Yang Liu
2 years ago
parent
bb6526ed86
commit
16c1547ba9
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function [t_new,x_new,y_new,LTE,LTE2,LTE3] = DT(t,x,f,GLO,h,K)
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% DT performs one-step integration of differential transformation
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% method to solve differential equation dx/dt = f(t,x,GLO);
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%
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% Input
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% k current order, 0,1,2,...
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% x current states
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% f differential equation
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% GLO parameters in the differential equation
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% h time step
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% K The degree of power series: X(0)+X(1)*h+...X(K)*h^K
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%
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% Output
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% t_new next time instant
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% x_new next states of state variables
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% y_new next states of algebraic variables
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% LTE local truncation error
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%
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% See also rk4, Parareal
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%
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%% Function handle to compute intermidate variables
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fun_y = str2func(strcat(func2str(f),'_AE'));
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fun_idx = str2func(strcat(func2str(f),'_idx'));
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%% Function handle for DT model X(k+1)=FB(X(0:k)) of differential equation dx/dt = f(x)
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F = str2func(strcat(func2str(f),'_DT'));
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%% compute intermidate variables y
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idx = fun_idx(GLO);
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y = fun_y(x,idx,GLO);
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%% Define matrix X Y to store coefficients, Xh to store terms
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Nx = length(x);
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X = zeros(Nx,K+1); %%why NAN
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Ny = length(y);
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Y = zeros(Ny,K+1);
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Xh= zeros(Nx,K+1);
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Yh= zeros(Ny,K+1);
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%% Initialize the 0th order coefficients
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X(:,1) = x;
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Y(:,1) = y;
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Xh(:,1) = x; % Term(0) = X(0)*h^0
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Yh(:,1) = y;
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%% Perform recursive calculation of high order coefficients and terms
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for k = 0:K-1
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% for k = 0:K-2
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%% DT Equation: X(k+1)=F(X(0:k)) or XX(k+2)=F(XX(1:k+1))
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[X,Y] = F(k,X,Y,GLO,idx);
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Xh(:,k+2) = X(:,k+2)*h^(k+1); % Term(k+1) = X(k+1)*h^(k+1) or XX(k+2)*h^(k+1)
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Yh(:,k+2) = Y(:,k+2)*h^(k+1); % Term(k+1) = X(k+1)*h^(k+1) or XX(k+2)*h^(k+1)
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end
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%% sum over all columns of matrix Xh to obtain x_new as a column vector
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x_new = sum(Xh(:,1:end-1),2);
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%%
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% y_new = sum(Yh,2);
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y_new = fun_y(x_new,idx,GLO);
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%% Update time
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t_new = t + h;
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eta = 0.0000000000000000001;
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%% Local truncation error: last term; maximum value over all variables
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% khuang: we can use relative error, since different variables have
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% differnet dynamics and quantities
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infcof = max(abs(Xh(:,end)./(x_new+eta)));
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trc = infcof^(1/K);
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LTE = infcof/(1-trc);
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% LTE = infcof;
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% LTE = max(abs(Xh(:,end)./x_new));
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LTE3 = max(abs(Xh(:,end-1)./(x_new+eta)));
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% relative error used to change order
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LTE2 = infcof/min([norm(Xh(:,end-1)./Xh(:,end),Inf), sqrt(norm(Xh(:,end-2)./Xh(:,end),Inf)), sqrt(norm(Xh(:,end-3)./Xh(:,end-1),Inf))]);
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% LTE2 = min(abs(Xh(:,end)./abs(Xh(:,end-1))))
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end
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@ -0,0 +1,368 @@
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function [t_dtm,sol_dtm]=DTsolver(TimeRange,Resolution,x,N_DTM,Sys)
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Gen_num=length(Sys.GenIdx);
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%% Asign space to store the series
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DTA=zeros(Gen_num,N_DTM+1); % machine number, term number, dimention of each term
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THETA=DTA;OMG=DTA; LAMBDA_F=DTA;LAMBDA_D=DTA;LAMBDA_Q1=DTA;LAMBDA_Q2=DTA;
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V1 =DTA; EFD=DTA; P1= DTA; P2= DTA; PM=DTA; W_R=DTA;
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SIN=DTA; COS=DTA; ID =DTA; IQ =DTA;
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LAMBDA_AD=DTA; LAMBDA_AQ=DTA; PE=DTA; VD_PP=DTA; VQ_PP=DTA;
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VPP_A=DTA; VPP_B=DTA; VPP_C=DTA;
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VT=DTA; VTP=DTA;
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VBUS5 = zeros(3,N_DTM+1);
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VBUS6 = VBUS5; VBUS7 =VBUS5; VBUS8 =VBUS5; VBUS9 =VBUS5; VBUS10 =VBUS5; VBUS11 =VBUS5;
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ILINE1 = VBUS5; ILINE2 = VBUS5; ILINE3 = VBUS5; ILINE4 = VBUS5; ILINE5 = VBUS5; ILINE6 = VBUS5;
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ILINE7 = VBUS5; ILINE8 = VBUS5; ILINE9 = VBUS5; ILINE10= VBUS5; ILINE11= VBUS5; ILINE12= VBUS5;
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ILOAD1 = VBUS5; ILOAD2 = VBUS5;
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%% Coefficients of t^0, initial value
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DTA(:,1)=x(1:4,1); THETA(:,1)=x(5:8,1); OMG(:,1)=x(9:12,1);
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LAMBDA_F(:,1)=x(13:16,1); LAMBDA_D(:,1)=x(17:20,1); LAMBDA_Q1(:,1)=x(21:24,1); LAMBDA_Q2(:,1)=x(25:28,1); V1(:,1)=x(29:32,1);
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efd = x(33:36,1); efd = min(max(efd,Sys.Emin),Sys.Emax); EFD(:,1)= efd;
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p1 = x(37:40,1); p1 = min(max(p1,Sys.GVmin),Sys.GVmax); P1(:,1) = p1;
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P2(:,1)= x(41:44,1);
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PM(:,1)= P2(:,1)-Sys.Gdt.*OMG(:,1);
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W_R(:,1) =OMG(:,1)+1;
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VBUS5(:,1) =x(45:47,1); VBUS6(:,1) =x(48:50,1); VBUS7(:,1) =x(51:53,1); VBUS8(:,1) =x(54:56,1);
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VBUS9(:,1) =x(57:59,1); VBUS10(:,1)=x(60:62,1); VBUS11(:,1)=x(63:65,1);
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ILINE1(:,1)=x(66:68,1); ILINE2(:,1)=x(69:71,1); ILINE3(:,1)=x(72:74,1); ILINE4(:,1)=x(75:77,1);
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ILINE5(:,1)=x(78:80,1); ILINE6(:,1)=x(81:83,1); ILINE7(:,1)=x(84:86,1); ILINE8(:,1)=x(87:89,1);
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ILINE9(:,1)=x(90:92,1); ILINE10(:,1)=x(93:95,1); ILINE11(:,1)=x(96:98,1); ILINE12(:,1)=x(99:101,1);
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ILOAD1(:,1)=x(102:104,1); ILOAD2(:,1)=x(105:107,1);
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VTP(:,1) =x(108:111,1);
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% some other terms
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SIN(:,1) =sin(THETA(:,1)); % sin(theta) no need to add '
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COS(:,1) =cos(THETA(:,1)); % cos(theta)
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ID(:,1) = 2/3*( [ILINE1(1,1); ILINE2(1,1); ILINE3(1,1); ILINE4(1,1)].*COS(:,1) + [ILINE1(2,1); ILINE2(2,1); ILINE3(2,1); ILINE4(2,1)].*( COS(:,1)*cos(2*pi/3)+SIN(:,1)*sin(2*pi/3) ) + [ILINE1(3,1); ILINE2(3,1); ILINE3(3,1); ILINE4(3,1)].*( COS(:,1)*cos(2*pi/3)-SIN(:,1)*sin(2*pi/3) ) );
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IQ(:,1) = 2/3*( -[ILINE1(1,1); ILINE2(1,1); ILINE3(1,1); ILINE4(1,1)].*SIN(:,1) - [ILINE1(2,1); ILINE2(2,1); ILINE3(2,1); ILINE4(2,1)].*( SIN(:,1)*cos(2*pi/3)-COS(:,1)*sin(2*pi/3) ) - [ILINE1(3,1); ILINE2(3,1); ILINE3(3,1); ILINE4(3,1)].*( SIN(:,1)*cos(2*pi/3)+COS(:,1)*sin(2*pi/3) ) );
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LAMBDA_AD(:,1) = Sys.Lad_pp.*(-ID(:,1)+LAMBDA_F(:,1)./Sys.Lfd+LAMBDA_D(:,1)./Sys.L1d);
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LAMBDA_AQ(:,1) = Sys.Laq_pp.*(-IQ(:,1)+LAMBDA_Q1(:,1)./Sys.L1q+LAMBDA_Q2(:,1)./Sys.L2q);
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PE(:,1) = LAMBDA_AD(:,1).*IQ(:,1)-LAMBDA_AQ(:,1).*ID(:,1);
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VD_PP(:,1)=Sys.Vd_pp_coeff1.*ID(:,1)+Sys.Vd_pp_coeff2.*LAMBDA_F(:,1)+Sys.Vd_pp_coeff3.*LAMBDA_D(:,1)...
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-W_R(:,1).*Sys.Laq_pp.*( LAMBDA_Q1(:,1)./Sys.L1q + LAMBDA_Q2(:,1)./Sys.L2q ) + Sys.Lad_pp./Sys.Lfd.*EFD(:,1) ;
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VQ_PP(:,1)=Sys.Vq_pp_coeff1.*IQ(:,1)+Sys.Vq_pp_coeff2.*LAMBDA_Q1(:,1)+Sys.Vq_pp_coeff3.*LAMBDA_Q2(:,1)...
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+W_R(:,1).*Sys.Lad_pp.*( LAMBDA_F(:,1)./Sys.Lfd + LAMBDA_D(:,1)./Sys.L1d );
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VPP_A(:,1) = COS(:,1).*VD_PP(:,1) -SIN(:,1).*VQ_PP(:,1);
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VPP_B(:,1) = ( COS(:,1)*cos(2*pi/3)+SIN(:,1)*sin(2*pi/3) ).*VD_PP(:,1) -( SIN(:,1)*cos(2*pi/3)-COS(:,1)*sin(2*pi/3) ).*VQ_PP(:,1);
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VPP_C(:,1) = ( COS(:,1)*cos(2*pi/3)-SIN(:,1)*sin(2*pi/3) ).*VD_PP(:,1) -( SIN(:,1)*cos(2*pi/3)+COS(:,1)*sin(2*pi/3) ).*VQ_PP(:,1);
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VT2(:,1) = abs(VD_PP(:,1)+1i*VQ_PP(:,1)).^2;
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VT(:,1) = abs(VD_PP(:,1)+1i*VQ_PP(:,1));
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%% preparation
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SimuTime = TimeRange(2)-TimeRange(1);
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t_dtm=(0:Resolution:SimuTime)'+TimeRange(1);
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% hh = TimeRange(2)-t_dtm(end);
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% if abs(hh)>1e-5
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% t_dtm = [t_dtm;TimeRange(2)];
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% end
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%% store the results at each time step
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% assign space
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res_dta = zeros(Gen_num,size(t_dtm,1));
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res_theta = res_dta;
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res_omg = res_dta;
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res_lambda_f = res_dta;
