spcomp_nr_nrs.m

电力系统电压稳定研究的图形化软件

%ttt2=lambda_sp;
%ttt3=aa(:,index(I));

%ttt2=lambda_sp;
%v(sub_strt:fn)=v_load;
%lambda_sp=ttt1;

  
 %===============================================================================
 
 % Locate singular point of algebraic equations (Newton-Raphson-Seydel Algorithm)
 %================================================================================


deltalambda_sp=-lambda_sp/(NRS_Steps);	%step-size while controlling the smallest eigenvalue of Dyg
for k=1:NRS_Steps+(0.51)*NRS_Steps
    ConvergenceFlag=0;
    for j=1:round(MaxIterations/ReportCycle),
       t0=clock;
        for i=1:ReportCycle,
           x_sub0=x(sub_strt:fn);
           alpha_sp0=alpha_sp;
           v0=v(sub_strt:fn);
           [f,J]=eval([CurrentSystem,'(data,x,[0;param],v)']);
           J=full(J);

           %the following is based on new parameterization,08/18/00
             JJ_sp=[   J(sub_strt+1:fn+1,sub_strt:fn)  zeros(2*no_pq,2*no_pq)                                 (J(sub_strt+1:fn+1,1:mm))*(x_inter)
                J(sub_strt+1:fn+1,fn+sub_strt:2*fn)  J(sub_strt+1:fn+1,sub_strt:fn)-lambda_sp*eye(2*no_pq)  J(sub_strt+1:fn+1,fn+1:fn+mm)*(x_inter)
                zeros(1,2*no_pq)                   (v(sub_strt:fn))'/norm(v(sub_strt:fn))                                   0
               ];

            ff_sp=[f(sub_strt+1:fn+1)
                (J(sub_strt+1:fn+1,sub_strt:fn)-lambda_sp*eye(2*no_pq))*v(sub_strt:fn)
                norm(v(sub_strt:fn))-1
               ];
                 
               delta_sp=-sparse(JJ_sp)\ff_sp;
               
               x(sub_strt:fn)=x_sub0+delta_sp(1:2*no_pq);
               x(no_gen:(no_gen-1)+no_pv+2*no_pq)=x(sub_strt:fn);
               v(sub_strt:fn)=v0+delta_sp(2*no_pq+1:4*no_pq);
                              
               alpha_sp=alpha_sp0+delta_sp(4*no_pq+1);
               
               x(1:mm)=[(1-alpha_sp)*x_up(1:mm)+alpha_sp*x_low(1:mm)];%11/17/00 
               %angle_temp=x(1:mm);
    %for i=1:length(angle_temp)
       %angle_temp(i)=unwrap(angle_temp(i),2*pi);
    %end
    %x(1:mm)=angle_temp;

               
               %x_temp=[(1-alpha_sp)*(x_up.*a)+alpha_sp*(x_low.*a)];  %08/18/00
               
               %x=x.*a1+x_temp;														% 08/18/00
               

              
              
              
         end
  
         % Define the errors in states, eigenvector and paramater
         %===========================================================================================
        AbsError=max([abs(x(sub_strt:fn)-x_sub0);abs(v(sub_strt:fn)-v0);abs(alpha_sp-alpha_sp0)]);
        if (x_sub0==0)&(v0==0)
            RelError='NA';
        else
            RelError=AbsError/max([abs(x_sub0);abs(v0);abs(alpha_sp0)]);
        end

        

        % set LF control control errors
        set(AbsErrorDisp,'String',num2str(AbsError));
        if isstr(RelError)
            set(RelErrorDisp,'String',RelError);
        else
            set(RelErrorDisp,'String',num2str(RelError));
        end

        set(NumIterations,'String',num2str(j*ReportCycle));
        set(IterationTime,'String',num2str(etime(clock,t0)/ReportCycle));

        if (AbsError<=LFAbsTol) ...
            & ((~isstr(RelError)) ...
            & (RelError<=LFRelTol) ...
            | isstr(RelError))
            ConvergenceFlag=1;
            break;
        end
    end

    if ConvergenceFlag==0
        'NRS Failed to Converge'
        break;
    end
    if k==NRS_Steps+1
       Dyg=J(sub_strt+1:fn+1,sub_strt:fn);		% The matrix Dyg at the singular point
       [n_sp,m_sp]=size(AA_sp);							% index
       XX_sing=x;												% singular point
       vpoc_sp=v(sub_strt:fn);							% right eigenvector corresponding to zero eigenvalue of Dyg(x,y)
       mismatch=f(1:no_gen);								% real power mismatch at the singular point
       lamda_smallest=lambda_sp;							% zero eigenvalue of Dyg
       

		wpoc_sp=-null(J(sub_strt+1:fn+1,sub_strt:fn)'); % left eigenvector corresponding to zero eigenvalue of Dyg(x,y)
      if ~exist('Total_mis'),Total_mis=[];end
      Total_mis=[Total_mis mismatch];						% real power mismatches at different singular points
       if ~exist('Total_sing'),Total_sing=[];end
       Total_sing=[Total_sing XX_sing];					% singular points
    end
  
