MATLAB: Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.770081e-17. > In NewtonRaphsomneda (line 415) Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 2.287521e-18. > In New

Question

now the matlab give me this message for this code

%%General Program For
clc
tic
clear all
% no type Vol del Pg QG Pl Ql Qmax Qmin
busdata= [1 1 1 0 0 0 0 0 0 0; 2 3 1 0 0 0 0 0 0 0; 3 3 1 0 0 0 0 0 0 0; 4 3 1 0 0 0 0.309 0.191 0 0; 5 3 1 0 0 0 0.488 0.303 0 0; 6 3 1 0 0 0 0 0 0 0; 7 3 1 0 0 0 0.309 0.191 0 0; 8 3 1 0 0 0 0 0 0 0; 9 3 1 0 0 0 0.488 0.303 0 0; 10 3 1 0 0 0 0 0 0 0; 11 3 1 0 0 0 0.488 0.303 0 0; 12 3 1 0 0 0 0 0 0 0; 13 3 1 0 0 0 0 0 0 0; 14 3 1 0 0 0 0.488 0.303 0 0; 15 3 1 0 0 0 0.488 0.303 0 0; 16 3 1 0 0 0 0.488 0.303 0 0; 17 3 1 0 0 0 0 0 0 0; 18 3 1 0 0 0 0.488 0.303 0 0; 19 3 1 0 0 0 0 0 0 0; 20 3 1 0 0 0 0.488 0.303 0 0; 21 3 1 0 0 0 0 0 0 0; 22 3 1 0 0 0 0 0 0 0; 23 3 1 0 0 0 0.488 0.303 0 0; 24 3 1 0 0 0 0.488 0.303 0 0; 25 3 1 0 0 0 0.309 0.191 0 0; 26 3 1 0 0 0 0 0 0 0; 27 3 1 0 0 0 0 0 0 0; 28 3 1 0 0 0 0.309 0.191 0 0; 29 3 1 0 0 0 0 0 0 0; 30 3 1 0 0 0 0 0 0 0; 31 3 1 0 0 0 0.193 0.119 0 0; 32 3 1 0 0 0 0 0 0 0; 33 3 1 0 0 0 0 0 0 0; 34 3 1 0 0 0 0.488 0.303 0 0; 35 3 1 0 0 0 0 0 0 0; 36 3 1 0 0 0 0.488 0.303 0 0; 37 3 1 0 0 0 0 0 0 0; 38 3 1 0 0 0 0 0 0 0; 39 3 1 0 0 0 0 0 0 0; 40 3 1 0 0 0 0.488 0.303 0 0; 41 3 1 0 0 0 0.488 0.303 0 0; 42 3 1 0 0 0 0 0 0 0; 43 3 1 0 0 0 0 0 0 0; 44 3 1 0 0 0 0.193 0.119 0 0; 45 3 1 0 0 0 0 0 0 0; 46 3 1 0 0 0 0 0 0 0; 47 3 1 0 0 0 0.309 0.191 0 0; 48 3 1 0 0 0 0 0 0 0; 49 3 1 0 0 0 0 0 0 0; 50 3 1 0 0 0 0.193 0.119 0 0; 51 3 1 0 0 0 0.193 0.119 0 0; 52 3 1 0 0 0 0 0 0 0; 53 3 1 0 0 0 0.193 0.119 0 0; 54 3 1 0 0 0 0 0 0 0; 55 3 1 0 0 0 0.488 0.303 0 0; 56 3 1 0 0 0 0 0 0 0; 57 3 1 0 0 0 0.488 0.303 0 0; 58 3 1 0 0 0 0.193 0.119 0 0; 59 3 1 0 0 0 0 0 0 0; 60 3 1 0 0 0 0 0 0 0; 61 3 1 0 0 0 0.193 0.119 0 0; 62 3 1 0 0 0 0 0 0 0; 63 3 1 0 0 0 0 0 0 0; 64 3 1 0 0 0 0.193 0.119 0 0; 65 3 1 0 0 0 0 0 0 0; 66 3 1 0 0 0 0 0 0 0; 67 3 1 0 0 0 0.488 0.303 0 0; 68 3 1 0 0 0 0.193 0.119 0 0; 69 3 1 0 0 0 0 0 0 0; 70 3 1 0 0 0 0 0 0 0; 71 3 1 0 0 0 0 0 0 0; 72 3 1 0 0 0 0.193 0.119 0 0; 73 3 1 0 0 0 0 0 0 0; 74 3 1 0 0 0 0.193 0.119 0 0; 75 3 1 0 0 0 0 0 0 0; 76 3 1 0 0 0 0.309 0.191 0 0; 77 3 1 0 0 0 0.193 0.119 0 0; 78 3 1 0 0 0 0.193 0.119 0 0; 79 3 1 0 0 0 0 0 0 0; 80 3 1 0 0 0 0 0 0 0; 81 3 1 0 0 0 0.488 0.303 0 0; 82 3 1 0 0 0 0 0 0 0; 83 3 1 0 0 0 0 0 0 0; 84 3 1 0 0 0 0 0 0 0; 85 3 1 0 0 0 0.193 0.119 0 0; 86 3 1 0 0 0 0 0 0 0; 87 