potential/GradualMirror.m

clc
clear
%% 逐次镜像法
% [1].	付宾兰, 邵.A., 高压输电线路分裂导线表面和周围电场的计算. 电网技术, 1984(Z1): 第83-91页.
% [2].	韦钢与李海峰, 同杆并架多回线下方的电场强度和感应电压. 中国电力, 1999(03): 第39-42页.
% 采用文献的结果：	蒋兴良, 胡.A.舒.A., Analysis of Conductors＇ Surface Electric Field of UHVDC Transmission Lines Based on Optimized Charge Simulation Method. 高电压技术, 2008(12): p. 2547-2551.
%%
%设置几个参数
semi_lineDistance=450;%分裂间距
semi_lineCount=6;%分裂数
ConductorX=[-11000,11000];%导线间距
ConductorY=[22000,22000,30000,30000];%导线距地高度
GroundX=[-11000,11000];%地线坐标
GroundY=[30000,30000];
subconductorR=16.8;%子导线半径
phaseN=2;%相数，单回三相
groundN=2;%地线数量
%%
eslong=8.854187817*10^-12*1000;
eslong=1;
%设置电压
% Volt_=[1100/sqrt(3);1100/sqrt(3)*exp(1j*4/3*pi);1100/sqrt(3)*exp(1j*2/3*pi);];
Volt_=[800;-800;0;0];
Volt=[];
for vLoop=1:phaseN
    Volt=[Volt;Volt_(vLoop)*ones(semi_lineCount,1);];
end
for vLoop=1:groundN
    Volt=[Volt;Volt_(vLoop+phaseN);];
end
%按分裂数和分裂导线间距布置单相线路导线
%用极坐标
arc=2*pi/semi_lineCount;
%子导线中心到导线中心的距离
R=semi_lineDistance/2/sin(arc/2);
%计算导线互电位和自电位系数
subconductorPos=[];
for phaseLoop=1:phaseN%导线
    for sC=1:semi_lineCount
        subconductorPos=[subconductorPos;ConductorX(phaseLoop)+1j*ConductorY(phaseLoop)+exp(1j*((sC-1)*arc+arc/2))*R];%移动到子导线中心
        %同时计算匹配点的位置
    end
end
for grondLoop=1:groundN%地线
        subconductorPos=[subconductorPos;GroundX(grondLoop)+1j*GroundY(grondLoop)];%移动到子导线中心
end
mirrorSubconductorPos=conj(subconductorPos);%获得子导线镜像
H=diag(imag(subconductorPos));
r=eye(length(H))*subconductorR;%暂时认为地线和导线半径一样
matSubconductor=repmat(subconductorPos,1,length(subconductorPos));
conductor2conductorDistance=abs(matSubconductor-conj(matSubconductor'));
conductor2MirrorDistance=abs(matSubconductor-repmat(conj(mirrorSubconductorPos'),length(subconductorPos),1));
P1=1/2/pi/eslong*log(2*H./r);
P1(isnan(P1))=0;
P2=1/2/pi/eslong*log(conductor2MirrorDistance./conductor2conductorDistance);
P2(isinf(P2))=0;
Pij=P1+P2;
%求电荷
QRI=Pij\Volt;
% 计算镜像电荷
%只计算同极性和同极性对地镜像的镜像
innerMirrorPos=[];
innerMirrorQ=[];%内部镜像的电荷
for phaseLoop=1:phaseN
    for sCOuter=1:semi_lineCount
        for sCInner=1:semi_lineCount
            if sCInner==sCOuter
                innerMirrorPos=[innerMirrorPos;subconductorPos((phaseLoop-1)*semi_lineCount+sCOuter)];%先预留一个位置
                innerMirrorQ=[innerMirrorQ;sum(QRI(1+(phaseLoop-1)*semi_lineCount:phaseLoop*semi_lineCount))];
                continue
            end
            innerMirrorPos=[innerMirrorPos;subconductorPos(sCOuter+(phaseLoop-1)*semi_lineCount)+subconductorR^2/abs(subconductorPos(sCOuter+(phaseLoop-1)*semi_lineCount)-subconductorPos(sCInner+(phaseLoop-1)*semi_lineCount))*(subconductorPos(sCInner+(phaseLoop-1)*semi_lineCount)-subconductorPos(sCOuter+(phaseLoop-1)*semi_lineCount))./(abs(subconductorPos(sCInner+(phaseLoop-1)*semi_lineCount)-subconductorPos(sCOuter+(phaseLoop-1)*semi_lineCount)))];
