3節(jié)電力系統(tǒng)狀態(tài)估計(jì)(WLS算法)

3節(jié)電系統(tǒng)狀態(tài)估計(jì)報(bào)告【任務(wù)說(shuō)明】3節(jié)點(diǎn)系統(tǒng)主接線圖任務(wù)：采用最小二乘狀態(tài)估計(jì)算法,所有量測(cè)的權(quán)重都取1.0,編寫(xiě)狀態(tài)估計(jì)程序(C/Matlab)。按量測(cè)類(lèi)型，列出量測(cè)方程（每一類(lèi)寫(xiě)出一個(gè)方程）畫(huà)出程序流程提交源程序，程序中每個(gè)函數(shù)的作用提交計(jì)算的輸出結(jié)果(屏幕拷貝)系統(tǒng)參數(shù)：功率基值：100MW電壓基值：230kV線路阻抗參數(shù)（標(biāo)么值）：線路首節(jié)點(diǎn)末節(jié)點(diǎn)R(標(biāo)么值)X(標(biāo)么值)半充電電納Line1-2120.0170.0920Line1-3130.0085 0.0720Line2-3230.0119 0.10080線路量測(cè)(流出母線為正)：線路首端量測(cè)首端真值末端量測(cè)末端真值Line1-2-61.3+j1.2-63.32+j1.2460+j2.463.99+j2.35Line1-3-46.7-j14.8-47.69-j14.7945.9+j16.547.9+j16.54Line2-324-j6.624.93-j6.6-24+j7.2-24.86+j7.24母線電壓量測(cè)：母線電壓量測(cè)真值(幅值/角度)1232233/02234.56235.56/3.233236.46236.46/1.82負(fù)荷量測(cè)(流出母線為正)：負(fù)荷量測(cè)真值Load1111+j13.50111.02+j13.55發(fā)電量測(cè)(流入母線為正)：發(fā)電機(jī)量測(cè)真值unit288-j4.2488.92-j4.24unit323+j2423.04+j23.78注：量測(cè)存在誤差【數(shù)據(jù)預(yù)處理】首先根據(jù)基值將已知的量測(cè)值均轉(zhuǎn)換為標(biāo)幺值，并將功率值轉(zhuǎn)換為流入量，得到如下數(shù)據(jù)：線路導(dǎo)納參數(shù)（標(biāo)么值）：線路首節(jié)點(diǎn)末節(jié)點(diǎn)G(標(biāo)么值)B(標(biāo)么值)半充電電納Line1-2121.9422-10.51070Line1-3131.6171-13.6980Line2-3231.1551-9.78430線路注入功率量測(cè)(標(biāo)幺值)：線路首端量測(cè)首端真值末端量測(cè)末端真值Line1-20.613-j0.0120.6332-j0.0124-0.60-j0.024-0.6399-j0.0235Line1-30.467+j0.1480.4769+j0.1479-0.459-j0.165-0.479-j0.1654Line2-3-0.24+j0.066-0.2493+j0.0660.24-j0.0720.2486-j0.0724負(fù)荷點(diǎn)注入功率量測(cè)(標(biāo)幺值)：負(fù)荷量測(cè)真值Load1-1.11-j0.1350-1.1102-j0.1355發(fā)電機(jī)節(jié)點(diǎn)注入量測(cè)(流入母線為正)：發(fā)電機(jī)量測(cè)真值unit20.88-j0.04240.8892-j0.0424unit30.23+j0.240.2304+j0.2378母線電壓量測(cè)（標(biāo)幺值）：母線電壓量測(cè)真值(幅值/角度)11.00871.0130/021.01981.0242/3.2331.02811.0281/1.82【量測(cè)方程】選擇節(jié)點(diǎn)1的電壓相角為參考，為0度，以vi表示誤差值。節(jié)點(diǎn)1電壓量測(cè)方程：Vi=Vi+v1即1.0087=V1+v12）1-3支路1號(hào)節(jié)點(diǎn)處注入有功功率功率：Pij=Vi2gij-ViVj(gijcosQUOTE胃ij胃ij+bijsinQUOTE胃ij胃ij)+v20.613=V12g13-V1V3(g13cosQUOTE胃13胃13+b13sinQUOTE胃13胃13)+v2即0.613=-1.6171V12-V1V3(-1.6171cosQUOTE胃13胃13+13.698sinQUOTE胃13胃13)+v23）1號(hào)節(jié)點(diǎn)注入功率：Pi=Vi2Gii+QUOTEGijcosQUOTE胃ij胃ij