3 1 0 0 0 0.193 0.119 0 0; 88 3 1 0 0 0 0 0 0 0; 89 3 1 0 0 0 0.488 0.303 0 0; 90 3 1 0 0 0 0 0 0 0; 91 3 1 0 0 0 0.193 0.119 0 0; 92 3 1 0 0 0 0 0 0 0; 93 3 1 0 0 0 0.488 0.303 0 0; 94 3 1 0 0 0 0 0 0 0; 95 3 1 0 0 0 0.488 0.303 0 0; 96 3 1 0 0 0 0 0 0 0; 97 3 1 0 0 0 0 0 0 0; 98 3 1 0 0 0 0.488 0.303 0 0; 99 3 1 0 0 0 0.488 0.303 0 0; 100 3 1 0 0 0 0.309 0.191 0 0; 101 3 1 0 0 0 0 0 0 0; 102 3 1 0 0 0 0.309 0.191 0 0; 103 3 1 0 0 0 0 0 0 0; 104 3 1 0 0 0 0 0 0 0; 105 3 1 0 0 0 0 0 0 0; 106 3 1 0 0 0 0.488 0.303 0 0; 107 3 1 0 0 0 0 0 0 0; 108 3 1 0 0 0 0.488 0.303 0 0; 109 3 1 0 0 0 0 0 0 0; 110 3 1 0 0 0 0 0 0 0; 111 3 1 0 0 0 0.309 0.191 0 0; 112 3 1 0 0 0 0.193 0.119 0 0; 113 3 1 0 0 0 0.488 0.303 0 0; 114 3 1 0 0 0 0 0 0 0; 115 3 1 0 0 0 0.488 0.303 0 0; 116 3 1 0 0 0 0 0 0 0; 117 3 1 0 0 0 0.309 0.191 0 0; 118 3 1 0 0 0 0 0 0 0; 119 3 1 0 0 0 0 0 0 0; 120 3 1 0 0 0 0 0 0 0; 121 3 1 0 0 0 0.193 0.119 0 0; 122 3 1 0 0 0 0 0 0 0; 123 3 1 0 0 0 0.193 0.119 0 0; 124 3 1 0 0 0 0 0 0 0; 125 3 1 0 0 0 0.193 0.119 0 0; 126 3 1 0 0 0 0 0 0 0; 127 3 1 0 0 0 0 0 0 0; 128 3 1 0 0 0 0.488 0.303 0 0; 129 3 1 0 0 0 0 0 0 0; 130 3 1 0 0 0 0 0 0 0; 131 3 1 0 0 0 0.488 0.303 0 0; 132 3 1 0 0 0 0 0 0 0; 133 3 1 0 0 0 0.488 0.303 0 0; 134 3 1 0 0 0 0 0 0 0; 135 3 1 0 0 0 0.309 0.191 0 0; 136 3 1 0 0 0 0 0 0 0; 137 3 1 0 0 0 0.309 0.191 0 0; 138 3 1 0 0 0 0 0 0 0; 139 3 1 0 0 0 0.488 0.303 0 0; 140 3 1 0 0 0 0 0 0 0; 141 3 1 0 0 0 0.193 0.119 0 0; 142 3 1 0 0 0 0.193 0.119 0 0];
 % From To R X B Tap % Bus Bus (pu) (pu) (pu) Ratio
 linedata=[ 54  55 0.3131409  1.878846 0 1; 49  51  3.162278  9.486834 0 1;  71  72  3.162278  9.486834 0 1;  17  18 0.3131409  1.878846 0 1;  94  95  0.3131409  1.878846 0 1;  92  93 0.3131409  1.878846 0 1; 4  25  1.030651  3.86494 0 1;  103  123 3.162278  9.486834 0 1;  30  31  3.162278  9.486834 0 1;  104  111 1.030651  3.86494 0 1;  109  112  3.162278  9.486834 0 1;  134  135 1.030651  3.86494 0 1;  42  128  0.3131409  1.878846 0 1;  43  44 3.162278  9.486834 0 1;  73  74  3.162278  9.486834 0 1;  88  142 3.162278  9.486834 0 1;  101  102  1.030651  3.86494 0 1;  114  113 0.3131409  1.878846 0 1;  130  131  0.3131409  1.878846 0 1;  86  87 3.162278  9.486834 0 1;  124  125  3.162278  9.486834 0 1;  63  64 3.162278  9.486834 0 1;  90  91  3.162278  9.486834 0 1;  48  50 3.162278  9.486834 0 1;  10  11  0.3131409  1.878846 0 1;  12  14 0.3131409  1.878846 0 1;  107  108  0.3131409  1.878846 0 1;  38  41 0.3131409  1.878846 0 1;  116  115  0.3131409  1.878846 0 1;  