            innerMirrorQ=[innerMirrorQ;-QRI(sCInner+(phaseLoop-1)*semi_lineCount)];
        end
    end
end

for groundLoop=1:groundN%地线只用一根导线等效
    innerMirrorPos=[innerMirrorPos;subconductorPos(groundLoop+semi_lineCount*phaseN)];%先预留一个位置
    innerMirrorQ=[innerMirrorQ;sum(QRI(groundLoop+semi_lineCount*phaseN))];
end
%以下是验证部分
%选检验导线上一个角度
verifyPointN=200;
vrfRelA=linspace(0,2*pi,verifyPointN)';%vrf=verify
%计算检验点相对于子导线的位置
vrfRelPos=exp(1j*vrfRelA)*subconductorR;
%移动坐标，使验证的子导线中心和实际子导线中心重合。
vrfPos=[];
for phaseLoop=1:phaseN
    for sC=1:semi_lineCount
        vrfPos=[vrfPos;exp(1j*((sC-1)*arc+arc/2))*R+ConductorX(phaseLoop)+1j*ConductorY(phaseLoop)+vrfRelPos];
    end
end
for groundLoop=1:groundN
        vrfPos=[vrfPos;GroundX(groundLoop)+1j*GroundY(groundLoop)+vrfRelPos];
end
%计算这一点的电位系数
matVrfPos=repmat(vrfPos,1,length(innerMirrorPos));
vrf2ConductorDistance=abs(matVrfPos-repmat(conj(innerMirrorPos'),length(vrfPos),1));
vrf2MirrorDistance=abs(matVrfPos-repmat(conj(conj(innerMirrorPos')),length(vrfPos),1));
Pij=1/2/pi/eslong*log(vrf2MirrorDistance./vrf2ConductorDistance);
%计算电压
V=Pij*innerMirrorQ;
Vvalidation=[];
for phaseLoop=1:phaseN
    Vvalidation=[Vvalidation;Volt_(phaseLoop)*ones(semi_lineCount*verifyPointN,1);];
end
for groundLoop=1:groundN
    Vvalidation=[Vvalidation;Volt_(groundLoop+phaseN)*ones(verifyPointN,1);];
end
error=abs((V-Vvalidation)./Vvalidation);
error=sum(error)/length(Vvalidation)
display('Finished.');
%计算场强
ABCy=imag(repmat(innerMirrorPos,1,length(vrfPos)));
ABCx=real(repmat(innerMirrorPos,1,length(vrfPos)));
y=imag(conj(matVrfPos'));
x=real(conj(matVrfPos'));
ERy=sum( ( (ABCy-y)./( (ABCy-y).^2+(ABCx-x).^2 )-(ABCy+y)./( (ABCy+y).^2+(ABCx-x).^2 ) ).*repmat(real(innerMirrorQ),1,length(vrfPos))./2/pi/eslong,1 );
EIy=sum( ( (ABCy-y)./( (ABCy-y).^2+(ABCx-x).^2 )-(ABCy+y)./( (ABCy+y).^2+(ABCx-x).^2 ) ).*repmat(imag(innerMirrorQ),1,length(vrfPos))./2/pi/eslong,1 );
ERx=sum( ( (ABCx-x)./( (ABCy-y).^2+(ABCx-x).^2 )-(ABCx-x)./( (ABCy+y).^2+(ABCx-x).^2 ) ).*repmat(real(innerMirrorQ),1,length(vrfPos))./2/pi/eslong,1 );
EIx=sum( ( (ABCx-x)./( (ABCy-y).^2+(ABCx-x).^2 )-(ABCx-x)./( (ABCy+y).^2+(ABCx-x).^2 ) ).*repmat(imag(innerMirrorQ),1,length(vrfPos))./2/pi/eslong,1 );
E2=sqrt(ERy.^2+EIy.^2+ERx.^2+EIx.^2+((ERy.^2-EIy.^2+ERx.^2-EIx.^2).^2+4*(ERy.*EIy+ERx.*EIx).^2).^.5);
E3=sqrt(ERy.^2+EIy.^2+ERx.^2+EIx.^2);
Emat=1/pi/2./eslong.*repmat(conj(innerMirrorQ'),length(vrfPos),1)./(vrf2ConductorDistance.^2).*(matVrfPos-repmat(conj(innerMirrorPos'),length(vrfPos),1))./vrf2ConductorDistance;
E=sum(Emat,2);
max(sqrt(2)*abs(E));
scatter(real(innerMirrorPos(1:length(innerMirrorPos)/1)),imag(innerMirrorPos(1:length(innerMirrorPos)/1)),[],'r');
axis equal
hold on;
scatter(real(vrfPos),imag(vrfPos),[],'k');