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res_lambda_d = res_dta;
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res_lambda_q1 = res_dta;
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res_lambda_q2 = res_dta;
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res_v1 = res_dta;
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res_efd = res_dta;
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res_p1 = res_dta;
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res_p2 = res_dta;
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res_vbus5 = zeros(3,size(t_dtm,1)); res_vbus6 = res_vbus5; res_vbus7 = res_vbus5;
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res_vbus8 = res_vbus5; res_vbus9 = res_vbus5; res_vbus10 = res_vbus5; res_vbus11 = res_vbus5;
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res_iline1 = res_vbus5; res_iline2 = res_vbus5; res_iline3 = res_vbus5; res_iline4 = res_vbus5;
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res_iline5 = res_vbus5; res_iline6 = res_vbus5; res_iline7 = res_vbus5; res_iline8 = res_vbus5;
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res_iline9 = res_vbus5; res_iline10= res_vbus5; res_iline11= res_vbus5; res_iline12= res_vbus5;
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res_iload1 = res_vbus5; res_iload2 = res_vbus5;
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res_vtp = res_dta;
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% store the first one
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res_dta(:,1) =DTA(:,1);
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res_theta(:,1)=THETA(:,1);
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res_omg(:,1) =OMG(:,1,1);
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res_lambda_f(:,1) =LAMBDA_F(:,1);
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res_lambda_d(:,1) =LAMBDA_D(:,1);
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res_lambda_q1(:,1) =LAMBDA_Q1(:,1);
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res_lambda_q2(:,1) =LAMBDA_Q2(:,1);
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res_v1(:,1) =V1(:,1);
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res_efd(:,1) =EFD(:,1);
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res_p1(:,1) =P1(:,1);
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res_p2(:,1) =P2(:,1);
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res_vbus5(:,1) = VBUS5(:,1); res_vbus6(:,1)= VBUS6(:,1); res_vbus7(:,1)= VBUS7(:,1); res_vbus8(:,1)= VBUS8(:,1);
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res_vbus9(:,1) = VBUS9(:,1); res_vbus10(:,1)= VBUS10(:,1); res_vbus11(:,1) = VBUS11(:,1);
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res_iline1(:,1) = ILINE1(:,1); res_iline2(:,1) = ILINE2(:,1); res_iline3(:,1) = ILINE3(:,1); res_iline4(:,1) = ILINE4(:,1);
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res_iline5(:,1) = ILINE5(:,1); res_iline6(:,1) = ILINE6(:,1); res_iline7(:,1) = ILINE7(:,1); res_iline8(:,1) = ILINE8(:,1);
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res_iline9(:,1) = ILINE9(:,1); res_iline10(:,1)= ILINE10(:,1); res_iline11(:,1)= ILINE11(:,1); res_iline12(:,1)= ILINE12(:,1);
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res_iload1(:,1) = ILOAD1(:,1); res_iload2(:,1) = ILOAD2(:,1);
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res_vtp(:,1) = VTP(:,1);
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%% begin the for loop to calculate
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Tvec=zeros(1,N_DTM+1);
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for Numstep=1:size(t_dtm,1)-1 % loop of time step
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hhh = t_dtm(Numstep+1)-t_dtm(Numstep);
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Tvec(1:N_DTM+1)=hhh.^(0:N_DTM);
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idx = zeros(N_DTM+1,1); idx(1) =1; % for constant terms
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% below are used to check limits
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def_dt = ( V1(:,1).*Sys.Ek-EFD(:,1).*Sys.Lad./Sys.Rfd )./Sys.Ete.*Sys.Rfd./Sys.Lad;
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dP1_dt = ( (Sys.Pref-OMG(:,1))./Sys.Gr-P1(:,1) )./Sys.Gt1;
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for k = 1:N_DTM % loop of order
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% synchronous generator differential equations
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DTA(:,k+1) = 1/k*2*pi*60*OMG(:,k);
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THETA(:,k+1) = 1/k*2*pi*60*(OMG(:,k)+1*idx(k));
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OMG(:,k+1) = 1/k*Sys.w0*(PM(:,k) - PE(:,k) - Sys.D.*OMG(:,k)./Sys.w0)./Sys.H/2;
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LAMBDA_F(:,k+1) = 1/k*120*pi*(EFD(:,k)-Sys.Rfd./Sys.Lfd.*(LAMBDA_F(:,k)-LAMBDA_AD(:,k)));
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LAMBDA_D(:,k+1) = 1/k*(-120)*pi*Sys.R1d./Sys.L1d.*(LAMBDA_D(:,k) -LAMBDA_AD(:,k));
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LAMBDA_Q1(:,k+1) = 1/k*(-120)*pi*Sys.R1q./Sys.L1q.*(LAMBDA_Q1(:,k)-LAMBDA_AQ(:,k));
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LAMBDA_Q2(:,k+1) = 1/k*(-120)*pi*Sys.R2q./Sys.L2q.*(LAMBDA_Q2(:,k)-LAMBDA_AQ(:,k));
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V1(:,k+1) = 1/k*( -VTP(:,k)+Sys.Vref*idx(k)-V1(:,k)-Sys.Eta.*(VT(:,k)-VTP(:,k))./Sys.T_vt )./Sys.Etb;
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EFD_high = 1/k*( V1(:,k).*Sys.Ek-EFD(:,k).*Sys.Lad./Sys.Rfd )./Sys.Ete.*Sys.Rfd./Sys.Lad;
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EFD_high(def_dt(EFD(:,1)>=Sys.Emax)>0)=0;
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EFD_high(def_dt(EFD(:,1)<=Sys.Emin)<0)=0;
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EFD(:,k+1) = EFD_high;
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P1_high = 1/k*( (Sys.Pref*idx(k)-OMG(:,k))./Sys.Gr-P1(:,k) )./Sys.Gt1;
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P1_high(dP1_dt(P1(:,1)>=Sys.GVmax)>0)=0;
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P1_high(dP1_dt(P1(:,1)<=Sys.GVmin)<0)=0;
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P1(:,k+1) = P1_high;
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% P2(:,k+1)= 1/k*(P1(:,k)-P2(:,k)+P1(:,k+1).*Sys.Gt2)./Sys.Gt3;
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P2(:,k+1)= 1/k*(P1(:,k)-P2(:,k)+k*P1(:,k+1).*Sys.Gt2)./Sys.Gt3;
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% network differential equations
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VBUS5(:,k+1) = 1/k*Sys.Cnode_3Phase(:,:,5)*(ILINE1(:,k)-ILINE5(:,k));
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VBUS6(:,k+1) = 1/k*Sys.Cnode_3Phase(:,:,6)*(ILINE2(:,k)+ILINE5(:,k)-ILINE6(:,k));
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VBUS7(:,k+1) = 1/k*Sys.Cnode_3Phase(:,:,7)*(ILINE6(:,k)-ILINE7(:,k)-ILINE8(:,k)-ILOAD1(:,k));
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VBUS8(:,k+1) = 1/k*Sys.Cnode_3Phase(:,:,8)*(ILINE7(:,k)+ILINE8(:,k)-ILINE9(:,k)-ILINE10(:,k));
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VBUS9(:,k+1) = 1/k*Sys.Cnode_3Phase(:,:,9)*(ILINE9(:,k)+ILINE10(:,k)-ILINE11(:,k)-ILOAD2(:,k));
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VBUS10(:,k+1)= 1/k*Sys.Cnode_3Phase(:,:,10)*(ILINE4(:,k)+ILINE11(:,k)-ILINE12(:,k));
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VBUS11(:,k+1)= 1/k*Sys.Cnode_3Phase(:,:,11)*(ILINE3(:,k)+ILINE12(:,k));
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ILINE1(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,1)*( [VPP_A(1,k); VPP_B(1,k); VPP_C(1,k)]- VBUS5(:,k) -Sys.Gen_R(:,:,1)*ILINE1(:,k) ); % IBR voltage
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ILINE2(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,2)*( [VPP_A(2,k); VPP_B(2,k); VPP_C(2,k)]- VBUS6(:,k) -Sys.Gen_R(:,:,2)*ILINE2(:,k) );
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ILINE3(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,3)*( [VPP_A(3,k); VPP_B(3,k); VPP_C(3,k)]- VBUS11(:,k) -Sys.Gen_R(:,:,3)*ILINE3(:,k) );
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ILINE4(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,4)*( [VPP_A(4,k); VPP_B(4,k); VPP_C(4,k)]- VBUS10(:,k) -Sys.Gen_R(:,:,4)*ILINE4(:,k) );
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ILINE5(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,5)*( VBUS5(:,k)-VBUS6(:,k)-Sys.Rline_3Phase(:,:,5) * ILINE5(:,k) );
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ILINE6(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,6)*( VBUS6(:,k)-VBUS7(:,k)-Sys.Rline_3Phase(:,:,6) * ILINE6(:,k) );
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ILINE7(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,7)*( VBUS7(:,k)-VBUS8(:,k)-Sys.Rline_3Phase(:,:,7) * ILINE7(:,k) );
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ILINE8(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,8)*( VBUS7(:,k)-VBUS8(:,k)-Sys.Rline_3Phase(:,:,8) * ILINE8(:,k) );
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ILINE9(:,k+1)= 1/k*Sys.Lline_3Phase(:,:,9)*( VBUS8(:,k)-VBUS9(:,k)-Sys.Rline_3Phase(:,:,9) * ILINE9(:,k) );
|
||||
ILINE10(:,k+1)=1/k*Sys.Lline_3Phase(:,:,10)*( VBUS8(:,k)-VBUS9(:,k)-Sys.Rline_3Phase(:,:,10) * ILINE10(:,k) );
|
||||
ILINE11(:,k+1)=1/k*Sys.Lline_3Phase(:,:,11)*( VBUS9(:,k)-VBUS10(:,k)-Sys.Rline_3Phase(:,:,11) * ILINE11(:,k) );
|
||||
ILINE12(:,k+1)=1/k*Sys.Lline_3Phase(:,:,12)*( VBUS10(:,k)-VBUS11(:,k)-Sys.Rline_3Phase(:,:,12) * ILINE12(:,k) );
|
||||
|
||||
ILOAD1(:,k+1)=1/k*Sys.Lload_3Phase(:,:,1)*( VBUS7(:,k)-Sys.Rload_3Phase(:,:,1) * ILOAD1(:,k) );
|
||||
ILOAD2(:,k+1)=1/k*Sys.Lload_3Phase(:,:,2)*( VBUS9(:,k)-Sys.Rload_3Phase(:,:,2) * ILOAD2(:,k) );
|
||||
|
||||
VTP(:,k+1)=1/k*(VT(:,k)-VTP(:,k))./Sys.T_vt;
|
||||
|
||||
% below is algebric part
|
||||
PM(:,k+1)= P2(:,k+1)-Sys.Gdt.*OMG(:,k+1);
|
||||
W_R(:,k+1) = OMG(:,k+1)+1*idx(k+1);
|
||||
|
||||
COS(:,k+1)= -1/(k)*sum(repmat([k:-1:1],Gen_num,1).*SIN(:,1:k).*THETA(:,k+1:-1:2),2);
|
||||
SIN(:,k+1)= 1/(k)*sum(repmat([k:-1:1],Gen_num,1).*COS(:,1:k).*THETA(:,k+1:-1:2),2);
|
||||
|
||||
ID(:,k+1) = 2/3*sum(( [ILINE1(1,1:k+1); ILINE2(1,1:k+1); ILINE3(1,1:k+1); ILINE4(1,1:k+1)].*COS(:,k+1:-1:1) + [ILINE1(2,1:k+1); ILINE2(2,1:k+1); ILINE3(2,1:k+1); ILINE4(2,1:k+1)].*( COS(:,k+1:-1:1)*cos(2*pi/3)+SIN(:,k+1:-1:1)*sin(2*pi/3) ) + [ILINE1(3,1:k+1); ILINE2(3,1:k+1); ILINE3(3,1:k+1); ILINE4(3,1:k+1)].*( COS(:,k+1:-1:1)*cos(2*pi/3)-SIN(:,k+1:-1:1)*sin(2*pi/3) ) ),2);
|
||||
IQ(:,k+1) = 2/3*sum((-[ILINE1(1,1:k+1); ILINE2(1,1:k+1); ILINE3(1,1:k+1); ILINE4(1,1:k+1)].*SIN(:,k+1:-1:1) - [ILINE1(2,1:k+1); ILINE2(2,1:k+1); ILINE3(2,1:k+1); ILINE4(2,1:k+1)].*( SIN(:,k+1:-1:1)*cos(2*pi/3)-COS(:,k+1:-1:1)*sin(2*pi/3) ) - [ILINE1(3,1:k+1); ILINE2(3,1:k+1); ILINE3(3,1:k+1); ILINE4(3,1:k+1)].*( SIN(:,k+1:-1:1)*cos(2*pi/3)+COS(:,k+1:-1:1)*sin(2*pi/3) ) ),2);
|
||||
|
||||
LAMBDA_AD(:,k+1) = Sys.Lad_pp.*(-ID(:,k+1)+LAMBDA_F(:,k+1)./Sys.Lfd+LAMBDA_D(:,k+1)./Sys.L1d);
|
||||
LAMBDA_AQ(:,k+1) = Sys.Laq_pp.*(-IQ(:,k+1)+LAMBDA_Q1(:,k+1)./Sys.L1q+LAMBDA_Q2(:,k+1)./Sys.L2q);
|
||||
|
||||
PE(:,k+1) = sum(LAMBDA_AD(:,1:k+1).*IQ(:,k+1:-1:1)-LAMBDA_AQ(:,1:k+1).*ID(:,k+1:-1:1),2);
|
||||
|
||||
VD_PP(:,k+1)=Sys.Vd_pp_coeff1.*ID(:,k+1)+Sys.Vd_pp_coeff2.*LAMBDA_F(:,k+1)+Sys.Vd_pp_coeff3.*LAMBDA_D(:,k+1)...
|
||||
-sum(W_R(:,1:k+1).*Sys.Laq_pp.*( LAMBDA_Q1(:,k+1:-1:1)./Sys.L1q + LAMBDA_Q2(:,k+1:-1:1)./Sys.L2q ),2) + Sys.Lad_pp./Sys.Lfd.*EFD(:,k+1) ;
|
||||
|
||||
VQ_PP(:,k+1)=Sys.Vq_pp_coeff1.*IQ(:,k+1)+Sys.Vq_pp_coeff2.*LAMBDA_Q1(:,k+1)+Sys.Vq_pp_coeff3.*LAMBDA_Q2(:,k+1)...
|
||||
+sum(W_R(:,1:k+1).*Sys.Lad_pp.*( LAMBDA_F(:,k+1:-1:1)./Sys.Lfd + LAMBDA_D(:,k+1:-1:1)./Sys.L1d ),2);
|
||||
|
||||
VPP_A(:,k+1) = sum(COS(:,1:k+1).*VD_PP(:,k+1:-1:1) -SIN(:,1:k+1).*VQ_PP(:,k+1:-1:1),2);
|
||||
VPP_B(:,k+1) = sum(( COS(:,1:k+1)*cos(2*pi/3)+SIN(:,1:k+1)*sin(2*pi/3) ).*VD_PP(:,k+1:-1:1) -( SIN(:,1:k+1)*cos(2*pi/3)-COS(:,1:k+1)*sin(2*pi/3) ).*VQ_PP(:,k+1:-1:1),2);
|
||||
VPP_C(:,k+1) = sum(( COS(:,1:k+1)*cos(2*pi/3)-SIN(:,1:k+1)*sin(2*pi/3) ).*VD_PP(:,k+1:-1:1) -( SIN(:,1:k+1)*cos(2*pi/3)+COS(:,1:k+1)*sin(2*pi/3) ).*VQ_PP(:,k+1:-1:1),2);
|
||||
|
||||
VT2(:,k+1) = sum(VD_PP(:,1:k+1).*VD_PP(:,k+1:-1:1)+ VQ_PP(:,1:k+1).*VQ_PP(:,k+1:-1:1),2);
|
||||
VT(:,k+1) = (VT2(:,k+1) - sum(VT(:,2:k).*VT(:,k:-1:2),2))./(2*VT(:,1));
|
||||
|
||||
end
|
||||
|
||||
%% Evaluation, contain only differential equations
|
||||
dta_2=sum(DTA.*repmat(Tvec,[Gen_num,1]),2);
|
||||
theta_2=sum(THETA.*repmat(Tvec,[Gen_num,1]),2);
|
||||
omg_2=sum(OMG.*repmat(Tvec,[Gen_num,1]),2);
|
||||
lambda_f_2=sum(LAMBDA_F.*repmat(Tvec,[Gen_num,1]),2);
|
||||
lambda_d_2=sum(LAMBDA_D.*repmat(Tvec,[Gen_num,1]),2);
|
||||
lambda_q1_2=sum(LAMBDA_Q1.*repmat(Tvec,[Gen_num,1]),2);
|
||||
lambda_q2_2=sum(LAMBDA_Q2.*repmat(Tvec,[Gen_num,1]),2);
|
||||
vtp_2=sum(VTP.*repmat(Tvec,[Gen_num,1]),2);
|
||||
v1_2=sum(V1.*repmat(Tvec,[Gen_num,1]),2);
|
||||
efd_2=sum(EFD.*repmat(Tvec,[Gen_num,1]),2);