46  47 1.030651  3.86494 0 1;  27  28  1.030651  3.86494 0 1; 126  106 0.3131409  1.878846 0 1;  22  24  0.3131409  1.878846 0 1;  79  78 3.162278  9.486834 0 1;  75  76  1.030651  3.86494 0 1;  52  53 3.162278  9.486834 0 1;  59  58  3.162278  9.486834 0 1; 60  61 3.162278  9.486834 0 1;  65  68  3.162278  9.486834 0 1;  35  36 0.3131409  1.878846 0 1;  136  137  1.030651  3.86494  0 1;  138  139 0.3131409  1.878846 0 1;  56  57  1.030651  3.86494  0 1;  3  5 0.3131409  1.878846 0 1;  8  9  0.3131409  1.878846 0 1;  66  67 0.3131409  1.878846 0 1;  33  98  0.3131409  1.878846 0 1;  33  99 0.3131409  1.878846 0 1;  33  100  1.030651  3.86494 0 1;  83  89 0.3131409  1.878846 0 1;  70  77  3.162278  9.486834 0 1;  39  40 0.3131409  1.878846 0 1;  122  121  3.162278  9.486834 0 1;  119  117 1.030651  3.86494  0 1;  140  141  3.162278  9.486834 0 1;  21  23 0.3131409  1.878846 0 1;  80  81  0.3131409  1.878846 0 1;  19  20 0.3131409  1.878846 0 1;  84  85  3.162278  9.486834 0 1;  13  15 0.3131409  1.878846 0 1; 13  16  0.3131409  1.878846 0 1;  6  7 1.030651  3.86494  0 1;  32  34  0.3131409  1.878846 0 1;  132  133 0.3131409  1.878846 0 1;  1  2  7.067975  4.334504 0 1;  3  2  1.738946 1.066426 0 1;  3  6  1.121901  0.6880165 0 1;  6  8  1.738946  1.066426 0 1;  8  10  1.738946  1.066426 0 1;  6  12  1.738946  1.066426 0 1;  12 13  1.738946  1.066426 0 1;  2  4  3.365702  2.064049 0 1;  4  26 4.824173  2.958471 0 1;  26  29  4.487603  2.752066 0 1;  29  35 7.292354  4.472107 0 1;  35  32  7.853304  4.816115 0 1; 32  37 6.731404  4.128099 0 1;  37  39  2.019421  1.23843  0 1;  37  38 6.394834  3.921694 0 1;  38  42  1.738946  1.066426 0 1;  29  30 8.526444  5.228925 0 1;  26  27  5.048553  3.096074 0 1;  4  17 7.292354  4.472107 0 1; 17  21  4.038843  2.47686  0 1;  17  19 0.8975205  0.5504132 0 1;  21  22  4.151032  2.545661 0 1;  22  43 6.170454  3.784091 0 1; 43  45  6.170454  3.784091 0 1;  45  62 0.5048553  0.3096074 0 1;  45  48  0.4487603  0.2752066 0 1;  45  46 1.738946  1.066426 0 1;  65  62  3.814462  2.339256 0 1;  62  63 9.199586  5.641736 0 1;  65  66  5.609503  3.440082 0 1;  65  69 4.824173  2.958471 0 1;  48  49  5.609503  3.440082 0 1;  49  52 8.975205  5.504132 0 1;  52  54  10.09711  6.192148 0 1;  54  60 13.46281  8.256198 0 1;  54  56  13.46281  8.256198 0 1;  60  59 10.09711  6.192148 0 1;  69  71  4.487603  2.752066 0 1;  69  70 6.170454  3.784091 0 1;  71  80  7.516735  4.609711 0 1;  88  73 1.795041  1.100826 0 1;  79  75  5.609503  3.440082 0 1;  82  80 