+BijsinQUOTE胃ij胃ij+v3P1=V12G11+QUOTEG1jcosQUOTE胃1j胃1j+B1jsinQUOTE胃1j胃1j+v3即-1.11=3.5613V12+V1V2(-1.9442cosQUOTE胃2胃2-10.5107sinQUOTE胃2胃2)+V1V3(-1.6171cosQUOTE胃3胃3-13.698sinQUOTE胃3胃3)+v3【流程圖】遙測(cè)數(shù)據(jù)遙測(cè)數(shù)據(jù)給定給定V0，QUOTE，k=0求解AQUOTE求解AQUOTEX=b,得QUOTEX計(jì)算H(V(k),)和h(V(k),)A=HTR-1H,b=HTR-1(Z-h)k=k+1k=k+1XX(k+1)=X(k)+QUOTEXmax|max|QUOTEX|<QUOTENNYY結(jié)束結(jié)束【計(jì)算結(jié)果】其中iterations為迭代次數(shù)，可見(jiàn)本例的迭代次數(shù)為4，收斂較快，狀態(tài)估計(jì)得到的節(jié)點(diǎn)1、2、3電壓分別為：234.01QUOTEPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXX【程序說(shuō)明】1、計(jì)算h矩陣的函數(shù)cal_hfunctionh=cal_h(V,th0,B,G)%其中，V為節(jié)點(diǎn)電壓估計(jì)值，th0為節(jié)點(diǎn)電壓相角估計(jì)%值，B為節(jié)點(diǎn)電導(dǎo)矩陣，G為節(jié)點(diǎn)電納矩陣b=-B;%線路電導(dǎo)矩陣g=-G;%線路電納矩陣P=zeros(3,1);%初始化，節(jié)點(diǎn)注入功率Q=zeros(3,1);PP=zeros(3,3);%線路注入功率QQ=PP;th=[0;th0];%節(jié)點(diǎn)1的電壓相角為0fori=1:3P_P=0;Q_Q=0;forj=1:3if(j~=i)P_P=P_P+V(i)*V(j)*(G(i,j)*cos(th(i)-th(j))+B(i,j)*sin(th(i)-th(j)));Q_Q=Q_Q+V(i)*V(j)*(G(i,j)*sin(th(i)-th(j))-B(i,j)*cos(th(i)-th(j)));PP(i,j)=(V(i)^2)*g(i,j)-V(i)*V(j)*(g(i,j)*cos(th(i)-th(j))+b(i,j)*sin(th(i)-th(j)));QQ(i,j)=-(V(i)^2)*b(i,j)-V(i)*V(j)*(g(i,j)*sin(th(i)-th(j))-b(i,j)*cos(th(i)-th(j)));endendP(i)=(V(i)^2)*G(i,i)+P_P;Q(i)=-(V(i)^2)*B(i,i)+Q_Q;endVV=[V(1);V(2);V(3)];h=[P;Q;PP(1,2);PP(2,3);PP(3,1);QQ(1,2);QQ(2,3);QQ(3,1);PP(1,3);PP(2,1);PP(3,2);QQ(1,3);QQ(2,1);QQ(3,2);VV];2、計(jì)算H矩陣的函數(shù)cal_HHfunctionH=cal_HH(V,th0,G,B,P,Q)%其中，P，Q為根據(jù)電壓估計(jì)值計(jì)算得到的節(jié)點(diǎn)%注入電壓b=-B;g=-G;PV=zeros(3,3);%節(jié)點(diǎn)注入功率對(duì)電壓幅值的偏導(dǎo)數(shù)QV=zeros(3,3);Pth=zeros(3,3);%節(jié)點(diǎn)注入功率對(duì)電壓相角的偏導(dǎo)數(shù)Qth=zeros(3,3);PPV=zeros(3,3);%Pij對(duì)Vj的偏導(dǎo)數(shù)QQV=zeros(3,3);%Qij對(duì)Vj的偏導(dǎo)數(shù)PPth=zeros(3,3);%Pij對(duì)thj的偏導(dǎo)數(shù)QQth=zeros(3,3);%Qij對(duì)thj的偏導(dǎo)數(shù)PPV1=zeros(3,3);%Pij對(duì)Vi的偏導(dǎo)數(shù)QQV1=zeros(3,3);%Qij對(duì)Vi的偏導(dǎo)數(shù)PPth1=zeros(3,3);%Pij對(duì)thi的偏導(dǎo)數(shù)QQth1=zeros(3,3);%Qij對(duì)thi的偏導(dǎo)數(shù)VV=eye(3);Vth=zeros(3,2);th=[0;th0];fori=1:3forj=1:3if(i~=j)PV(i,j)=V(i)*(G(i,j)*cos