|
||||
p1_2=sum(P1.*repmat(Tvec,[Gen_num,1]),2);
|
||||
p2_2=sum(P2.*repmat(Tvec,[Gen_num,1]),2);
|
||||
vbus5_2=sum(VBUS5.*repmat(Tvec,[3,1]),2);
|
||||
vbus6_2=sum(VBUS6.*repmat(Tvec,[3,1]),2);
|
||||
vbus7_2=sum(VBUS7.*repmat(Tvec,[3,1]),2);
|
||||
vbus8_2=sum(VBUS8.*repmat(Tvec,[3,1]),2);
|
||||
vbus9_2=sum(VBUS9.*repmat(Tvec,[3,1]),2);
|
||||
vbus10_2=sum(VBUS10.*repmat(Tvec,[3,1]),2);
|
||||
vbus11_2=sum(VBUS11.*repmat(Tvec,[3,1]),2);
|
||||
iline1_2=sum(ILINE1.*repmat(Tvec,[3,1]),2);
|
||||
iline2_2=sum(ILINE2.*repmat(Tvec,[3,1]),2);
|
||||
iline3_2=sum(ILINE3.*repmat(Tvec,[3,1]),2);
|
||||
iline4_2=sum(ILINE4.*repmat(Tvec,[3,1]),2);
|
||||
iline5_2=sum(ILINE5.*repmat(Tvec,[3,1]),2);
|
||||
iline6_2=sum(ILINE6.*repmat(Tvec,[3,1]),2);
|
||||
iline7_2=sum(ILINE7.*repmat(Tvec,[3,1]),2);
|
||||
iline8_2=sum(ILINE8.*repmat(Tvec,[3,1]),2);
|
||||
iline9_2=sum(ILINE9.*repmat(Tvec,[3,1]),2);
|
||||
iline10_2=sum(ILINE10.*repmat(Tvec,[3,1]),2);
|
||||
iline11_2=sum(ILINE11.*repmat(Tvec,[3,1]),2);
|
||||
iline12_2=sum(ILINE12.*repmat(Tvec,[3,1]),2);
|
||||
iload1_2=sum(ILOAD1.*repmat(Tvec,[3,1]),2);
|
||||
iload2_2=sum(ILOAD2.*repmat(Tvec,[3,1]),2);
|
||||
|
||||
% Save the results
|
||||
res_dta(:,Numstep+1)=dta_2;
|
||||
res_theta(:,Numstep+1)=theta_2;
|
||||
res_omg(:,Numstep+1)=omg_2;
|
||||
res_lambda_f(:,Numstep+1)=lambda_f_2;
|
||||
res_lambda_d(:,Numstep+1)=lambda_d_2;
|
||||
res_lambda_q1(:,Numstep+1)=lambda_q1_2;
|
||||
res_lambda_q2(:,Numstep+1)=lambda_q2_2;
|
||||
res_v1(:,Numstep+1)=v1_2;
|
||||
res_efd(:,Numstep+1)=efd_2;
|
||||
res_p1(:,Numstep+1)=p1_2;
|
||||
res_p2(:,Numstep+1)=p2_2;
|
||||
res_vtp(:,Numstep+1)=vtp_2;
|
||||
res_vbus5(:,Numstep+1)=vbus5_2;
|
||||
res_vbus6(:,Numstep+1)=vbus6_2;
|
||||
res_vbus7(:,Numstep+1)=vbus7_2;
|
||||
res_vbus8(:,Numstep+1)=vbus8_2;
|
||||
res_vbus9(:,Numstep+1)=vbus9_2;
|
||||
res_vbus10(:,Numstep+1)=vbus10_2;
|
||||
res_vbus11(:,Numstep+1)=vbus11_2;
|
||||
res_iline1(:,Numstep+1)=iline1_2;
|
||||
res_iline2(:,Numstep+1)=iline2_2;
|
||||
res_iline3(:,Numstep+1)=iline3_2;
|
||||
res_iline4(:,Numstep+1)=iline4_2;
|
||||
res_iline5(:,Numstep+1)=iline5_2;
|
||||
res_iline6(:,Numstep+1)=iline6_2;
|
||||
res_iline7(:,Numstep+1)=iline7_2;
|
||||
res_iline8(:,Numstep+1)=iline8_2;
|
||||
res_iline9(:,Numstep+1)=iline9_2;
|
||||
res_iline10(:,Numstep+1)=iline10_2;
|
||||
res_iline11(:,Numstep+1)=iline11_2;
|
||||
res_iline12(:,Numstep+1)=iline12_2;
|
||||
res_iload1(:,Numstep+1)=iload1_2;
|
||||
res_iload2(:,Numstep+1)=iload2_2;
|
||||
|
||||
%% Update Initial value
|
||||
% differential part
|
||||
DTA(:,1)=dta_2;
|
||||
THETA(:,1)=theta_2;
|
||||
OMG(:,1)=omg_2;
|
||||
LAMBDA_F(:,1)=lambda_f_2;
|
||||
LAMBDA_D(:,1)=lambda_d_2;
|
||||
LAMBDA_Q1(:,1)=lambda_q1_2;
|
||||
LAMBDA_Q2(:,1)=lambda_q2_2;
|
||||
V1(:,1)=v1_2;
|
||||
EFD(:,1)=efd_2;
|
||||
P1(:,1)=p1_2;
|
||||
P2(:,1)=p2_2;
|
||||
VTP(:,1)=vtp_2;
|
||||
VBUS5(:,1)=vbus5_2;
|
||||
VBUS6(:,1)=vbus6_2;
|
||||
VBUS7(:,1)=vbus7_2;
|
||||
VBUS8(:,1)=vbus8_2;
|
||||
VBUS9(:,1)=vbus9_2;
|
||||
VBUS10(:,1)=vbus10_2;
|
||||
VBUS11(:,1)=vbus11_2;
|
||||
ILINE1(:,1)=iline1_2;
|
||||
ILINE2(:,1)=iline2_2;
|
||||
ILINE3(:,1)=iline3_2;
|
||||
ILINE4(:,1)=iline4_2;
|
||||
ILINE5(:,1)=iline5_2;
|
||||
ILINE6(:,1)=iline6_2;
|
||||
ILINE7(:,1)=iline7_2;
|
||||
ILINE8(:,1)=iline8_2;
|
||||
ILINE9(:,1)=iline9_2;
|
||||
ILINE10(:,1)=iline10_2;
|
||||
ILINE11(:,1)=iline11_2;
|
||||
ILINE12(:,1)=iline12_2;
|
||||
ILOAD1(:,1)=iload1_2;
|
||||
ILOAD2(:,1)=iload2_2;
|
||||
|
||||
% algebric part
|
||||
PM(:,1)= P2(:,1)-Sys.Gdt.*OMG(:,1);
|
||||
W_R(:,1) = OMG(:,1)+1;
|
||||
SIN(:,1) =sin(THETA(:,1)); % sin(theta) no need to add '
|
||||
COS(:,1) =cos(THETA(:,1)); % cos(theta)
|
||||
|
||||
ID(:,1) = 2/3*( [ILINE1(1,1); ILINE2(1,1); ILINE3(1,1); ILINE4(1,1)].*COS(:,1) + [ILINE1(2,1); ILINE2(2,1); ILINE3(2,1); ILINE4(2,1)].*( COS(:,1)*cos(2*pi/3)+SIN(:,1)*sin(2*pi/3) ) + [ILINE1(3,1); ILINE2(3,1); ILINE3(3,1); ILINE4(3,1)].*( COS(:,1)*cos(2*pi/3)-SIN(:,1)*sin(2*pi/3) ) );
|
||||
IQ(:,1) = 2/3*( -[ILINE1(1,1); ILINE2(1,1); ILINE3(1,1); ILINE4(1,1)].*SIN(:,1) - [ILINE1(2,1); ILINE2(2,1); ILINE3(2,1); ILINE4(2,1)].*( SIN(:,1)*cos(2*pi/3)-COS(:,1)*sin(2*pi/3) ) - [ILINE1(3,1); ILINE2(3,1); ILINE3(3,1); ILINE4(3,1)].*( SIN(:,1)*cos(2*pi/3)+COS(:,1)*sin(2*pi/3) ) );
|
||||
|
||||
LAMBDA_AD(:,1) = Sys.Lad_pp.*(-ID(:,1)+LAMBDA_F(:,1)./Sys.Lfd+LAMBDA_D(:,1)./Sys.L1d);
|
||||
LAMBDA_AQ(:,1) = Sys.Laq_pp.*(-IQ(:,1)+LAMBDA_Q1(:,1)./Sys.L1q+LAMBDA_Q2(:,1)./Sys.L2q);
|
||||
|
||||
PE(:,1) = LAMBDA_AD(:,1).*IQ(:,1)-LAMBDA_AQ(:,1).*ID(:,1);
|
||||
|
||||
VD_PP(:,1)=Sys.Vd_pp_coeff1.*ID(:,1)+Sys.Vd_pp_coeff2.*LAMBDA_F(:,1)+Sys.Vd_pp_coeff3.*LAMBDA_D(:,1)...
|
||||
-W_R(:,1).*Sys.Laq_pp.*( LAMBDA_Q1(:,1)./Sys.L1q + LAMBDA_Q2(:,1)./Sys.L2q ) + Sys.Lad_pp./Sys.Lfd.*EFD(:,1) ;
|
||||
|
||||
VQ_PP(:,1)=Sys.Vq_pp_coeff1.*IQ(:,1)+Sys.Vq_pp_coeff2.*LAMBDA_Q1(:,1)+Sys.Vq_pp_coeff3.*LAMBDA_Q2(:,1)...
|
||||
+W_R(:,1).*Sys.Lad_pp.*( LAMBDA_F(:,1)./Sys.Lfd + LAMBDA_D(:,1)./Sys.L1d );
|
||||
|
||||
VPP_A(:,1) = COS(:,1).*VD_PP(:,1) -SIN(:,1).*VQ_PP(:,1);
|
||||
VPP_B(:,1) = ( COS(:,1)*cos(2*pi/3)+SIN(:,1)*sin(2*pi/3) ).*VD_PP(:,1) -( SIN(:,1)*cos(2*pi/3)-COS(:,1)*sin(2*pi/3) ).*VQ_PP(:,1);
|
||||
VPP_C(:,1) = ( COS(:,1)*cos(2*pi/3)-SIN(:,1)*sin(2*pi/3) ).*VD_PP(:,1) -( SIN(:,1)*cos(2*pi/3)+COS(:,1)*sin(2*pi/3) ).*VQ_PP(:,1);
|
||||
|
||||
VT2(:,1) = abs(VD_PP(:,1)+1i*VQ_PP(:,1)).^2;
|
||||
VT(:,1) = abs(VD_PP(:,1)+1i*VQ_PP(:,1));
|
||||
|
||||
end
|
||||
|
||||
sol_dtm = zeros(110,size(t_dtm,1)); % generator state variables
|
||||
sol_dtm(1:4,:) = res_dta;
|
||||
sol_dtm(5:8,:) = res_theta;
|
||||
sol_dtm(9:12,:) = res_omg;
|
||||
sol_dtm(13:16,:) = res_lambda_f;
|
||||
sol_dtm(17:20,:) = res_lambda_d;
|
||||
sol_dtm(21:24,:) = res_lambda_q1;
|
||||
sol_dtm(25:28,:) = res_lambda_q2;
|
||||
sol_dtm(29:32,:) = res_v1;
|
||||
sol_dtm(33:36,:) = res_efd;
|
||||
sol_dtm(37:40,:) = res_p1;
|
||||
sol_dtm(41:44,:) = res_p2;
|
||||
|
||||
sol_dtm(45:47,:) = res_vbus5;
|
||||
sol_dtm(48:50,:) = res_vbus6;
|
||||
sol_dtm(51:53,:) = res_vbus7;
|
||||
sol_dtm(54:56,:) = res_vbus8;
|
||||
sol_dtm(57:59,:) = res_vbus9;
|
||||
sol_dtm(60:62,:) = res_vbus10;
|
||||
sol_dtm(63:65,:) = res_vbus11;
|
||||
sol_dtm(66:68,:) = res_iline1;
|
||||
sol_dtm(69:71,:) = res_iline2;
|
||||
sol_dtm(72:74,:) = res_iline3;
|
||||
sol_dtm(75:77,:) = res_iline4;
|
||||
sol_dtm(78:80,:) = res_iline5;
|
||||
sol_dtm(81:83,:) = res_iline6;
|
||||
sol_dtm(84:86,:) = res_iline7;
|
||||
sol_dtm(87:89,:) = res_iline8;
|
||||
sol_dtm(90:92,:) = res_iline9;
|
||||
sol_dtm(93:95,:) = res_iline10;
|
||||
sol_dtm(96:98,:) = res_iline11;
|
||||
sol_dtm(99:101,:) = res_iline12;
|
||||
sol_dtm(102:104,:) = res_iload1;
|
||||
sol_dtm(105:107,:) = res_iload2;
|
||||
sol_dtm(108:111,:) = res_vtp;
|
||||
|
||||
@ -0,0 +1,54 @@
|
||||
|
||||
function [t_final, sol_final] = calEMT(testSystem)
|
||||
%%
|
||||
[orderOfDT, timeStepOfDT] = setSASParameters();
|
||||
|
||||
[Base, w, FtBus, time_step, time_step_on, TimeRange1, FtTime, TotalTime, TimeRange2, TimeRange3] = set_simulation_parameters();
|
||||
|
||||
%%
|
||||
[R_line_positive, wL_line_positive, B_line_positive, int_t, LC_fre, t_base] = setDefaultParameters();
|
||||
|
||||
[mpc, SUCESS] = runpf(testSystem);
|
||||
|
||||
Sys = myFunction(mpc);
|
||||
|
||||
[Sys,Laa0_pp,Lab0_pp,Laa2_pp] = transformParameters(Sys,t_base);
|
||||
|
||||
[Vt,dta,Id, Iq, Edp, Eqp, Edpp, Eqpp, Pm, Efd, Sys, omg, V1, efd, P1, P2, Epp] = generator_states(mpc, Sys, Base);
|
||||
|
||||
[Lambda_F, Lambda_D, Lambda_Q1, Lambda_Q2] = calculateLambda(Sys, Id, Iq, efd);
|
||||
|
||||
[R_line, L_line, C_line] = tline_to_matrix(R_line_positive, wL_line_positive, B_line_positive,LC_fre);
|
||||
|
||||
[L_tf_positive L_tf LoadPQ Zload R_load L_load Sys LoadShunt YShunt C_Shunt CShunt] = fun1(Sys,LC_fre,mpc,Vt,Base);
|
||||
|
||||
[Vbus_3Phase branch_number c Sys Iline_3Phase ind_line1 ind_line2 Zbranch Ibranch ...
|
||||
Amp Ang Iload_3Phase ind_load theta] = fun2(Sys, mpc, dta, int_t, w, Zload);
|
||||
|
||||
L_temp = calculate_L_temp(L_tf, L_line, Laa0_pp, Lab0_pp);
|
||||
|
||||
[Sys] = calculateSystemMatrices(mpc, Sys, CShunt, R_line, wL_line_positive, branch_number, L_temp, C_line);
|
||||
|
||||
[Vbus, Iline, Iload] = convert_to_single_vector(Vbus_3Phase, Iline_3Phase, Iload_3Phase, Sys, branch_number);
|
||||
|
||||
Sys = update_system_parameters(Sys, Laa0_pp, Lab0_pp);
|
||||
|
||||
x_ini=[dta; theta; omg; Lambda_F; Lambda_D; Lambda_Q1; Lambda_Q2; V1; efd; P1; P2;...
|
||||
Vbus(3*length(Sys.GenIdx)+1:end); Iline; Iload; abs(Epp)];
|
||||
|
||||
|
||||
%%
|
||||
options = odeset('RelTol',1e-4,'AbsTol',1e-4); % limit the error
|
||||
[t_pre,x_pre]= ode23t(@funEMT_pre,TimeRange1(1):time_step:TimeRange1(2),x_ini,options,Sys);
|
||||
|
||||
x_ini_on = x_pre(end,:)';
|
||||
[t_on,x_on] = ode23t(@funEMT_on,TimeRange2(1):time_step_on:TimeRange2(2),x_ini_on,options,Sys);
|
||||
|
||||
x_ini_post = x_on(end,:)';
|
||||
[t_dt,x_dt]=DTsolver(TimeRange3,timeStepOfDT,x_ini_post,orderOfDT,Sys); %x_ini_post
|
||||
|
||||
t_post = t_dt;
|
||||
x_post = x_dt';
|
||||
t_final = [t_pre; t_on(2:end); t_post(2:end)];
|
||||
sol_final = [x_pre; x_on(2:end,:); x_post(2:end,:)];
|
||||
return
|
||||
@ -0,0 +1,7 @@
|
||||
function [Lambda_F, Lambda_D, Lambda_Q1, Lambda_Q2] = calculateLambda(Sys, Id, Iq, efd)
|
||||
|
||||
Ifd=efd./Sys.Rfd;
|
||||
Lambda_F = -Sys.Lad.*Id+(Sys.Lfd+Sys.Lad).*Ifd; % steady state Id1=0
|
||||
Lambda_D = -Sys.Lad.*Id+Sys.Lad.*Ifd;
|
||||
Lambda_Q1 = -Sys.Laq.*Iq;
|
||||
Lambda_Q2 = -Sys.Laq.*Iq;
|
||||
@ -0,0 +1,68 @@
|
||||
function [Sys] = calculateSystemMatrices(mpc, Sys, CShunt, R_line, wL_line_positive, branch_number, L_temp, C_line);
|
||||
|
||||
% Calculate System Matrices
|
||||
% Inputs:
|
||||
% - mpc: power system data
|
||||
% - Sys: structure containing system matrices
|
||||
% - CShunt: shunt capacitance matrix
|
||||
% - L_tf: transformer leakage inductance matrix
|
||||
% - R_line: transmission line resistance
|
||||
% - L_line: transmission line inductance
|
||||
% - wL_line_positive: positive sequence angular frequency
|
||||
% - Laa0_pp: stator inductance matrix element Laa0, prime-prime frame
|
||||
% - Lab0_pp: stator inductance matrix element Lab0, prime-prime frame
|
||||
% Output:
|
||||
% - Sys: structure containing calculated system matrices
|
||||
|
||||
L_tf = L_temp.L_tf;
|
||||
L_line = L_temp.L_line;
|
||||
Laa0_pp = L_temp.Laa0_pp;
|
||||
Lab0_pp = L_temp.Lab0_pp;
|
||||
|
||||
|
||||
Sys.Cnode_3Phase=zeros(3,3,Sys.bus_number);
|
||||
% T line
|
||||
for k=1:1:branch_number
|
||||
ind_line1=mpc.branch(k,1);
|
||||
ind_line2=mpc.branch(k,2);
|
||||
% if it is transmission line branch
|
||||
if ismember(ind_line1,Sys.NonGenIdx)
|
||||
term=mpc.branch(k,4)/wL_line_positive*C_line;
|
||||
Sys.Cnode_3Phase(:,:,ind_line1) = Sys.Cnode_3Phase(:,:,ind_line1) + term;
|
||||
Sys.Cnode_3Phase(:,:,ind_line2) = Sys.Cnode_3Phase(:,:,ind_line2) + term;
|
||||
end
|
||||
end
|
||||
% Fix shunt
|
||||
for k=1:1:length(Sys.ShuntIdx)
|
||||
Sys.Cnode_3Phase(:,:,Sys.ShuntIdx(k))= Sys.Cnode_3Phase(:,:,Sys.ShuntIdx(k))+ CShunt(:,:,k);
|
||||
end
|
||||
% transformed into inverse matrices
|
||||
for k=1:1:Sys.bus_number
|
||||
Sys.Cnode_3Phase(:,:,k)= inv(Sys.Cnode_3Phase(:,:,k));
|
||||
end
|
||||
|
||||
% all the Branch R L, consider transformer, T line, and load
|
||||
Sys.Rline_3Phase=zeros(3,3,branch_number);
|
||||
Sys.Lline_3Phase=zeros(3,3,branch_number);
|
||||
L_stator=zeros(3,3,length(Sys.GenIdx));
|
||||
% T line
|
||||
for k=1:1:branch_number
|
||||
ind_line1=mpc.branch(k,1);
|
||||
ind_line2=mpc.branch(k,2);
|
||||
if ismember(ind_line1,Sys.GenIdx)
|
||||
L_stator(:,:,k)= [Laa0_pp(k) Lab0_pp(k) Lab0_pp(k); Lab0_pp(k) Laa0_pp(k) Lab0_pp(k); Lab0_pp(k) Lab0_pp(k) Laa0_pp(k)]/120/pi;
|
||||
Sys.Rline_3Phase(:,:,k) = zeros(3,3);
|
||||
Sys.Lline_3Phase(:,:,k) = inv(L_tf+L_stator(:,:,k));
|
||||
% if it is transmission line branch
|
||||
elseif ismember(ind_line1,Sys.NonGenIdx)
|
||||
Sys.Rline_3Phase(:,:,k) = mpc.branch(k,4)/wL_line_positive*R_line;
|
||||
Sys.Lline_3Phase(:,:,k) = inv(mpc.branch(k,4)/wL_line_positive*L_line);
|
||||
end
|
||||
end
|
||||
|
||||
for k=1:1:length(Sys.GenIdx)
|
||||
Sys.Gen_R(:,:,k)= [Sys.Ra(k), 0, 0; 0, Sys.Ra(k), 0; 0, 0, Sys.Ra(k)];
|
||||
L_stator(:,:,k)= [Laa0_pp(k) Lab0_pp(k) Lab0_pp(k); Lab0_pp(k) Laa0_pp(k) Lab0_pp(k); Lab0_pp(k) Lab0_pp(k) Laa0_pp(k)]/120/pi;
|
||||
% because Sys.Laa0_pp is already updated
|
||||
Sys.Lline_3Phase(:,:,k) = Sys.Lline_3Phase(:,:,k)+ L_stator(:,:,k);
|
||||
end
|
||||
@ -0,0 +1,6 @@
|
||||
function L_temp = calculate_L_temp(L_tf, L_line, Laa0_pp, Lab0_pp)
|
||||
L_temp.L_tf = L_tf;
|
||||
L_temp.L_line = L_line;
|
||||
L_temp.Laa0_pp = Laa0_pp;
|
||||
L_temp.Lab0_pp = Lab0_pp;
|
||||
end
|
||||
@ -0,0 +1,26 @@
|
||||
function [Vbus, Iline, Iload] = convert_to_single_vector(Vbus_3Phase, Iline_3Phase, Iload_3Phase, Sys, branch_number)
|
||||
% This function converts the three-phase voltage, branch current, and load current
|
||||
% vectors into a single vector format for each of them.