11.21901  6.880165 0 1;  80  92  5.160743  3.164876 0 1;  92  94 4.936363  3.027273 0 1;  94  96  5.272933  3.233678 0 1;  96  97 6.731404  4.128099 0 1;  84  86  2.243801  1.376033 0 1;  82  83 1.121901  0.6880165 0 1;  83  84  7.292354  4.472107 0 1;  90  83 4.319318  2.648864 0 1; 124  90  9.984916  6.123347 0 1;  96  110 1.907231  1.169628 0 1;  97  101  5.609503  3.440082 0 1;  101  103 7.292354  4.472107 0 1;  105  126  4.487603  2.752066 0 1;  110  105 8.414255  5.160124 0 1;  104  105  4.038843  2.47686  0 1; 109  104 2.243801  1.376033 0 1;  105  107  4.151032  2.545661 0 1;  114  109 5.272933  3.233678 0 1;  116  114  3.814462  2.339256 0 1;  118  116 1.458471  0.8944215 0 1;  127  118  2.468182  1.513636 0 1;  127  120 1.682851  1.032025 0 1;  120  122  1.907231  1.169628 0 1;  118  119 1.795041  1.100826 0 1;  42  129  8.975205  5.504132 0 1;  129  130 3.029132  1.857645 0 1;  132  129  1.738946  1.066426 0 1;  134  132 6.170454  3.784091 0 1;  136  134  7.292354  4.472107 0 1;  138  136 10.09711  6.192148 0 1;  127  140  2.243801  1.376033 0 1;  75  88 9.536156  5.84814  0 1;  97  33  3.365702  2.06404  0 1;  73  69 0.01121901  0.006880165 0 1];
fb=linedata(:,1);
tb=linedata(:,2);
r=linedata(:,3);
x=linedata(:,4);
b=linedata(:,5);
a=linedata(:,6);
z=r+1i*x;
y=1./z;
b=1i*b;
nl=length(fb);
nbus=max(max(fb),max(tb));
Y=zeros(nbus,nbus);
for k=1:nl
  Y(fb(k),tb(k))=Y(fb(k),tb(k))-y(k)/a(k);
  Y(tb(k),fb(k))=Y(fb(k),tb(k));
end
for m=1:nbus
  for n=1:nl
    if fb(n)==m
      Y(m,m)=Y(m,m)+y(n)/a(n)^2+b(n);
    elseif tb(n)==m
      Y(m,m)=Y(m,m)+y(n)+b(n);
    end
  end
end
G=real(Y);
B=imag(Y);
BMva=100;
busNo=busdata(:,1);
type=busdata(:,2);
V=busdata(:,3);
del=busdata(:,4);
Pg=busdata(:,5)/BMva;
Qg=busdata(:,6)/BMva;
Pl=busdata(:,7)/BMva;
Ql=busdata(:,8)/BMva;
Qmin=busdata(:,9)/BMva;
Qmax=busdata(:,10)/BMva;
pv=find(type==2|type==1);
pq=find(type==3);
npq=length(pq);
npv=length(pv);
Psp=Pg-Pl;
Qsp=Qg-Ql;
Iter=1;
Tol=1;
while Tol>1e-5
  P=zeros(nbus,1);
  Q=zeros(nbus,1);
  for i=1:nbus
    for j=1:nbus
      P(i)=P(i)+V(i)*V(j)*(G(i,j)*cos(del(i)-del(j))+B(i,j)*sin(del(i)-del(j)));
      Q(i)=Q(i)+V(i)*V(j)*(G(i,j)*sin(del(i)-del(j))-B(i,j)*cos(del(i)-del(j)));
    end
  end
  if Iter>2 && Iter<=7
    for n=2:nbus
      if type(n)==2;
        QG=Q(n)+Ql(n);
        if QG > Qmax(n)
          V(n)=V(n)-0.01;
        elseif QG < Qmin(n)
          V(n)=V(n)+0.01;
        end
      end
    end
  end
    dPa=Psp-P;
    dQa=Qsp-Q;
    dP=dPa(2:nbus);
    k=1;