(th(i)-th(j))+B(i,j)*sin(th(i)-th(j)));QV(i,j)=V(i)*(G(i,j)*sin(th(i)-th(j))-B(i,j)*cos(th(i)-th(j)));PPV(i,j)=-V(i)*(g(i,j)*cos(th(i)-th(j))+b(i,j)*sin(th(i)-th(j)));QQV(i,j)=-V(i)*(g(i,j)*sin(th(i)-th(j))-b(i,j)*cos(th(i)-th(j)));PPV1(i,j)=2*V(i)*g(i,j)-V(j)*(g(i,j)*cos(th(i)-th(j))+b(i,j)*sin(th(i)-th(j)));QQV1(i,j)=-2*V(i)*b(i,j)-V(j)*(g(i,j)*sin(th(i)-th(j))-b(i,j)*cos(th(i)-th(j)));if(j~=1)Pth(i,j)=V(i)*V(j)*(G(i,j)*sin(th(i)-th(j))-B(i,j)*cos(th(i)-th(j)));Qth(i,j)=-V(i)*V(j)*(G(i,j)*cos(th(i)-th(j))+B(i,j)*sin(th(i)-th(j)));PPth(i,j)=-V(i)*V(j)*(g(i,j)*sin(th(i)-th(j))-b(i,j)*cos(th(i)-th(j)));QQth(i,j)=-V(i)*V(j)*(-g(i,j)*cos(th(i)-th(j))-b(i,j)*sin(th(i)-th(j)));endif(i~=1)PPth1(i,j)=V(i)*V(j)*(g(i,j)*sin(th(i)-th(j))-b(i,j)*cos(th(i)-th(j)));QQth1(i,j)=-V(i)*V(j)*(g(i,j)*cos(th(i)-th(j))+b(i,j)*sin(th(i)-th(j)));endelsePV(i,j)=(G(i,i)*(V(i)^2)+P(i))/V(i);QV(i,j)=(Q(i)-(V(i)^2)*B(i,i))/V(i);if(j~=1)Pth(i,j)=-B(i,i)*(V(i)^2)-Q(i);Qth(i,j)=P(i)-(V(i)^2)*G(i,i);endendendendH=[[PV,Pth(:,2:3)];[QV,Qth(:,2:3)];...[PPV1(1,2),PPV(1,2),0,PPth(1,2),0;...0,PPV1(2,3),PPV(2,3),PPth1(2,3),PPth(2,3);...PPV(3,1),0,PPV1(3,1),0,PPth1(3,1)];...[QQV1(1,2),QQV(1,2),0,QQth(1,2),0;...0,QQV1(2,3),QQV(2,3),QQth1(2,3),QQth(2,3);...QQV(3,1),0,QQV1(3,1),0,QQth1(3,1)];...[PPV1(1,3),0,PPV(1,3),0,PPth(1,3);...PPV(2,1),PPV1(2,1),0,PPth1(2,1),0;...0,PPV(3,2),PPV1(3,2),PPth(3,2),PPth1(3,2)];...[QQV1(1,3),0,QQV(1,3),0,QQth(1,3);...QQV(2,1),QQV1(2,1),0,QQth1(2,1),0;...0,QQV(3,2),QQV1(3,2),QQth(3,2),QQth1(3,2)];...[VV,Vth]];3、主程序calculate_all.m文件formatlongG=[3.5613,-1.9442,-1.6171;...-1.9442,3.0993,-1.1551;...-1.6171,-1.1551,2.7722];%B為節(jié)點(diǎn)電導(dǎo)矩陣B=[-24.2087,10.5107,13.698;...10.5107,-20.295,9.7843;...13.698,9.7843,-23.4832];%G為節(jié)點(diǎn)電納矩陣P=[-1.11;0.88;0.23];%節(jié)點(diǎn)注入功率量測(cè)值Q=[-0.135;-0.0424;0.24];PP=[0.613;-0.24;-0.459];%線路1-2,2-3,3-1注入功率在首端的量測(cè)值QQ=[-0.012;0.066;-0.165];PP1=[0.467;-0.6;0.24];%線路1-3,2-1,3-2注入功率在首端的量測(cè)值QQ1=[0.148;-0.024;-0.072];V=[1.0087;1.0198;1.0281];%節(jié)點(diǎn)電壓幅值量測(cè)值R=diag(ones(21,1));%權(quán)重都取