|
||||
|
||||
Vbus=zeros(3*Sys.bus_number,1);
|
||||
for k=1:1:Sys.bus_number
|
||||
for k1= 1:1:3
|
||||
Vbus((k-1)*3+k1)=Vbus_3Phase(k1,1,k);
|
||||
end
|
||||
end
|
||||
|
||||
% change three phase branch current to a single vector
|
||||
Iline=zeros(3*branch_number,1);
|
||||
for k=1:1:branch_number
|
||||
for k1= 1:1:3
|
||||
Iline((k-1)*3+k1)=Iline_3Phase(k1,1,k);
|
||||
end
|
||||
end
|
||||
|
||||
% change three phase load current to a single vector
|
||||
Iload=zeros(3*length(Sys.LoadIdx),1);
|
||||
for k=1:1:length(Sys.LoadIdx)
|
||||
for k1= 1:1:3
|
||||
Iload((k-1)*3+k1)=Iload_3Phase(k1,1,k);
|
||||
end
|
||||
end
|
||||
@ -0,0 +1,27 @@
|
||||
function [L_tf_positive L_tf LoadPQ Zload R_load L_load Sys LoadShunt YShunt C_Shunt CShunt] = fun1(Sys,LC_fre,mpc,Vt,Base)
|
||||
%% transformer parameters, per unit
|
||||
% Assume all the transformers have the same impedance
|
||||
L_tf_positive=mpc.branch(Sys.GenIdx(1),4)/(LC_fre); %positive sequence leakage reactance
|
||||
L_tf=[L_tf_positive 0 0; 0 L_tf_positive 0; 0 0 L_tf_positive];
|
||||
|
||||
%% Constant PQ load parameter, per unit
|
||||
% PQ load
|
||||
LoadPQ = (mpc.bus(Sys.LoadIdx,3)+1i*mpc.bus(Sys.LoadIdx,4))./Base;
|
||||
Zload = conj((abs(Vt(Sys.LoadIdx,:)).^2)./LoadPQ); % constant Z load
|
||||
R_load = real(Zload);
|
||||
L_load = imag(Zload)/(LC_fre);
|
||||
Sys.Rload_3Phase = zeros(3,3,length(R_load));
|
||||
Sys.Lload_3Phase = Sys.Rload_3Phase;
|
||||
for k=1:1:size(R_load)
|
||||
Sys.Rload_3Phase(:,:,k)=[R_load(k) 0 0; 0 R_load(k) 0; 0 0 R_load(k)];
|
||||
Sys.Lload_3Phase(:,:,k)=inv([L_load(k) 0 0; 0 L_load(k) 0; 0 0 L_load(k)]);
|
||||
end
|
||||
|
||||
% fixed shunt
|
||||
LoadShunt = (mpc.bus(Sys.ShuntIdx,5)-1i*mpc.bus(Sys.ShuntIdx,6))./Base; % fixed shunt load, use - because it generate reactive power
|
||||
YShunt = conj(LoadShunt./1.^2 ); % constant Z load, do not use abs(Vt(LoadIdx,:)).^2, because voltage should be 1
|
||||
C_Shunt = imag(YShunt)/(LC_fre);
|
||||
CShunt = zeros(3,3,length(C_Shunt));
|
||||
for k=1:1:length(C_Shunt)
|
||||
CShunt(:,:,k)=[C_Shunt(k) 0 0; 0 C_Shunt(k) 0; 0 0 C_Shunt(k)];
|
||||
end
|
||||
@ -0,0 +1,42 @@
|
||||
function [Vbus_3Phase branch_number c Sys Iline_3Phase ind_line1 ind_line2 Zbranch Ibranch ...
|
||||
Amp Ang Iload_3Phase ind_load theta] = fun2(Sys, mpc, dta, int_t, w, Zload)
|
||||
%% current and voltage, three phase
|
||||
% all the bus voltage, three phase, assume t=ini_t, and Va=sin(wt+angle)
|
||||
Vbus_3Phase=zeros(3,1,Sys.bus_number);
|
||||
for k=1:1:Sys.bus_number
|
||||
Vbus_3Phase(:,:,k) = [mpc.bus(k,8).*sin(w*int_t+ mpc.bus(k,9)*pi/180);...
|
||||
mpc.bus(k,8).*sin(w*int_t+(mpc.bus(k,9)-120)*pi/180);...
|
||||
mpc.bus(k,8).*sin(w*int_t+(mpc.bus(k,9)+120)*pi/180)];
|
||||
end
|
||||
|
||||
% all the branch circuit current, three phase, assume t=0, and Ia=sin(wt+angle)
|
||||
[branch_number,c] = size(mpc.branch);
|
||||
Sys.branch_number=branch_number;
|
||||
Iline_3Phase=zeros(3,1,branch_number);
|
||||
for k=1:1:branch_number % consider all branch and load
|
||||
ind_line1=mpc.branch(k,1);
|
||||
ind_line2=mpc.branch(k,2);
|
||||
Zbranch = mpc.branch(k,3)+1i*mpc.branch(k,4);
|
||||
Ibranch= ( mpc.bus(ind_line1,8)*exp(1i*mpc.bus(ind_line1,9)*pi/180)- ...
|
||||
mpc.bus(ind_line2,8)*exp(1i*mpc.bus(ind_line2,9)*pi/180) )/Zbranch;
|
||||
Amp=abs(Ibranch);
|
||||
Ang=angle(Ibranch);
|
||||
Iline_3Phase(:,:,k)=[Amp.*sin(w*int_t+Ang);...
|
||||
Amp.*sin(w*int_t+Ang-120*pi/180);...
|
||||
Amp.*sin(w*int_t+Ang+120*pi/180)];
|
||||
end
|
||||
|
||||
% all load current
|
||||
Iload_3Phase=zeros(3,1,length(Sys.LoadIdx));
|
||||
for k=1:1:length(Sys.LoadIdx) % consider all branch and load
|
||||
ind_load=Sys.LoadIdx(k);
|
||||
Iload= mpc.bus(ind_load,8)*exp(1i*mpc.bus(ind_load,9)*pi/180)/Zload(k);
|
||||
Amp=abs(Iload);
|
||||
Ang=angle(Iload);
|
||||
Iload_3Phase(:,:,k)=[Amp.*sin(w*int_t+Ang);...
|
||||
Amp.*sin(w*int_t+Ang-120*pi/180);...
|
||||
Amp.*sin(w*int_t+Ang+120*pi/180)];
|
||||
end
|
||||
|
||||
%% Initialization of Theta angle
|
||||
theta=dta-pi+120*pi*int_t; % I found that if int_t=0, theta=dta-pi
|
||||
@ -0,0 +1,33 @@
|
||||
function [Sys, Laa0_pp, Lab0_pp, Laa2_pp, t_base] = fun3(Sys)
|
||||
|
||||
%% old, good version
|
||||
t_base=1/(120*pi);
|
||||
|
||||
Sys.Lad=Sys.Xd-Sys.Xl;
|
||||
Sys.Lfd=1./(1./(Sys.Xdp-Sys.Xl)-1./Sys.Lad);
|
||||
Sys.Rfd=(Sys.Lad+Sys.Lfd)./(Sys.Td0p./t_base);
|
||||
Sys.L1d=1./(1./(Sys.Xdpp-Sys.Xl)-1./Sys.Lfd-1./Sys.Lad);
|
||||
Sys.R1d=(1./(1./Sys.Lad+1./Sys.Lfd)+Sys.L1d)./(Sys.Td0pp./t_base);
|
||||
|
||||
Sys.Laq=Sys.Xq-Sys.Xl;
|
||||
Sys.L1q=1./(1./(Sys.Xqp-Sys.Xl)-1./Sys.Laq);
|
||||
Sys.R1q=(Sys.Laq+Sys.L1q)./(Sys.Tq0p./t_base);
|
||||
Sys.L2q=1./(1./(Sys.Xqpp-Sys.Xl)-1./Sys.L1q-1./Sys.Laq);
|
||||
Sys.R2q=(1./(1./Sys.Laq+1./Sys.L1q)+Sys.L2q)./(Sys.Tq0pp./t_base);
|
||||
|
||||
Sys.Lad_pp=Sys.Xdpp-Sys.Xl;
|
||||
Sys.Laq_pp=Sys.Xdpp-Sys.Xl;
|
||||
|
||||
Laa0_pp= Sys.Xl+( Sys.Lad_pp+ Sys.Laq_pp+Sys.L0-Sys.Xl )/3;
|
||||
Lab0_pp= ( 2*Sys.L0-2*Sys.Xl-Sys.Lad_pp-Sys.Laq_pp )/6;
|
||||
Laa2_pp= ( Sys.Lad_pp-Sys.Laq_pp )/3;
|
||||
|
||||
Sys.Vd_pp_coeff1=-(Sys.Rfd./(Sys.Lfd).^2+Sys.R1d./(Sys.L1d).^2).*(Sys.Lad_pp).^2;
|
||||
Sys.Vd_pp_coeff2=-(Sys.Lad_pp.*Sys.Rfd./(Sys.Lfd).^2.*(1-Sys.Lad_pp./Sys.Lfd) - Sys.Lad_pp.^2.*Sys.R1d./(Sys.L1d).^2./Sys.Lfd);
|
||||
Sys.Vd_pp_coeff3=(Sys.Lad_pp.^2.*Sys.Rfd./(Sys.Lfd).^2./Sys.L1d - Sys.Lad_pp.*Sys.R1d./(Sys.L1d).^2.*(1-Sys.Lad_pp./Sys.L1d));
|
||||
|
||||
Sys.Vq_pp_coeff1=-(Sys.R1q./(Sys.L1q).^2+Sys.R2q./(Sys.L2q).^2).*(Sys.Laq_pp).^2;
|
||||
Sys.Vq_pp_coeff2=-(Sys.Laq_pp.*Sys.R1q./(Sys.L1q).^2.*(1-Sys.Laq_pp./Sys.L1q) - Sys.Laq_pp.^2.*Sys.R2q./(Sys.L2q).^2./Sys.L1q);
|
||||
Sys.Vq_pp_coeff3=(Sys.Laq_pp.^2.*Sys.R1q./(Sys.L1q).^2./Sys.L2q - Sys.Laq_pp.*Sys.R2q./(Sys.L2q).^2.*(1-Sys.Laq_pp./Sys.L2q));
|
||||
|
||||
|
||||
@ -0,0 +1,99 @@
|
||||
function [xp] = funEMT_on(t,x,Sys)
|
||||
xp = zeros(size(x));
|
||||
R_ground = eye(3)*100000;
|
||||
|
||||
% global GLO
|
||||
dta = x(1:4,1);
|
||||
theta = x(4+1:2*4,1);
|
||||
omg = x(2*4+1:3*4,1);
|
||||
Lambda_F = x(3*4+1:4*4,1);
|
||||
Lambda_D = x(4*4+1:5*4,1);
|
||||
Lambda_Q1 = x(5*4+1:6*4,1);
|
||||
Lambda_Q2 = x(6*4+1:7*4,1);
|
||||
|
||||
V1 = x(7*4+1:8*4,1);
|
||||
efd = x(8*4+1:9*4,1);
|
||||
% efd = min(max(efd,Sys.Emin),Sys.Emax);
|
||||
|
||||
P1 = x(9*4+1:10*4,1);
|
||||
% P1 = min(max(P1,Sys.GVmin),Sys.GVmax);
|
||||
|
||||
P2 = x(10*4+1:11*4,1);
|
||||
Pm = P2-Sys.Gdt.*omg;
|
||||
Vbus = x(11*4+1:11*4+3*(11-4),1);
|
||||
Iline = x(11*4+3*(11-4)+1:11*4+3*(11-4)+3*12,1);
|
||||
Iload = x(11*4+3*(11-4)+3*12+1:11*4+3*(11-4)+3*12+3*2,1);
|
||||
Vtp = x(107+1:107+4,1);
|
||||
|
||||
w_r = omg+1;
|
||||
COS = cos(theta);
|
||||
SIN = sin(theta);
|
||||
|
||||
Id = 2/3*( Iline(1:3:3*4).*COS + Iline(2:3:3*4).*( COS*cos(2*pi/3)+SIN*sin(2*pi/3) ) + Iline(3:3:3*4).*( COS*cos(2*pi/3)-SIN*sin(2*pi/3) ) );
|
||||
Iq = 2/3*( -Iline(1:3:3*4).*SIN - Iline(2:3:3*4).*( SIN*cos(2*pi/3)-COS*sin(2*pi/3) ) - Iline(3:3:3*4).*( SIN*cos(2*pi/3)+COS*sin(2*pi/3) ) );
|
||||
|
||||
Lambda_ad = Sys.Lad_pp.*(-Id+Lambda_F./Sys.Lfd+Lambda_D./Sys.L1d);
|
||||
Lambda_aq = Sys.Laq_pp.*(-Iq+Lambda_Q1./Sys.L1q+Lambda_Q2./Sys.L2q);
|
||||
Pe = (Lambda_ad.*Iq-Lambda_aq.*Id);
|
||||
|
||||
Vd_pp=Sys.Vd_pp_coeff1.*Id+Sys.Vd_pp_coeff2.*Lambda_F+Sys.Vd_pp_coeff3.*Lambda_D...
|
||||
-w_r.*Sys.Laq_pp.*( Lambda_Q1./Sys.L1q + Lambda_Q2./Sys.L2q ) + Sys.Lad_pp./Sys.Lfd.*efd ;
|
||||
|
||||
Vq_pp=Sys.Vq_pp_coeff1.*Iq+Sys.Vq_pp_coeff2.*Lambda_Q1+Sys.Vq_pp_coeff3.*Lambda_Q2...
