭代次數(shù)U_It=zeros(n1,1);%初始化電壓向量fori=1:n1U_It(i,1)=B2(i,3)*cos(B2(i,4))+B2(i,3)*sin(B2(i,4))*1j;endangle_It=zeros(n1,1);%將電壓角度的弧度值轉(zhuǎn)為角度值fori=1:n1angle_It(i,1)=B2(i,4)*180/pi;endNode_S_It=U_It.*(conj(Y)*conj(U_It));%求解節(jié)點(diǎn)功率disp('【迭代收斂后各節(jié)點(diǎn)的電壓幅值:】');Node_U_It=abs(U_It)%顯示迭代收斂后各節(jié)點(diǎn)的電壓幅值disp('【迭代收斂后各節(jié)點(diǎn)的電壓角度:】');angle_It%顯示迭代收斂后各節(jié)點(diǎn)的電壓角度disp('【迭代收斂后各節(jié)點(diǎn)的功率:】');Node_S_It%顯示迭代收斂后各節(jié)點(diǎn)的功率Branch_It=zeros(n,10);fori=1:n;ifB1(i,6)==0;%不帶變壓器支路m=B1(i,1);%得到支路號(hào)n=B1(i,2);Branch_It(i,1)=m;%顯示支路號(hào)Branch_It(i,2)=n;a=U_It(m,1)*(conj(U_It(m,1))*conj(B1(i,4))*0.5+(conj(U_It(m,1))-conj(U_It(n,1)))/conj(B1(i,3)));Branch_It(i,3)=real(a);%顯示PijBranch_It(i,4)=imag(a);%顯示Qijb=U_It(m,1)*B1(i,4)*0.5+(U_It(m,1)-U_It(n,1))/B1(i,3);Branch_It(i,5)=sqrt(real(b)^2+imag(b)^2);%顯示Iijc=U_It(n,1)*(conj(U_It(n,1))*conj(B1(i,4))*0.5+(conj(U_It(n,1))-conj(U_It(m,1)))/conj(B1(i,3)));Branch_It(i,6)=real(c);%顯示PjiBranch_It(i,7)=imag(c);%顯示Qjid=U_It(n,1)*B1(i,4)*0.5+(U_It(n,1)-U_It(m,1))/B1(i,3);Branch_It(i,8)=sqrt(real(d)^2+imag(d)^2);%顯示Ijie=a+c;Branch_It(i,9)=real(e);%顯示線路損耗有功分量Branch_It(i,10)=imag(e);%顯示線路損耗無(wú)功分量else%帶變壓器支路(同以上內(nèi)容)m=B1(i,1);n=B1(i,2);Branch_It(i,1)=m;Branch_It(i,2)=n;a=U_It(m,1)*(conj(U_It(m,1))/conj(B1(i,3))-conj(U_It(n,1))*conj(1/(B1(i,5)*B1(i,3))));Branch_It(i,3)=real(a);Branch_It(i,4)=imag(a);b=U_It(m,1)*(B1(i,5)-1)/B1(i,3)/B1(i,5)+(U_It(m,1)-U_It(n,1))/(B1(i,5)*B1(i,3));Branch_It(i,5)=sqrt(real(b)^2+imag(b)^2);c=U_It(n,1)*(conj(U_It(n,1))/(conj(B1(i,5)*B1(i,5)*B1(i,3)))