3节电力系统状态估计(WLS算法)

3节电系统状态估计报告【任务说明】3节点系统主接线图任务：采用最小二乘状态估计算法,所有量测的权重都取1.0,编写状态估计程序(C/Matlab)。按量测类型，列出量测方程（每一类写出一个方程）画出程序流程提交源程序，程序中每个函数的作用提交计算的输出结果(屏幕拷贝)系统参数：功率基值：100MW电压基值：230kV线路阻抗参数（标么值）：线路首节点末节点R(标么值)X(标么值)半充电电纳Line1-2120.0170.0920Line1-3130.0085 0.0720Line2-3230.0119 0.10080线路量测(流出母线为正)：线路首端量测首端真值末端量测末端真值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母线电压量测：母线电压量测真值(幅值/角度)1232233/02234.56235.56/3.233236.46236.46/1.82负荷量测(流出母线为正)：负荷量测真值Load1111+j13.50111.02+j13.55发电量测(流入母线为正)：发电机量测真值unit288-j4.2488.92-j4.24unit323+j2423.04+j23.78注：量测存在误差【数据预处理】首先根据基值将已知的量测值均转换为标幺值，并将功率值转换为流入量，得到如下数据：线路导纳参数（标么值）：线路首节点末节点G(标么值)B(标么值)半充电电纳Line1-2121.9422-10.51070Line1-3131.6171-13.6980Line2-3231.1551-9.78430线路注入功率量测(标幺值)：线路首端量测首端真值末端量测末端真值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负荷点注入功率量测(标幺值)：负荷量测真值Load1-1.11-j0.1350-1.1102-j0.1355发电机节点注入量测(流入母线为正)：发电机量测真值unit20.88-j0.04240.8892-j0.0424unit30.23+j0.240.2304+j0.2378母线电压量测（标幺值）：母线电压量测真值(幅值/角度)11.00871.0130/021.01981.0242/3.2331.02811.0281/1.82【量测方程】选择节点1的电压相角为参考，为0度，以vi表示误差值。节点1电压量测方程：Vi=Vi+v1即1.0087=V1+v12）1-3支路1号节点处注入有功功率功率：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号节点注入功率：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【流程图】遥测数据遥测数据给定给定V0，QUOTE，k=0求解AQUOTE求解AQUOTEX=b,得QUOTEX计算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结束结束【计算结果】其中iterations为迭代次数，可见本例的迭代次数为4，收敛较快，状态估计得到的节点1、2、3电压分别为：234.01QUOTEPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXXPAGEXXX【程序说明】1、计算h矩阵的函数cal_hfunctionh=cal_h(V,th0,B,G)%其中，V为节点电压估计值，th0为节点电压相角估计%值，B为节点电导矩阵，G为节点电纳矩阵b=-B;%线路电导矩阵g=-G;%线路电纳矩阵P=zeros(3,1);%初始化，节点注入功率Q=zeros(3,1);PP=zeros(3,3);%线路注入功率QQ=PP;th=[0;th0];%节点1的电压相角为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、计算H矩阵的函数cal_HHfunctionH=cal_HH(V,th0,G,B,P,Q)%其中，P，Q为根据电压估计值计算得到的节点%注入电压b=-B;g=-G;PV=zeros(3,3);%节点注入功率对电压幅值的偏导数QV=zeros(3,3);Pth=zeros(3,3);%节点注入功率对电压相角的偏导数Qth=zeros(3,3);PPV=zeros(3,3);%Pij对Vj的偏导数QQV=zeros(3,3);%Qij对Vj的偏导数PPth=zeros(3,3);%Pij对thj的偏导数QQth=zeros(3,3);%Qij对thj的偏导数PPV1=zeros(3,3);%Pij对Vi的偏导数QQV1=zeros(3,3);%Qij对Vi的偏导数PPth1=zeros(3,3);%Pij对thi的偏导数QQth1=zeros(3,3);%Qij对thi的偏导数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为节点电导矩阵B=[-24.2087,10.5107,13.698;...10.5107,-20.295,9.7843;...13.698,9.7843,-23.4832];%G为节点电纳矩阵P=[-1.11;0.88;0.23];%节点注入功率量测值Q=[-0.135;-0.0424;0.24];PP=[0.613;-0.24;-0.459];%线路1-2,2-3,3-1注入功率在首端的量测值QQ=[-0.012;0.066;-0.165];PP1=[0.467;-0.6;0.24];%线路1-3,2-1,3-2注入功率在首端的量测值QQ1=[0.148;-0.024;-0.072];V=[1.0087;1.0198;1.0281];%节点电压幅值量测值R=diag(ones(21,1));%权重都取