|
||||
+w_r.*Sys.Lad_pp.*( Lambda_F./Sys.Lfd + Lambda_D./Sys.L1d );
|
||||
|
||||
% Inv_Park(:,:,k)*[0; Vd_pp(k); Vq_pp(k)]
|
||||
Vpp_a = COS.*Vd_pp -SIN.*Vq_pp;
|
||||
Vpp_b = ( COS*cos(2*pi/3)+SIN*sin(2*pi/3) ).*Vd_pp -( SIN*cos(2*pi/3)-COS*sin(2*pi/3) ).*Vq_pp;
|
||||
Vpp_c = ( COS*cos(2*pi/3)-SIN*sin(2*pi/3) ).*Vd_pp -( SIN*cos(2*pi/3)+COS*sin(2*pi/3) ).*Vq_pp;
|
||||
|
||||
Vt = sqrt(Vd_pp.^2+Vq_pp.^2); % in fact it is internal voltage
|
||||
|
||||
% ODEs
|
||||
xp(1:4,1) = 2*pi*60*omg;
|
||||
xp(4+1 : 2*4,1) = 2*pi*60*(omg+1);
|
||||
xp(2*4+1: 3*4,1) = Sys.w0*(Pm - Pe - Sys.D.*omg./Sys.w0)./Sys.H/2;
|
||||
xp(3*4+1: 4*4,1) = 120*pi*(efd-Sys.Rfd./Sys.Lfd.*(Lambda_F-Lambda_ad));
|
||||
xp(4*4+1: 5*4,1) = -120*pi*Sys.R1d./Sys.L1d.*(Lambda_D-Lambda_ad);
|
||||
xp(5*4+1: 6*4,1) = -120*pi*Sys.R1q./Sys.L1q.*(Lambda_Q1-Lambda_aq);
|
||||
xp(6*4+1: 7*4,1) = -120*pi*Sys.R2q./Sys.L2q.*(Lambda_Q2-Lambda_aq);
|
||||
|
||||
xp(7*4+1: 8*4,1) = ( -Vtp+Sys.Vref-V1-Sys.Eta.*(Vt-Vtp)./Sys.T_vt )./Sys.Etb; % substitute d(Vt')=(Vt-Vtp)./Sys.T_vt
|
||||
xp(8*4+1: 9*4,1) = ( V1.*Sys.Ek-efd.*Sys.Lad./Sys.Rfd )./Sys.Ete.*Sys.Rfd./Sys.Lad;
|
||||
|
||||
xp(9*4+1: 10*4,1) = ( (Sys.Pref-omg)./Sys.Gr-P1 )./Sys.Gt1;
|
||||
xp(10*4+1: 11*4,1) = (P1-P2+( (Sys.Pref-omg)./Sys.Gr-P1 )./Sys.Gt1.*Sys.Gt2)./Sys.Gt3;
|
||||
|
||||
xp(44+1:44+3,1) = Sys.Cnode_3Phase(:,:,5)*([sum(Iline(([1 ]-1)*3+1,1));sum(Iline(([1 ]-1)*3+2,1));sum(Iline(([1 ]-1)*3+3,1))]-[sum(Iline(([5 ]-1)*3+1,1));sum(Iline(([5 ]-1)*3+2,1));sum(Iline(([5 ]-1)*3+3,1))]);
|
||||
xp(47+1:47+3,1) = Sys.Cnode_3Phase(:,:,6)*([sum(Iline(([2 5 ]-1)*3+1,1));sum(Iline(([2 5 ]-1)*3+2,1));sum(Iline(([2 5 ]-1)*3+3,1))]-[sum(Iline(([6 ]-1)*3+1,1));sum(Iline(([6 ]-1)*3+2,1));sum(Iline(([6 ]-1)*3+3,1))]);
|
||||
xp(50+1:50+3,1) = Sys.Cnode_3Phase(:,:,7)*([sum(Iline(([6 ]-1)*3+1,1));sum(Iline(([6 ]-1)*3+2,1));sum(Iline(([6 ]-1)*3+3,1))]-[sum(Iline(([7 8 ]-1)*3+1,1));sum(Iline(([7 8 ]-1)*3+2,1));sum(Iline(([7 8 ]-1)*3+3,1))]-[sum(Iload(([1 ]-1)*3+1,1));sum(Iload(([1 ]-1)*3+2,1));sum(Iload(([1 ]-1)*3+3,1))]-R_ground*Vbus((7-5)*3+1:(7-5)*3+3));
|
||||
xp(53+1:53+3,1) = Sys.Cnode_3Phase(:,:,8)*([sum(Iline(([7 8 ]-1)*3+1,1));sum(Iline(([7 8 ]-1)*3+2,1));sum(Iline(([7 8 ]-1)*3+3,1))]-[sum(Iline(([9 10 ]-1)*3+1,1));sum(Iline(([9 10 ]-1)*3+2,1));sum(Iline(([9 10 ]-1)*3+3,1))]);
|
||||
xp(56+1:56+3,1) = Sys.Cnode_3Phase(:,:,9)*([sum(Iline(([9 10 ]-1)*3+1,1));sum(Iline(([9 10 ]-1)*3+2,1));sum(Iline(([9 10 ]-1)*3+3,1))]-[sum(Iline(([11 ]-1)*3+1,1));sum(Iline(([11 ]-1)*3+2,1));sum(Iline(([11 ]-1)*3+3,1))]-[sum(Iload(([2 ]-1)*3+1,1));sum(Iload(([2 ]-1)*3+2,1));sum(Iload(([2 ]-1)*3+3,1))]);
|
||||
xp(59+1:59+3,1) = Sys.Cnode_3Phase(:,:,10)*([sum(Iline(([4 11 ]-1)*3+1,1));sum(Iline(([4 11 ]-1)*3+2,1));sum(Iline(([4 11 ]-1)*3+3,1))]-[sum(Iline(([12 ]-1)*3+1,1));sum(Iline(([12 ]-1)*3+2,1));sum(Iline(([12 ]-1)*3+3,1))]);
|
||||
xp(62+1:62+3,1) = Sys.Cnode_3Phase(:,:,11)*([sum(Iline(([3 12 ]-1)*3+1,1));sum(Iline(([3 12 ]-1)*3+2,1));sum(Iline(([3 12 ]-1)*3+3,1))]);
|
||||
|
||||
xp(65+1:65+3,1)= Sys.Lline_3Phase(:,:,1)*( [Vpp_a(1); Vpp_b(1); Vpp_c(1)]- Vbus((5-5)*3+1:(5-5)*3+3) -Sys.Gen_R(:,:,1)*Iline((1-1)*3+1:(1-1)*3+3)); % IBR voltage
|
||||
xp(68+1:68+3,1)= Sys.Lline_3Phase(:,:,2)*( [Vpp_a(2); Vpp_b(2); Vpp_c(2)]- Vbus((6-5)*3+1:(6-5)*3+3) -Sys.Gen_R(:,:,2)*Iline((2-1)*3+1:(2-1)*3+3));
|
||||
xp(71+1:71+3,1)= Sys.Lline_3Phase(:,:,3)*( [Vpp_a(3); Vpp_b(3); Vpp_c(3)]- Vbus((11-5)*3+1:(11-5)*3+3)-Sys.Gen_R(:,:,3)*Iline((3-1)*3+1:(3-1)*3+3));
|
||||
xp(74+1:74+3,1)= Sys.Lline_3Phase(:,:,4)*( [Vpp_a(4); Vpp_b(4); Vpp_c(4)]- Vbus((10-5)*3+1:(10-5)*3+3)-Sys.Gen_R(:,:,4)*Iline((4-1)*3+1:(4-1)*3+3));
|
||||
|
||||
xp(77+1:77+3,1)=Sys.Lline_3Phase(:,:,5)*( Vbus((5-5)*3+1:(5-5)*3+3)-Vbus((6-5)*3+1:(6-5)*3+3)-Sys.Rline_3Phase(:,:,5) * Iline((5-1)*3+1:(5-1)*3+3) );
|
||||
xp(80+1:80+3,1)=Sys.Lline_3Phase(:,:,6)*( Vbus((6-5)*3+1:(6-5)*3+3)-Vbus((7-5)*3+1:(7-5)*3+3)-Sys.Rline_3Phase(:,:,6) * Iline((6-1)*3+1:(6-1)*3+3) );
|
||||
xp(83+1:83+3,1)=Sys.Lline_3Phase(:,:,7)*( Vbus((7-5)*3+1:(7-5)*3+3)-Vbus((8-5)*3+1:(8-5)*3+3)-Sys.Rline_3Phase(:,:,7) * Iline((7-1)*3+1:(7-1)*3+3) );
|
||||
xp(86+1:86+3,1)=Sys.Lline_3Phase(:,:,8)*( Vbus((7-5)*3+1:(7-5)*3+3)-Vbus((8-5)*3+1:(8-5)*3+3)-Sys.Rline_3Phase(:,:,8) * Iline((8-1)*3+1:(8-1)*3+3) );
|
||||
xp(89+1:89+3,1)=Sys.Lline_3Phase(:,:,9)*( Vbus((8-5)*3+1:(8-5)*3+3)-Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rline_3Phase(:,:,9) * Iline((9-1)*3+1:(9-1)*3+3) );
|
||||
xp(92+1:92+3,1)=Sys.Lline_3Phase(:,:,10)*( Vbus((8-5)*3+1:(8-5)*3+3)-Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rline_3Phase(:,:,10) * Iline((10-1)*3+1:(10-1)*3+3) );
|
||||
xp(95+1:95+3,1)=Sys.Lline_3Phase(:,:,11)*( Vbus((9-5)*3+1:(9-5)*3+3)-Vbus((10-5)*3+1:(10-5)*3+3)-Sys.Rline_3Phase(:,:,11) * Iline((11-1)*3+1:(11-1)*3+3) );
|
||||
xp(98+1:98+3,1)=Sys.Lline_3Phase(:,:,12)*( Vbus((10-5)*3+1:(10-5)*3+3)-Vbus((11-5)*3+1:(11-5)*3+3)-Sys.Rline_3Phase(:,:,12) * Iline((12-1)*3+1:(12-1)*3+3) );
|
||||
|
||||
xp(101+1:101+3,1)=Sys.Lload_3Phase(:,:,1)*( Vbus((7-5)*3+1:(7-5)*3+3)-Sys.Rload_3Phase(:,:,1) * Iload((1-1)*3+1:(1-1)*3+3) );
|
||||
xp(104+1:104+3,1)=Sys.Lload_3Phase(:,:,2)*( Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rload_3Phase(:,:,2) * Iload((2-1)*3+1:(2-1)*3+3) );
|
||||
|
||||
xp(107+1:107+4,1)=(Vt-Vtp)./Sys.T_vt;
|
||||
|
||||
% GLO.V1 =[GLO.V1, Vt(1)];
|
||||
% GLO.V2 =[GLO.V2, Vt(2)];
|
||||
% GLO.V3 =[GLO.V3, Vt(3)];
|
||||
% GLO.V4 =[GLO.V4, Vt(4)];
|
||||
|
||||
end
|
||||
@ -0,0 +1,97 @@
|
||||
function [xp] = funEMT_pre(t,x,Sys)
|
||||
xp = zeros(size(x));
|
||||
% global GLO
|
||||
dta = x(1:4,1);
|
||||
theta = x(4+1:2*4,1);
|
||||
omg = x(2*4+1:3*4,1);
|
||||
Lambda_F = x(3*4+1:4*4,1);
|
||||
Lambda_D = x(4*4+1:5*4,1);
|
||||
Lambda_Q1 = x(5*4+1:6*4,1);
|
||||
Lambda_Q2 = x(6*4+1:7*4,1);
|
||||
|
||||
V1 = x(7*4+1:8*4,1);
|
||||
efd = x(8*4+1:9*4,1);
|
||||
% efd = min(max(efd,Sys.Emin),Sys.Emax);
|
||||
|
||||
P1 = x(9*4+1:10*4,1);
|
||||
% P1 = min(max(P1,Sys.GVmin),Sys.GVmax);
|
||||
|
||||
P2 = x(10*4+1:11*4,1);
|
||||
Pm = P2-Sys.Gdt.*omg;
|
||||
Vbus = x(11*4+1:11*4+3*(11-4),1);
|
||||
Iline = x(11*4+3*(11-4)+1:11*4+3*(11-4)+3*12,1);
|
||||
Iload = x(11*4+3*(11-4)+3*12+1:11*4+3*(11-4)+3*12+3*2,1);
|
||||
Vtp = x(107+1:107+4,1);
|
||||
|
||||
w_r = omg+1;
|
||||
COS = cos(theta);
|
||||
SIN = sin(theta);
|
||||
|
||||
Id = 2/3*( Iline(1:3:3*4).*COS + Iline(2:3:3*4).*( COS*cos(2*pi/3)+SIN*sin(2*pi/3) ) + Iline(3:3:3*4).*( COS*cos(2*pi/3)-SIN*sin(2*pi/3) ) );
|
||||
Iq = 2/3*( -Iline(1:3:3*4).*SIN - Iline(2:3:3*4).*( SIN*cos(2*pi/3)-COS*sin(2*pi/3) ) - Iline(3:3:3*4).*( SIN*cos(2*pi/3)+COS*sin(2*pi/3) ) );
|
||||
|
||||
Lambda_ad = Sys.Lad_pp.*(-Id+Lambda_F./Sys.Lfd+Lambda_D./Sys.L1d);
|
||||
Lambda_aq = Sys.Laq_pp.*(-Iq+Lambda_Q1./Sys.L1q+Lambda_Q2./Sys.L2q);
|
||||
Pe = (Lambda_ad.*Iq-Lambda_aq.*Id);
|
||||
|
||||
Vd_pp=Sys.Vd_pp_coeff1.*Id+Sys.Vd_pp_coeff2.*Lambda_F+Sys.Vd_pp_coeff3.*Lambda_D...
|
||||
-w_r.*Sys.Laq_pp.*( Lambda_Q1./Sys.L1q + Lambda_Q2./Sys.L2q ) + Sys.Lad_pp./Sys.Lfd.*efd ;
|
||||
|
||||
Vq_pp=Sys.Vq_pp_coeff1.*Iq+Sys.Vq_pp_coeff2.*Lambda_Q1+Sys.Vq_pp_coeff3.*Lambda_Q2...