    dQ=zeros(npq,1); for i=1:nbus if type(i)==3 dQ(k,1)=dQa(i); k=k+1; end end M=[dP;dQ]; J1=zeros(nbus-1,nbus-1); for i=1:nbus-1 m=i+1; for j=1:nbus-1; n=j+1; if m==n for n=1:nbus J1(i,j)=J1(i,j)+V(m)*V(n)*(-G(m,n)*sin(del(m)-del(n))+B(m,n)*cos(del(m)-del(n))); end J1(i,j)=J1(i,j)-V(m)^2*B(m,m); else J1(i,j)=V(m)*V(n)*(G(m,n)*sin(del(m)-del(n))-B(m,n)*cos(del(m)-del(n))); end end end J2=zeros(nbus-1,npq); for i=1:nbus-1 m=i+1; for j=1:npq n=pq(j); if m==n for n=1:nbus J2(i,j)=J2(i,j)+V(n)*(G(m,n)*cos(del(m)-del(n))+B(m,n)*sin(del(m)-del(n))); end J2(i,j)=J2(i,j)+V(m)*G(m,m); else J2(i,j)=V(m)*(G(m,n)*cos(del(m)-del(n))+B(m,n)*sin(del(m)-del(n))); end end end J3=zeros(npq,nbus-1); for i=1:npq m=pq(i); for j=1:nbus-1 n=j+1; if m==n for n=1:nbus J3(i,j)=J3(i,j)+V(m)*V(n)*(G(m,n)*cos(del(m)-del(n))+B(m,n)*sin(del(m)-del(n))); end J3(i,j)=J3(i,j)-V(m)^2*G(m,m); else J3(i,j)=V(m)*V(n)*(-G(m,n)*cos(del(m)-del(n))-B(m,n)*sin(del(m)-del(n))); end end end J4=zeros(npq,npq); for i=1:npq m=pq(i); for j=1:npq n=pq(j); if m==n for n=1:nbus J4(i,j)=J4(i,j)+V(n)*(G(m,n)*sin(del(m)-del(n))-B(m,n)*cos(del(m)-del(n))); end J4(i,j)=J4(i,j)-V(m)*B(m,m); else J4(i,j)=V(m)*(G(m,n)*sin(del(m)-del(n))-B(m,n)*cos(del(m)-del(n))); end end end J=[J1 J2;J3 J4]; X=inv(J)*M; dTh=X(1:nbus-1); dV=X(nbus:end); del(2:nbus)=del(2:nbus)+dTh; k=1; for n=2:nbus if type(n)==3 V(n)=V(n)+dV(k); k=k+1; end end Iter=Iter+1; Tol=max(abs(M)); end Q=zeros(nbus,1); for i=1:nbus for j=1:nbus P(i)=P(i)+V(i)*V(j)*(G(i,j)*cos(del(i)-del(j))+B(i,j)*sin(del(i)-del(j))); Q(i)=Q(i)+V(i)*V(j)*(G(i,j)*sin(del(i)-del(j))-B(i,j)*cos(del(i)-del(j))); end end for i=1:nbus del(i)=180*del(i)/pi; end disp('----------------------------------------'); disp(' Newton Raphson Loadflow Solution '); disp('----------------------------------------'); disp(' Bus | |Voltage Angle |'); disp(' | No. pu | |Radian'); disp('----------------------------------------'); for m=1:nbus fprintf(' %3g ' ,m); fprintf(' %8.3f ' ,V(m)); fprintf(' %8.3f ' ,del(m)); fprintf(' %8.3f ',Pg(m)*BMva); if type(m)==2 fprintf(' %8.3f ',(Q(m)+Ql(m))*BMva);
      end
      fprintf('\n');
  end
  disp('----------------------------------------');
  fprintf( 'Number Of Ieration %3g \n',Iter)
  toc

Answer 1

The message is clear: You solve an matzrix equation with a matrix which is badly conditioned. This might be caused by a programming error (this would be sad, because it looks impossible to debug your code - it is simply not readable due to the absence of comments) or the problem is instable itself.