	XX_sp=[XX_sp x];
	AA_sp=[AA_sp alpha_sp];
	PP_sp=[PP_sp param];
	LAMBDA_SP=[LAMBDA_SP lambda_sp];  
   lambda_sp=lambda_sp+deltalambda_sp;
   
   %eig_Dyg=[eig_Dyg eigs(J(sub_strt+1:fn+1,sub_strt:fn),1,'SM',options)]; 
   %ee=eig(J(sub_strt+1:fn+1,sub_strt:fn));		
	%all_eig_Dyg=[all_eig_Dyg ee]; 
   %sign_Dyg=[sign_Dyg sign(det(J(sub_strt+1:fn+1,sub_strt:fn)))];
   %[ind1]=find((imag(ee)==0)&(real(ee)<0));
   %[ind2]=find((imag(ee)==0)&(real(ee)>0));
   %reg_index1=[reg_index1 length(ind1)];			
   %reg_index2=[reg_index2 length(ind2)];
   
   %angle_temp=x(1:mm);
    %for i=1:length(angle_temp)
       %angle_temp(i)=unwrap(angle_temp(i),2*pi);
    %end
    %x(1:mm)=angle_temp;


end
%Back to NR algorithm
[n_rows_sp,n_cols_sp]=size(AA_sp);
delta_alpha_sp=-(AA_sp(n_cols_sp))/(NR_steps);
for k=1:2*NR_steps+1
   
    ConvergenceFlag=0;
    for j=1:round(MaxIterations/ReportCycle),
        t0=clock;
        for i=1:ReportCycle,
            x_sub0=x(sub_strt:fn);
            [f,J]=eval([CurrentSystem,'(data,x,[0;param],v)']);
           J=full(J);
          delta=-J(sub_strt+1:fn+1,sub_strt:fn)\f(sub_strt+1:fn+1);
          x(sub_strt:fn)=x_sub0+delta;
          x(no_gen:(no_gen-1)+no_pv+2*no_pq)=x(sub_strt:fn);			%update load bus variables
          
			end

		 %Error checking
        AbsError=max(abs(x(sub_strt:fn)-x_sub0));
       if x_sub0==0
            RelError='NA';
        else
            RelError=AbsError/max(abs(x_sub0));
        end
          
        %set LF control control errors
        set(AbsErrorDisp,'String',num2str(AbsError));
        if isstr(RelError)
            set(RelErrorDisp,'String',RelError);
        else
            set(RelErrorDisp,'String',num2str(RelError));
        end

        set(NumIterations,'String',num2str(j*ReportCycle));
        set(IterationTime,'String',num2str(etime(clock,t0)/ReportCycle))
        
        % Compare errors with the tolerances
        %=========================================================================
        if (AbsError<=LFAbsTol*0.001) ...
            & ((~ischar(RelError)) ...
            & (RelError<=LFRelTol*0.01) ...
            | ischar(RelError))
            ConvergenceFlag=1;
            break;
        end
    end

if ConvergenceFlag==0
   'NR fails to converge'
   k
        break;
     end
      

    XX_sp=[XX_sp x];																%update XX_sp
    AA_sp=[AA_sp alpha_sp];													%update AA_sp
    PP_sp=[PP_sp param];														%update PP_sp
    alpha_sp=alpha_sp+delta_alpha_sp;
    x(1:mm)=[(1-alpha_sp)*x_up(1:mm)+alpha_sp*x_low(1:mm)];
    
    if alpha_sp >1.01
        return;
     end
  end
  




t2=cputime-t1;		%total simulation time


for i=1:k_temp
   paramx(i)=param(i);
   end
for i=1:no_pq
   ii=k_temp+i;
   jj=k_temp+1+2*(i-1);
   paramx(jj)=param(ii);
   paramx(jj+1)=param(ii+no_pq); 
   end
   param=paramx;