|
||||
+w_r.*Sys.Lad_pp.*( Lambda_F./Sys.Lfd + Lambda_D./Sys.L1d );
|
||||
|
||||
% Inv_Park(:,:,k)*[0; Vd_pp(k); Vq_pp(k)]
|
||||
Vpp_a = COS.*Vd_pp -SIN.*Vq_pp;
|
||||
Vpp_b = ( COS*cos(2*pi/3)+SIN*sin(2*pi/3) ).*Vd_pp -( SIN*cos(2*pi/3)-COS*sin(2*pi/3) ).*Vq_pp;
|
||||
Vpp_c = ( COS*cos(2*pi/3)-SIN*sin(2*pi/3) ).*Vd_pp -( SIN*cos(2*pi/3)+COS*sin(2*pi/3) ).*Vq_pp;
|
||||
|
||||
Vt = sqrt(Vd_pp.^2+Vq_pp.^2); % in fact it is internal voltage
|
||||
|
||||
% ODEs
|
||||
xp(1:4,1) = 2*pi*60*omg;
|
||||
xp(4+1 : 2*4,1) = 2*pi*60*(omg+1);
|
||||
xp(2*4+1: 3*4,1) = Sys.w0*(Pm - Pe - Sys.D.*omg./Sys.w0)./Sys.H/2;
|
||||
xp(3*4+1: 4*4,1) = 120*pi*(efd-Sys.Rfd./Sys.Lfd.*(Lambda_F-Lambda_ad));
|
||||
xp(4*4+1: 5*4,1) = -120*pi*Sys.R1d./Sys.L1d.*(Lambda_D-Lambda_ad);
|
||||
xp(5*4+1: 6*4,1) = -120*pi*Sys.R1q./Sys.L1q.*(Lambda_Q1-Lambda_aq);
|
||||
xp(6*4+1: 7*4,1) = -120*pi*Sys.R2q./Sys.L2q.*(Lambda_Q2-Lambda_aq);
|
||||
|
||||
xp(7*4+1: 8*4,1) = ( -Vtp+Sys.Vref-V1-Sys.Eta.*(Vt-Vtp)./Sys.T_vt )./Sys.Etb; % substitute d(Vt')=(Vt-Vtp)./Sys.T_vt
|
||||
xp(8*4+1: 9*4,1) = ( V1.*Sys.Ek-efd.*Sys.Lad./Sys.Rfd )./Sys.Ete.*Sys.Rfd./Sys.Lad;
|
||||
|
||||
xp(9*4+1: 10*4,1) = ( (Sys.Pref-omg)./Sys.Gr-P1 )./Sys.Gt1;
|
||||
xp(10*4+1: 11*4,1) = (P1-P2+( (Sys.Pref-omg)./Sys.Gr-P1 )./Sys.Gt1.*Sys.Gt2)./Sys.Gt3;
|
||||
|
||||
xp(44+1:44+3,1) = Sys.Cnode_3Phase(:,:,5)*([sum(Iline(([1 ]-1)*3+1,1));sum(Iline(([1 ]-1)*3+2,1));sum(Iline(([1 ]-1)*3+3,1))]-[sum(Iline(([5 ]-1)*3+1,1));sum(Iline(([5 ]-1)*3+2,1));sum(Iline(([5 ]-1)*3+3,1))]);
|
||||
xp(47+1:47+3,1) = Sys.Cnode_3Phase(:,:,6)*([sum(Iline(([2 5 ]-1)*3+1,1));sum(Iline(([2 5 ]-1)*3+2,1));sum(Iline(([2 5 ]-1)*3+3,1))]-[sum(Iline(([6 ]-1)*3+1,1));sum(Iline(([6 ]-1)*3+2,1));sum(Iline(([6 ]-1)*3+3,1))]);
|
||||
xp(50+1:50+3,1) = Sys.Cnode_3Phase(:,:,7)*([sum(Iline(([6 ]-1)*3+1,1));sum(Iline(([6 ]-1)*3+2,1));sum(Iline(([6 ]-1)*3+3,1))]-[sum(Iline(([7 8 ]-1)*3+1,1));sum(Iline(([7 8 ]-1)*3+2,1));sum(Iline(([7 8 ]-1)*3+3,1))]-[sum(Iload(([1 ]-1)*3+1,1));sum(Iload(([1 ]-1)*3+2,1));sum(Iload(([1 ]-1)*3+3,1))]);
|
||||
xp(53+1:53+3,1) = Sys.Cnode_3Phase(:,:,8)*([sum(Iline(([7 8 ]-1)*3+1,1));sum(Iline(([7 8 ]-1)*3+2,1));sum(Iline(([7 8 ]-1)*3+3,1))]-[sum(Iline(([9 10 ]-1)*3+1,1));sum(Iline(([9 10 ]-1)*3+2,1));sum(Iline(([9 10 ]-1)*3+3,1))]);
|
||||
xp(56+1:56+3,1) = Sys.Cnode_3Phase(:,:,9)*([sum(Iline(([9 10 ]-1)*3+1,1));sum(Iline(([9 10 ]-1)*3+2,1));sum(Iline(([9 10 ]-1)*3+3,1))]-[sum(Iline(([11 ]-1)*3+1,1));sum(Iline(([11 ]-1)*3+2,1));sum(Iline(([11 ]-1)*3+3,1))]-[sum(Iload(([2 ]-1)*3+1,1));sum(Iload(([2 ]-1)*3+2,1));sum(Iload(([2 ]-1)*3+3,1))]);
|
||||
xp(59+1:59+3,1) = Sys.Cnode_3Phase(:,:,10)*([sum(Iline(([4 11 ]-1)*3+1,1));sum(Iline(([4 11 ]-1)*3+2,1));sum(Iline(([4 11 ]-1)*3+3,1))]-[sum(Iline(([12 ]-1)*3+1,1));sum(Iline(([12 ]-1)*3+2,1));sum(Iline(([12 ]-1)*3+3,1))]);
|
||||
xp(62+1:62+3,1) = Sys.Cnode_3Phase(:,:,11)*([sum(Iline(([3 12 ]-1)*3+1,1));sum(Iline(([3 12 ]-1)*3+2,1));sum(Iline(([3 12 ]-1)*3+3,1))]);
|
||||
|
||||
xp(65+1:65+3,1)= Sys.Lline_3Phase(:,:,1)*( [Vpp_a(1); Vpp_b(1); Vpp_c(1)]- Vbus((5-5)*3+1:(5-5)*3+3) -Sys.Gen_R(:,:,1)*Iline((1-1)*3+1:(1-1)*3+3)); % IBR voltage
|
||||
xp(68+1:68+3,1)= Sys.Lline_3Phase(:,:,2)*( [Vpp_a(2); Vpp_b(2); Vpp_c(2)]- Vbus((6-5)*3+1:(6-5)*3+3) -Sys.Gen_R(:,:,2)*Iline((2-1)*3+1:(2-1)*3+3));
|
||||
xp(71+1:71+3,1)= Sys.Lline_3Phase(:,:,3)*( [Vpp_a(3); Vpp_b(3); Vpp_c(3)]- Vbus((11-5)*3+1:(11-5)*3+3)-Sys.Gen_R(:,:,3)*Iline((3-1)*3+1:(3-1)*3+3));
|
||||
xp(74+1:74+3,1)= Sys.Lline_3Phase(:,:,4)*( [Vpp_a(4); Vpp_b(4); Vpp_c(4)]- Vbus((10-5)*3+1:(10-5)*3+3)-Sys.Gen_R(:,:,4)*Iline((4-1)*3+1:(4-1)*3+3));
|
||||
|
||||
xp(77+1:77+3,1)=Sys.Lline_3Phase(:,:,5)*( Vbus((5-5)*3+1:(5-5)*3+3)-Vbus((6-5)*3+1:(6-5)*3+3)-Sys.Rline_3Phase(:,:,5) * Iline((5-1)*3+1:(5-1)*3+3) );
|
||||
xp(80+1:80+3,1)=Sys.Lline_3Phase(:,:,6)*( Vbus((6-5)*3+1:(6-5)*3+3)-Vbus((7-5)*3+1:(7-5)*3+3)-Sys.Rline_3Phase(:,:,6) * Iline((6-1)*3+1:(6-1)*3+3) );
|
||||
xp(83+1:83+3,1)=Sys.Lline_3Phase(:,:,7)*( Vbus((7-5)*3+1:(7-5)*3+3)-Vbus((8-5)*3+1:(8-5)*3+3)-Sys.Rline_3Phase(:,:,7) * Iline((7-1)*3+1:(7-1)*3+3) );
|
||||
xp(86+1:86+3,1)=Sys.Lline_3Phase(:,:,8)*( Vbus((7-5)*3+1:(7-5)*3+3)-Vbus((8-5)*3+1:(8-5)*3+3)-Sys.Rline_3Phase(:,:,8) * Iline((8-1)*3+1:(8-1)*3+3) );
|
||||
xp(89+1:89+3,1)=Sys.Lline_3Phase(:,:,9)*( Vbus((8-5)*3+1:(8-5)*3+3)-Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rline_3Phase(:,:,9) * Iline((9-1)*3+1:(9-1)*3+3) );
|
||||
xp(92+1:92+3,1)=Sys.Lline_3Phase(:,:,10)*( Vbus((8-5)*3+1:(8-5)*3+3)-Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rline_3Phase(:,:,10) * Iline((10-1)*3+1:(10-1)*3+3) );
|
||||
xp(95+1:95+3,1)=Sys.Lline_3Phase(:,:,11)*( Vbus((9-5)*3+1:(9-5)*3+3)-Vbus((10-5)*3+1:(10-5)*3+3)-Sys.Rline_3Phase(:,:,11) * Iline((11-1)*3+1:(11-1)*3+3) );
|
||||
xp(98+1:98+3,1)=Sys.Lline_3Phase(:,:,12)*( Vbus((10-5)*3+1:(10-5)*3+3)-Vbus((11-5)*3+1:(11-5)*3+3)-Sys.Rline_3Phase(:,:,12) * Iline((12-1)*3+1:(12-1)*3+3) );
|
||||
|
||||
xp(101+1:101+3,1)=Sys.Lload_3Phase(:,:,1)*( Vbus((7-5)*3+1:(7-5)*3+3)-Sys.Rload_3Phase(:,:,1) * Iload((1-1)*3+1:(1-1)*3+3) );
|
||||
xp(104+1:104+3,1)=Sys.Lload_3Phase(:,:,2)*( Vbus((9-5)*3+1:(9-5)*3+3)-Sys.Rload_3Phase(:,:,2) * Iload((2-1)*3+1:(2-1)*3+3) );
|
||||
|
||||
xp(107+1:107+4,1)=(Vt-Vtp)./Sys.T_vt;
|
||||
|
||||
% GLO.V1 =[GLO.V1, Vt(1)];
|
||||
% GLO.V2 =[GLO.V2, Vt(2)];
|
||||
% GLO.V3 =[GLO.V3, Vt(3)];
|
||||
% GLO.V4 =[GLO.V4, Vt(4)];
|
||||
% plot(0:2*10^(-6):t,GLO.V2(1:4:end))
|
||||
end
|
||||
@ -0,0 +1,48 @@
|
||||
function [Vt,dta,Id, Iq, Edp, Eqp, Edpp, Eqpp, Pm, Efd, Sys, omg, V1, efd, P1, P2, Epp] = generator_states(mpc, Sys, Base);
|
||||
%GENERATOR_STATES calculates generator states for a given power system
|
||||
|
||||
%% generator inside states
|
||||
Vtx = mpc.bus(:,8).*cos(mpc.bus(:,9)*pi/180);
|
||||
Vty = mpc.bus(:,8).*sin(mpc.bus(:,9)*pi/180);
|
||||
Vt = Vtx + 1i*Vty; % terminal voltage phasor value
|
||||
Vt_gen = Vt(Sys.GenIdx,:); % terminal voltage of generator bus
|
||||
GenPQ = (mpc.gen(:,2)+1i*mpc.gen(:,3))./Base;
|
||||
It_gen = conj(GenPQ./Vt_gen); % current injection
|
||||
|
||||
Zbranch = mpc.branch(1,3)+1i*mpc.branch(1,4);
|
||||
Ibr=(Vt(1,:)-Vt(5,:))/Zbranch;
|
||||
|
||||
EQ = Vt_gen + (Sys.Ra+1i*Sys.Xq).*It_gen;
|
||||
dta = angle(EQ); % rotor angle, angle of Eq, not angle of E''
|
||||
omg = zeros(length(Sys.GenIdx),1); % rotor speed
|
||||
|
||||
% next step, because the past calculation starts from Vt It, which are grid reference based
|
||||
% thus the E' E'' are also grid state, we need to change it to d,q state
|
||||
% from grid to d,q, multiply exp(-j(delta-pi/2))
|
||||
Vt_gen = Vt_gen.*exp(1i*(pi/2-dta)); % d-q based
|
||||
It_gen = It_gen.*exp(1i*(pi/2-dta));
|
||||
Id = real(It_gen);
|
||||
Iq = imag(It_gen);
|
||||
|
||||
% Ed''= real(E''), Eq''=imag(E'')
|
||||
Ep = Vt_gen + Sys.Ra.*It_gen -Sys.Xqp.*Iq+1i*Sys.Xdp.*Id; % d-q based
|
||||
Edp = real(Ep); % real of E' , d-q based
|
||||
Eqp = imag(Ep); % imag of E' , d-q based
|
||||
Epp = Vt_gen + Sys.Ra.*It_gen -Sys.Xqpp.*Iq+1i*Sys.Xdpp.*Id; % d-q based
|
||||
Edpp = real(Epp); % real of E''
|
||||
Eqpp = imag(Epp); % imag of E''
|
||||
|
||||
Pe = real(GenPQ) + (abs(It_gen).^2).*Sys.Ra; % electrical power
|
||||
Pm = Pe + Sys.D.*omg./Sys.w0; % mechanical power
|
||||
|
||||
% exciter field voltage from 6th-order equation, derivative=0
|
||||
Efd = (Sys.Xd-Sys.Xdpp)./(Sys.Xdp-Sys.Xdpp).*Eqp - (Sys.Xd-Sys.Xdp)./(Sys.Xdp-Sys.Xdpp).*Eqpp;
|
||||
efd = Efd.*Sys.Rfd./Sys.Lad; % transfer to efd
|
||||
% set Vref for exciter equation
|
||||
% from transfer equation, steady state Vref-Et-V1=0
|
||||
Sys.Vref = abs(Epp)+ abs(Efd)./Sys.Ek; % abs(Vt_gen) changed to abs(Epp)
|
||||
V1 = abs(Efd)./Sys.Ek; % V1 is a mid-term in exciter
|
||||
% from transfer equation,steady state Pref=P1*Gr; P1=P2; Pm=P2;
|
||||
Sys.Pref = Pm.*Sys.Gr;
|
||||
P1 = Pm;
|
||||
P2 = Pm;
|
||||
@ -0,0 +1,375 @@
|
||||
function [t,x,y,hh,KK,bx,by,bz] = multiwindow(daeModelEquations,simu_T,x0,GLO,method,solverOptions,bx0)
|
||||
format long
|
||||
% multiwindow performs general multi-stage numerical integration. It
|
||||
% applies to RK4, DT or other use-specified numerical solvers
|
||||
%
|
||||
% Inputs
|
||||
% daeModelEquations the struct for equations related to a DAE model
|
||||
% simu_T the simulation window: start, step length, end
|
||||
% x0 initial values of the DAE
|
||||
% GLO parameters in the DAE model
|
||||
% method solution method
|
||||
% solverOptions settings and parameters of the solution method
|
||||
% Outputs
|
||||
% t vector of time steps in the whole simulation
|
||||
% x trajectory of state variables
|
||||
% y trajectory of algebraic variables
|
||||
% hh the time step used in each simulation step
|
||||
% KK the order used in each simulation step
|
||||
%
|
||||
% See also Parareal, rk4, DT, getDAEModelEquations, getDAESolver
|
||||
|
||||
f = daeModelEquations.fun_DAE;
|
||||
fun_idx = daeModelEquations.fun_idx;
|
||||
|
||||
%%
|
||||
K = solverOptions.K;
|
||||
% FS1_VS0 = solverOptions.FS1_VS0;
|
||||
% FO1_VO0 = solverOptions.FO1_VO0;
|
||||
hmax = solverOptions.hmax;
|
||||
hmin = solverOptions.hmin;
|
||||
Kmax = solverOptions.Kmax;
|
||||
Kmin = solverOptions.Kmin;
|
||||
% eps1 = solverOptions.eps1;
|
||||
% eps2 = solverOptions.eps2;
|
||||
% eps3 = solverOptions.eps3;
|
||||
% eps4 = solverOptions.eps4;
|
||||
tol = solverOptions.RBtol;
|
||||
% q1 = solverOptions.q1;
|
||||
% q2 = solverOptions.q2;
|
||||
% dK = solverOptions.dK;
|
||||
%%
|
||||
a = simu_T(1); % start time of simulation
|
||||
b = simu_T(2); % end time of simulation
|
||||
h = simu_T(3); % time step length
|
||||
|
||||
%% Judge if x0 is column vector or not. If rox vector, convert to column vector.
|
||||
m = size(x0,1); % number of rows
|
||||
if m == 1
|
||||
x0 = x0';
|
||||
m =size(x0,1);
|
||||
end
|
||||
bm = size(bx0,1); % number of rows
|
||||
if bm == 1
|
||||
bx0 = bx0';
|
||||
end
|
||||
%%
|
||||
fun_y = str2func(strcat(func2str(f),'_AE'));
|
||||
idx = fun_idx(GLO);
|
||||
y0 = fun_y(x0,idx,GLO);
|
||||
by0 = fun_y(bx0,idx,GLO);
|
||||
%% Initial values of t and x
|
||||
% mite = ceil((b-a)./hmin);
|
||||
mite = 20000;
|
||||
bt = zeros(1,mite);
|
||||
bx = zeros(m,mite);
|
||||
by = zeros(size(y0,1),mite);
|
||||
t = zeros(1,mite);
|
||||
x = zeros(m,mite);
|
||||
y = zeros(size(y0,1),mite);
|
||||
hh = zeros(1,mite);
|
||||
KK = zeros(1,mite);
|
||||
t(1) = a;
|
||||
x(:,1) = x0; %initial conditions
|
||||
bt(:,1) = a;
|
||||
bx(:,1) = bx0;
|
||||
|
||||
y(:,1) = y0;
|
||||
by(:,1) = by0;
|
||||
hh(:,1)= h;
|
||||
KK(:,1)= K;
|
||||
|
||||
%% Implement the integration method
|
||||
ratio_b4= nan;
|
||||
theta_max=2;
|
||||
|
||||
|
||||
|
||||
ite = 1 ;
|
||||
|
||||
% K = -(1/2)*log(tol);
|
||||
M = 1;
|
||||
fac1= 0.98;
|
||||
fac2 = 1;
|
||||
|
||||
% fac1 = 0;
|
||||
% fac2 = 0;
|
||||
%
|
||||
|
||||
p= 1 ;
|
||||
pf1 = 2*GLO.machine;
|
||||
pf2 = 2*GLO.machine+4*GLO.machine*GLO.machine+idx.Nx*(idx.Nx+idx.Ny)+(idx.Nx);
|
||||
pf3 = (idx.Nx);
|
||||
% pf1 = 17*GLO.machine/2;
|
||||
% pf2 = 27*GLO.machine/2+4*GLO.machine*GLO.machine+idx.Nx*(idx.Nx+idx.Ny)+(idx.Nx);
|
||||
% pf2 = 0;
|
||||
% pf3 = 0;
|
||||
while t(ite)+h <= b
|
||||
|
||||
switch solverOptions.solver
|
||||
case 'DT'
|
||||
|
||||
[t_new,x_new,y_new, LTE,LTE2,LTE3] = method(t(ite),x(:,ite),f,GLO,h,K);
|
||||
ratio = LTE/h;
|
||||
K_I = 0.3/K;
|
||||
K_p = 0.4/K;
|
||||
if isnan(ratio_b4)
|
||||
else
|
||||
theta = ((tol/ratio)^(K_I))*((ratio_b4/ratio)^(K_p));
|
||||
|
||||
if mod(ite,M)==0
|
||||
% Lin = ((K+p)/(K))
|
||||
% Lin = ((K+p)^2/(K)^2)
|
||||
Lin = (pf1*(K+p)^2+pf2*(K+p)+pf3)/(pf1*(K)^2+pf2*(K)+pf3);
|
||||
% Lde = ((K-p)/(K))
|
||||
% Lde = ((K-p)^2/(K)^2)
|
||||
Lde = (pf1*(K-p)^2+pf2*(K-p)+pf3)/(pf1*(K)^2+pf2*(K)+pf3);
|
||||
|
||||
% trc_in =(LTE2);
|
||||
% trc_de= (LTE3);
|
||||
|
||||
trc_in =(LTE2)/(1-LTE2^((K+p)));
|
||||
trc_de= (LTE3)/(1-LTE3^((K-p)));
|
||||
|
||||
tol_in = tol;
|
||||
tol_de = tol;
|
||||
|
||||
theta_in =1*(h*tol_in/trc_in)^(1/(K+p));
|
||||
theta_de =1*(h*tol_de/trc_de)^(1/(K-p));
|
||||
|
||||
%
|
||||
% theta_in =1*(tol_in/trc_in)^(1/(K+p));
|
||||
% theta_de =1*(tol_de/trc_de)^(1/(K-p));
|
||||
|
||||
% %
|
||||
% % theta_in =0.9*(h*tol/trc_in)^(1/(K+p));
|
||||
% % theta_de =0.9*(h*tol/trc_de)^(1/(K-p));
|
||||
|
||||
if theta> theta_max
|
||||
h_can = theta_max*h;
|
||||
else
|
||||
h_can = theta*h;
|
||||
end
|
||||
|
||||
|
||||
if h_can > hmax
|
||||
h_can = hmax;
|
||||
|
||||
elseif h < hmin
|
||||
h_can = hmin;
|
||||
|
||||
end
|
||||
|
||||
if theta_in> theta_max
|
||||
theta_in = theta_max;
|
||||
end
|
||||
if theta_de> theta_max
|
||||
theta_de = theta_max;
|
||||
end
|
||||
|
||||
|
||||
|
||||
if h*theta_in > hmax
|
||||
h_inp = hmax;
|
||||
|
||||
elseif h*theta_in < hmin
|
||||
h_inp = hmin;
|
||||
else
|
||||
|
||||
h_inp = h*theta_in;
|
||||
end
|
||||
|
||||
|
||||
if h*theta_de > hmax
|
||||
h_dep = hmax;
|
||||
|
||||
elseif h*theta_de < hmin
|
||||
h_dep = hmin;
|
||||
else
|
||||
h_dep = h*theta_de;
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% if min(hh(end-1:-1:end-M))>= h*theta&&Lin <fac1*(h_inp./h)
|
||||
%
|
||||
% K=K+p;
|
||||
% theta =theta_in
|
||||
% elseif Lde<fac2*(h_dep./h) &&max(hh(end-1:-1:end-M))<= h*theta
|
||||
% K=K-p;
|
||||
% theta =theta_de
|
||||
%
|
||||
% end
|
||||
|
||||
% if (min(hh(end:-1:end-M+1))>= h_can||KK(end-1)<K)&&Lin <fac1*(h_inp./h_can)
|
||||
%
|
||||
% K=K+p;
|
||||
% theta =theta_in
|
||||
% elseif Lde<fac2*(h_dep./h_can) &&(max(hh(end:-1:end-M+1))<= h_can||KK(end-1)>K)
|
||||
% K=K-p;
|
||||
% theta =theta_de
|
||||
%
|
||||
% end
|
||||
|
||||
|
||||
if (Lde<fac2*(h_dep./h_can) &&(h<= h_can||(h==hmin&&KK(1,ite+1)>=K)))&&((h>= h_can||(h==hmax&&KK(1,ite+1)<=K))&&Lin <fac1*(h_inp./h_can))
|
||||
% check which one is better
|
||||
cri1 = h_inp/(pf1*(K+p)^2+pf2*(K+p)+pf3);
|
||||
cri2 = h_can/(pf1*K^2+pf2*K+pf3);
|
||||
cri3 = h_dep/(pf1*(K-p)^2+pf2*(K-p)+pf3);
|
||||
od_stratg=[cri1 cri2 cri3;
|
||||
K+p K K-p
|
||||
theta_in theta theta_de
|
||||
tol_in tol tol_de];
|
||||
[~,opi] = max(od_stratg(1,:));
|
||||
K = od_stratg(2,opi);
|
||||
theta = od_stratg(3,opi);
|
||||
tol = od_stratg(4,opi);
|
||||
elseif Lde<fac2*(h_dep./h_can) &&(h<= h_can||(h_can==hmin&&KK(1,ite+1)>=K))
|
||||
K=K-p;
|
||||
theta =theta_de;
|
||||
tol = tol_de;
|
||||
|
||||
elseif (h>= h_can||(h_can==hmax&&KK(1,ite+1)<=K))&&Lin <fac1*(h_inp./h_can)
|
||||
|
||||
K=K+p;
|
||||
theta =theta_in;
|
||||
tol = tol_in;
|
||||
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% if Lin <fac1*(h_inp./h)
|
||||
%
|
||||
% K=K+p;
|
||||
% theta =theta_in
|
||||
% tol = tol_in;
|
||||
% elseif Lde<fac2*(h_dep./h)
|
||||
% K=K-p;
|
||||
% theta =theta_de
|
||||
% tol = tol_de;
|
||||
%
|
||||
% end
|
||||
|
||||
|
||||
end
|
||||
|
||||
if theta> theta_max
|
||||
h = theta_max*h;
|
||||
else
|
||||
h = theta*h;
|
||||
end
|
||||
|
||||
|
||||
end
|
||||
ratio_b4 = ratio;
|
||||
|
||||
|
||||
|
||||
case 'RK4'
|
||||
[t_new,x_new,y_new] = method(t(ite),x(:,ite),f,GLO,h,K);
|
||||
|
||||
end
|
||||
|
||||
|
||||
|
||||
% bhx = bx(:,ite);
|
||||
% for bht =t(ite):0.00031: t_new(end)
|
||||
% if t_new(end)-bht>=0.00031
|
||||
% [bht_new,bhx_new,bhy_new] = rk4(bht,bhx,f,GLO,0.00031,8);
|
||||
% bhx = bhx_new(:,end);
|
||||
% else
|
||||
% [bht_new,bhx_new,bhy_new] = rk4(bht,bhx,f,GLO,t_new(end)-bht,8);
|
||||
% break
|
||||
% % bht = t_new(end);
|
||||
% end
|
||||
% end
|
||||
|
||||
if ite+1 > mite
|
||||
mite = mite + 20000;
|
||||
% bt(:,mite) = 0;
|
||||
% bx(:,mite) = 0;
|
||||
% by(:,mite) = 0;
|
||||
t(:,mite) = 0;
|
||||
x(:,mite) = 0;
|
||||
y(:,mite) = 0;
|
||||
hh(:,mite) = 0;
|
||||
KK(:,mite) = 0;
|
||||
end
|
||||
|
||||
|
||||
|
||||
if h > hmax
|
||||
h = hmax;
|
||||
|
||||
elseif h < hmin
|
||||
h = hmin;
|
||||
|
||||
end
|
||||
|
||||
if K > Kmax; K = Kmax; end
|
||||
if K < Kmin; K = Kmin; end
|
||||
% bt(:,ite+1) = bht_new(end);
|
||||
% bx(:,ite+1) = bhx_new(:,end);
|
||||
% by(:,ite+1) = bhy_new(:,end);
|
||||
t(:,ite+1) = t_new;
|
||||
x(:,ite+1) = x_new;
|
||||
y(:,ite+1) = y_new;
|
||||
hh(:,ite+1) = h;
|
||||
KK(:,ite+1) = K;
|
||||
|
||||
% r = tol^(1/(1+K));
|
||||
|
||||
% theta =(tol*h/r_norm)^(1/K);
|
||||
|
||||
|
||||
% K;
|
||||
ite = ite+1;
|
||||
|
||||
% if FS1_VS0 == 0
|
||||
% if LTE < eps1; h = h*q1; end
|
||||
% if LTE > eps2; h = h*q2; end
|
||||
% if h > hmax; h = hmax; end
|
||||
% if h < hmin; h = hmin; end
|
||||
% end
|
||||
%
|
||||
% if FO1_VO0 == 0
|
||||
% if LTE < eps3
|
||||
% K = K-dK;
|
||||
% end
|
||||
% if LTE > eps4
|
||||
% K = K+dK;
|
||||
% end
|
||||
% if K > Kmax; K = Kmax; end
|
||||
% if K < Kmin; K = Kmin; end
|
||||
% end
|
||||
if b-t(ite)<h&&b-t(ite)>0
|
||||
h = b-t(ite);
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
%% transpose: use .' to avoid conjugate transpose in case some variables are complex
|
||||
t = t(:,1:ite).';
|
||||
x = x(:,1:ite).';
|
||||
y = y(:,1:ite).';
|
||||
hh = hh(:,1:ite).';
|
||||
KK = KK(:,1:ite).';
|
||||
% bx = bx(:,1:ite).';
|
||||
% by = by(:,1:ite).';
|
||||
% bz =max(abs(x-bx),[],2);
|
||||
bx = x;
|
||||
by = y;
|
||||
bz =max(abs(x-bx),[],2);
|
||||
% bz =max((x-bx)./(max(bx+10^(-19),[],1)),[],2);
|
||||
end
|
||||
@ -0,0 +1,39 @@
|
||||
function Sys = myFunction(mpc)
|
||||
|
||||
%% Generator parameters
|
||||
Sys.H = [6.5 6.5 6.175 6.175]'*9; % base of 900 MW to base 100 MW
|
||||
Sys.Xl = [0.2 0.2 0.2 0.2]'/9;
|
||||
Sys.Xd = [1.8 1.8 1.8 1.8]'/9;
|
||||
Sys.Xq = [1.7 1.7 1.7 1.7]'/9;
|
||||
Sys.Xdp = [0.3 0.3 0.3 0.3]'/9;
|
||||
Sys.Xqp = [0.55 0.55 0.55 0.55]'/9;
|
||||
Sys.Xdpp = [0.25 0.25 0.25 0.25]'/9;
|
||||
Sys.Xqpp = [0.25 0.25 0.25 0.25]'/9;
|
||||
Sys.Ra = [0.0025 0.0025 0.0025 0.0025]'/9;
|
||||
Sys.D = [45 45 45 45]'; % 0 on Kunder book
|
||||
Sys.Td0p = [8 8 8 8]';
|
||||
Sys.Tq0p = [0.4 0.4 0.4 0.4]';
|
||||
Sys.Td0pp= [0.03 0.03 0.03 0.03]';
|
||||
Sys.Tq0pp= [0.05 0.05 0.05 0.05]';
|
||||
|
||||
% add by myself
|
||||
Sys.L0 = Sys.Xl*2; % L0 in VBR synchronous generator model
|
||||
Sys.T_vt= 0.05; % time constant for terminal voltage measurement
|
||||
|
||||
%% transfer generator parameters EMT model parameters
|
||||
% Paremeter_transform % provide parameters for VBR generator model
|
||||
|
||||
%% contollers
|
||||
% exciter
|
||||
Sys.Eta=1; Sys.Etb=10; Sys.Ek=100; Sys.Ete=0.1; Sys.Emax=3; Sys.Emin=0;
|
||||
% TGov
|
||||
Sys.Gr= 0.33; Sys.Gt1=2; Sys.Gt2=3; Sys.Gt3=15; Sys.Gdt=0.4; Sys.GVmax=10; Sys.GVmin=0;
|
||||
|
||||
%% Index
|
||||
Sys.w0 = 1.0; % nominal frequency, p.u. useful in swing equation
|
||||
Sys.GenIdx = [1 2 3 4];
|
||||
Sys.NonGenIdx = [5 6 7 8 9 10 11];
|
||||
Sys.LoadIdx = [7 9];
|
||||
Sys.ShuntIdx = [7 9];
|
||||
Sys.bus_number = mpc.bus(end,1); % total number of buses
|
||||
|
||||
@ -0,0 +1,216 @@
|
||||
close all
|
||||
|
||||
% t_final = [t_pre; t_on(2:end); t_post(2:end)];
|
||||
% sol_final = [x_pre; x_on(2:end,:); x_post(2:end,:)];
|
||||
% % t_final = [t_pre; t_on(2:end)];
|
||||
% % sol_final = [x_pre; x_on(2:end,:)];
|
||||
% % t_final = [t_pre];
|
||||
% % sol_final = [x_pre];
|
||||
|
||||
%% relative rotor angles
|
||||
figure(1)
|
||||
% EMT result
|
||||
plot(t_final, (sol_final(:,1)-sol_final(:,1) )*180/pi,'r--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, (sol_final(:,2)-sol_final(:,1) )*180/pi,'g--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, (sol_final(:,3)-sol_final(:,1) )*180/pi,'b--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, (sol_final(:,4)-sol_final(:,1) )*180/pi,'b--','LineWidth',3)
|
||||
hold on
|
||||
% ylim([-60,10])
|
||||
xlabel('Time (s)')
|
||||
ylabel('Relative rotor angles (degree)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Relative rotor angles')
|
||||
legend('EMT G1','EMT G2','EMT G3','EMT G4')
|
||||
|
||||
%% frequency deviation
|
||||
figure(2)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,9),'r--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,10),'g--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,11),'b--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,12),'m--','LineWidth',3)
|
||||
hold on
|
||||
% ylim([-60,10])
|
||||
% xlim([0,0.25])
|
||||
xlabel('Time (s)')
|
||||
ylabel('Frequency deviation (p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Frequency deviation')
|
||||
legend('EMT G1','EMT G2','EMT G3','EMT G4')
|
||||
|
||||
%% Exciter field voltage
|
||||
figure(3)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,33),'r--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,34),'g--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,35),'b--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,36),'m--','LineWidth',3)
|
||||
xlabel('Time (s)')
|
||||
xlim([0,0.4])
|
||||
ylabel('Exciter field voltage (p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Exciter field voltage')
|
||||
legend('EMT G1','EMT G2','EMT G3','EMT G4')
|
||||
|
||||
%% P1
|
||||
figure(4)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,37),'r--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,38),'g--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,39),'b--','LineWidth',3)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,40),'m--','LineWidth',3)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('P1(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('P1')
|
||||
legend('EMT G1','EMT G2','EMT G3','EMT G4')
|
||||
|
||||
%% Voltage at bus 7
|
||||
figure(5)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,51),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,52),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,53),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Voltage at bus 7(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Voltage at bus 7')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% Voltage at bus 8
|
||||
figure(6)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,54),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,55),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,56),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Voltage at bus 8(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Voltage at bus 8')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% Voltage at bus 10
|
||||
figure(7)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,60),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,61),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,62),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Voltage at bus 10(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Voltage at bus 10')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% Voltage at bus 6
|
||||
figure(8)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,48),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,49),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,50),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Voltage at bus 6(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Voltage at bus 6')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% current on branch 5-6
|
||||
figure(9)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,78),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,79),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,80),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Current on branch 5-6(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Current on branch 5-6')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% current on branch 6-7
|
||||
figure(10)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,81),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,82),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,83),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Current on branch 6-7(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Current on branch 6-7')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% current on branch 7-8
|
||||
figure(11)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,84),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,85),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,86),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Current on branch 7-8(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Current on branch 7-8')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% current on branch 9-10
|
||||
figure(12)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,96),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,97),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,98),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Current on branch 9-10(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Current on branch 9-10')
|
||||
legend('EMT phase A','EMT phase B','EMT phase C')
|
||||
|
||||
%% Voltage at bus 6
|
||||
figure(13)
|
||||
% EMT result
|
||||
plot(t_final, sol_final(:,108),'r','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,109),'g','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,110),'b','LineWidth',1)
|
||||
hold on
|
||||
plot(t_final, sol_final(:,111),'b','LineWidth',1)
|
||||
|
||||
xlabel('Time (s)')
|
||||
ylabel('Voltage at bus 6(p.u.)')
|
||||
set(gca, 'Fontname', 'Times New Roman', 'Fontsize', 12);
|
||||
title('Voltage at bus 6')
|
||||
legend('Gen1','Gen2','Gen3','Gen4')
|
||||
@ -0,0 +1,9 @@
|
||||
function [R_line_positive, wL_line_positive, B_line_positive, int_t, LC_fre, t_base] = setDefaultParameters()
|
||||
|
||||
R_line_positive = 0.0001;
|
||||
wL_line_positive = 0.001;
|
||||
B_line_positive = 0.00175;
|
||||
int_t = 0; % could change to any number
|
||||
LC_fre = 120*pi; % divide all L by w, consider time base is 1/120/pi
|
||||
t_base =1/(120*pi);
|
||||
end
|
||||
@ -0,0 +1,4 @@
|
||||
function [orderOfDT, timeStepOfDT] = setSASParameters()
|
||||
orderOfDT=10;
|
||||
timeStepOfDT=179*10^(-6);
|
||||
end
|
||||
@ -0,0 +1,15 @@
|
||||
function [Base, w, FtBus, time_step, time_step_on, TimeRange1, FtTime, TotalTime, TimeRange2, TimeRange3] = set_simulation_parameters()
|
||||
% This function sets the simulation parameters.
|
||||
|
||||
%% settings
|
||||
Base = 100; % baseMVA
|
||||
w = 120*pi;
|
||||
FtBus = 7; % grounding fault bus
|
||||
time_step = 1*10^(-6); % pre and post fault
|
||||
% time_step_on = 2*10^(-8); % during fault
|
||||
time_step_on = 1*10^(-6); % during fault
|
||||
TimeRange1 = [0,0.1]; % pre-fault simulation time (second)
|
||||
FtTime = 5/60; % Fault lasting time (second) (5/60 is five cycles)
|
||||
TotalTime = 0.5; %1; % Total simulation time (second)
|
||||
TimeRange2 = [TimeRange1(2),TimeRange1(2)+FtTime]; % fault-on simulation period
|
||||
TimeRange3 = [TimeRange2(2),TotalTime]; % post-fault simulation time
|
||||
@ -0,0 +1,25 @@
|
||||
function [R_line, L_line, C_line] = tline_to_matrix(R_line_positive, wL_line_positive, B_line_positive, LC_fre)
|
||||
% Unit is per unit per km, pu/km
|
||||
% Assume all the lines have the same per unit parameters
|
||||
|
||||
R_line_zero = R_line_positive*6; % from PSCAD line parameters, we can generally get this relationship
|
||||
wL_line_zero = wL_line_positive*3;
|
||||
L_line_positive = wL_line_positive/(LC_fre);
|
||||
L_line_zero = wL_line_zero/(LC_fre);
|
||||
B_line_zero = B_line_positive/1.5;
|
||||
C_line_positive = 0.5*B_line_positive/(LC_fre); % multiply 0.5 because it is divided in to two parts
|
||||
C_line_zero = 0.5*B_line_zero/(LC_fre);
|
||||
|
||||
% three phase self and mutual parameters
|
||||
% Z_zero=Zs+2Zm, Z_positive=Zs-Zm
|
||||
% so we get: Z_self=1/3*(Z_zero+2*Z_positive), Z_mutual=1/3*(Z_zero-Z_positive)
|
||||
Rs_line=1/3*(R_line_zero+2*R_line_positive); Rm_line=1/3*(R_line_zero-R_line_positive);
|
||||
Ls_line=1/3*(L_line_zero+2*L_line_positive); Lm_line=1/3*(L_line_zero-L_line_positive);
|
||||
Cs_line=1/3*(C_line_zero+2*C_line_positive); Cm_line=1/3*(C_line_zero-C_line_positive);
|
||||
|
||||
% R L C three phase matrix
|
||||
R_line=[Rs_line, Rm_line, Rm_line; Rm_line, Rs_line, Rm_line; Rm_line, Rm_line, Rs_line];
|
||||
L_line=[Ls_line, Lm_line, Lm_line; Lm_line, Ls_line, Lm_line; Lm_line, Lm_line, Ls_line];
|
||||
C_line=[Cs_line, Cm_line, Cm_line; Cm_line, Cs_line, Cm_line; Cm_line, Cm_line, Cs_line];
|
||||
|
||||
end
|
||||
@ -0,0 +1,30 @@
|
||||
function [Sys,Laa0_pp,Lab0_pp,Laa2_pp] = transformParameters(Sys,t_base)
|
||||
|
||||
Sys.Lad=Sys.Xd-Sys.Xl;
|
||||
Sys.Lfd=1./(1./(Sys.Xdp-Sys.Xl)-1./Sys.Lad);
|
||||
Sys.Rfd=(Sys.Lad+Sys.Lfd)./(Sys.Td0p./t_base);
|
||||
Sys.L1d=1./(1./(Sys.Xdpp-Sys.Xl)-1./Sys.Lfd-1./Sys.Lad);
|
||||
Sys.R1d=(1./(1./Sys.Lad+1./Sys.Lfd)+Sys.L1d)./(Sys.Td0pp./t_base);
|
||||
|
||||
Sys.Laq=Sys.Xq-Sys.Xl;
|
||||
Sys.L1q=1./(1./(Sys.Xqp-Sys.Xl)-1./Sys.Laq);
|
||||
Sys.R1q=(Sys.Laq+Sys.L1q)./(Sys.Tq0p./t_base);
|
||||
Sys.L2q=1./(1./(Sys.Xqpp-Sys.Xl)-1./Sys.L1q-1./Sys.Laq);
|
||||
Sys.R2q=(1./(1./Sys.Laq+1./Sys.L1q)+Sys.L2q)./(Sys.Tq0pp./t_base);
|
||||
|
||||
Sys.Lad_pp=Sys.Xdpp-Sys.Xl;
|
||||
Sys.Laq_pp=Sys.Xdpp-Sys.Xl;
|
||||
|
||||
Laa0_pp= Sys.Xl+( Sys.Lad_pp+ Sys.Laq_pp+Sys.L0-Sys.Xl )/3;
|
||||
Lab0_pp= ( 2*Sys.L0-2*Sys.Xl-Sys.Lad_pp-Sys.Laq_pp )/6;
|
||||
Laa2_pp= ( Sys.Lad_pp-Sys.Laq_pp )/3;
|
||||
|
||||
Sys.Vd_pp_coeff1=-(Sys.Rfd./(Sys.Lfd).^2+Sys.R1d./(Sys.L1d).^2).*(Sys.Lad_pp).^2;
|
||||
Sys.Vd_pp_coeff2=-(Sys.Lad_pp.*Sys.Rfd./(Sys.Lfd).^2.*(1-Sys.Lad_pp./Sys.Lfd) - Sys.Lad_pp.^2.*Sys.R1d./(Sys.L1d).^2./Sys.Lfd);
|
||||
Sys.Vd_pp_coeff3=(Sys.Lad_pp.^2.*Sys.Rfd./(Sys.Lfd).^2./Sys.L1d - Sys.Lad_pp.*Sys.R1d./(Sys.L1d).^2.*(1-Sys.Lad_pp./Sys.L1d));
|
||||
|
||||
Sys.Vq_pp_coeff1=-(Sys.R1q./(Sys.L1q).^2+Sys.R2q./(Sys.L2q).^2).*(Sys.Laq_pp).^2;
|
||||
Sys.Vq_pp_coeff2=-(Sys.Laq_pp.*Sys.R1q./(Sys.L1q).^2.*(1-Sys.Laq_pp./Sys.L1q) - Sys.Laq_pp.^2.*Sys.R2q./(Sys.L2q).^2./Sys.L1q);
|
||||
Sys.Vq_pp_coeff3=(Sys.Laq_pp.^2.*Sys.R1q./(Sys.L1q).^2./Sys.L2q - Sys.Laq_pp.*Sys.R2q./(Sys.L2q).^2.*(1-Sys.Laq_pp./Sys.L2q));
|
||||
|
||||
end
|
||||
@ -0,0 +1,82 @@
|
||||
function mpc = twoarea
|
||||
%2_AREA_PSSE30
|
||||
% April 12, 2016 13:35:48; Simulator Version 19; BuildDate 2016_2_6
|
||||
%
|
||||
% Converted by MATPOWER 6.0 using PSSE2MPC on 08-Apr-2018
|
||||
% from '2-area_psse30.raw' using PSS/E rev 30 format.
|
||||
%
|
||||
% WARNINGS:
|
||||
% Conversion explicitly using PSS/E revision 30
|
||||
% Section label mismatch, found 'VSC DC LINE', expected 'VOLTAGE SOURCE CONVERTER'
|
||||
% Section label mismatch, found 'IMPEDANCE CORRECTION TABLE', expected 'IMPEDANCE CORRECTION'
|
||||
% Skipped 1 line of zone data.
|
||||
% Skipped 1 line of owner data.
|
||||
% Section label mismatch, found 'FACTS', expected 'FACTS CONTROL DEVICE'
|
||||
% Using default voltage magnitude limits: VMIN = 0.9 p.u., VMAX = 1.1 p.u.
|
||||
%
|
||||
% See CASEFORMAT for details on the MATPOWER case file format.
|
||||
|
||||
%% MATPOWER Case Format : Version 2
|
||||
mpc.version = '2';
|
||||
|
||||
%%----- Power Flow Data -----%%
|
||||
%% system MVA base
|
||||
mpc.baseMVA = 100;
|
||||
|
||||
%% bus data
|
||||
% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin
|
||||
mpc.bus = [
|
||||
1 3 0 0 0 0 1 1.03 20.07 20 1 1.1 0.9;
|
||||
2 2 0 0 0 0 1 1.01 10.30 20 1 1.1 0.9;
|
||||
3 2 0 0 0 0 1 1.03 -7.0145 20 1 1.1 0.9;
|
||||
4 2 0 0 0 0 1 1.01 -17.20 20 1 1.1 0.9;
|
||||
5 1 0 0 0 0 1 1.00645 13.6071 230 1 1.1 0.9;
|
||||
6 1 0 0 0 0 1 0.97812 3.5208 230 1 1.1 0.9;
|
||||
7 1 967 100 0 200 1 0.9610 -4.889 230 1 1.1 0.9;
|
||||
8 1 0 0 0 0 1 0.9486 -18.76 230 1 1.1 0.9;
|
||||
9 1 1767 100 0 350 1 0.9714 -32.364 230 1 1.1 0.9;
|
||||
10 1 0 0 0 0 1 0.9835 -23.949 230 1 1.1 0.9;
|
||||
11 1 0 0 0 0 1 1.0083 -13.6407 230 1 1.1 0.9;
|
||||
];
|
||||
|
||||
|
||||
%% generator data
|
||||
% bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf mu_Pmax mu_Pmin mu_Qmax mu_Qmin
|
||||
mpc.gen = [
|
||||
1 700.10 185 300 -300 1.03 900 1 9999 -9999 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000;
|
||||
2 700 234.67 300 -300 1.01 900 1 9999 -9999 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000;
|
||||
3 719 176 300 -300 1.03 900 1 9999 -9999 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000;
|
||||
4 700 202.07 300 -300 1.01 900 1 9999 -9999 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000;
|
||||
];
|
||||
|
||||
%% branch data
|
||||
% fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax
|
||||
mpc.branch = [
|
||||
1 5 0 0.15/9 0 0 0 0 0 0 1 -360 360; % transformer. based given in Kunder's book is 900
|
||||
2 6 0 0.15/9 0 0 0 0 0 0 1 -360 360; % So, using a base of 100, we need to
|
||||
3 11 0 0.15/9 0 0 0 0 0 0 1 -360 360;
|
||||
4 10 0 0.15/9 0 0 0 0 0 0 1 -360 360;
|
||||
5 6 0.0025 0.025 0.04375 0 0 0 0 0 1 -360 360;
|
||||
6 7 0.0010 0.010 0.01750 0 0 0 0 0 1 -360 360;
|
||||
7 8 0.0110 0.110 0.19250 0 0 0 0 0 1 -360 360;
|
||||
7 8 0.0110 0.110 0.19250 0 0 0 0 0 1 -360 360;
|
||||
8 9 0.0110 0.110 0.19250 0 0 0 0 0 1 -360 360;
|
||||
8 9 0.0110 0.110 0.19250 0 0 0 0 0 1 -360 360;
|
||||
9 10 0.0010 0.010 0.01750 0 0 0 0 0 1 -360 360;
|
||||
10 11 0.0025 0.025 0.04375 0 0 0 0 0 1 -360 360;
|
||||
];
|
||||
|
||||
%% bus names
|
||||
mpc.bus_name = {
|
||||
'GEN BUS1 ';
|
||||
'GEN BUS2 ';
|
||||
'GEN BUS3 ';
|
||||
'GEN BUS4 ';
|
||||
'STA B230 ';
|
||||
'STA C230 ';
|
||||
'STA 2 7 ';
|
||||
'STA A230 ';
|
||||
'STA 3 9 ';
|
||||
'STA 3 10 ';
|
||||
'STA 3 11 ';
|
||||
};
|
||||
@ -0,0 +1,13 @@
|
||||
function Sys = update_system_parameters(Sys, Laa0_pp, Lab0_pp)
|
||||
% This function updates the system parameters including Emax, Emin, Gen_R and Lline_3Phase.
|
||||
|
||||
Sys.Emax=Sys.Emax.*Sys.Rfd./Sys.Lad;
|
||||
Sys.Emin=Sys.Emin.*Sys.Rfd./Sys.Lad;
|
||||
|
||||
for k=1:1:length(Sys.GenIdx)
|
||||
Sys.Gen_R(:,:,k)= [Sys.Ra(k), 0, 0; 0, Sys.Ra(k), 0; 0, 0, Sys.Ra(k)];
|
||||
L_stator(:,:,k)= [Laa0_pp(k) Lab0_pp(k) Lab0_pp(k); Lab0_pp(k) Laa0_pp(k) Lab0_pp(k); Lab0_pp(k) Lab0_pp(k) Laa0_pp(k)]/120/pi;
|
||||
% because Sys.Laa0_pp is already updated
|
||||
Sys.Lline_3Phase(:,:,k) = Sys.Lline_3Phase(:,:,k)+ L_stator(:,:,k);
|
||||
end
|
||||
|
||||
@ -0,0 +1,10 @@
|
||||
|
||||
clc; clear; close;
|
||||
addpath('EMT')
|
||||
|
||||
testSystem = 'twoarea';
|
||||
|
||||
[t_final, sol_final] = calEMT(testSystem);
|
||||
|
||||
plotEMTResults();
|
||||
|
||||
Loading…
Reference in new issue