Fwd: Singular in radial networks

Shri Thu, 05 Dec 2013 19:16:06 -0800

Hi,

I don't understand the need for running an OPF since there is only one generator in your test case. You can instead simply run a power flow with the appropriate set point voltage for the generator bus. The OPF and the power flow "WILL" yield the same result if the case is feasible and solvable (no voltage/flow limits exceeded and loading less than the maximum limit). Running a power flow on your case shows that there are many buses whose voltage is below the min. voltage limit of 0.9 pu. This explains the divergence of the OPF.

Please do not send emails to me personally. Always send it to the mailing list so that others can also chime in their suggestions.

Shri

Begin forwarded message:

From: Spyridon Gian <[email protected]>
Subject: Singular in radial networks
Date: December 5, 2013 6:53:43 PM CST
To: "[email protected]" <[email protected]>

Dear Shri,

I have attached a 11-bus radial network (R/X=3) , that after performing runopf, yields a warning that the matrix is close to singular
with rcond = approximately 0. As you can see, there are no line constraints, and the voltage limits are 0.9pu and 1.1 pu.
I would assume that this warning is due to the high R/X ratio. In other words, this warning is never yielded if the system is meshed
with a lower R/X ratio . Do you agree ?

For the radial network, the OPF is not converging because of the reason explained above. For the meshed system, the OPF does converge presumably because the bus voltages are within the set limits.

Kind regards,
Spyros Gian

function mpc = singular
\%% MATPOWER Case Format : Version 2
mpc.version = '2';
\%% 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      0       
33      1       1.1    0.9;       
        2       2       13.6    1.938       0   0       1        1      0       
33      1       1.1    0.9;
        3       2       0       0           0   0       1        1      0       
33      1       1.1    0.9;       
        4   2   13.6    1.938       0   0       1        1      0       33      
1       1.1    0.9;
        5       2       13.6    1.938       0   0       1        1      0       
33      1       1.1    0.9;
    6   2       0       0           0   0       1        1      0   33      1   
    1.1    0.9;
    7   2   13.6        1.938       0   0       1        1      0       33      
1       1.1    0.9;
    8   2   13.6        1.938       0   0       1        1      0       33      
1       1.1    0.9;
    9   2   0       0           0       0       1        1      0   33      1   
    1.1    0.9;
    10  2   13.6        1.938       0   0       1        1      0       33      
1       1.1    0.9;
    11  1   0       0           0       0       1        1      0   33      1   
    1.1    0.9;
];
\%% generator data
%       bus     Pg      Qg      Qmax    Qmin    Vg      mBase   status  Pmax    
Pmin
mpc.gen = [
        1       0       0       1000        0       1   100     1   1000      0 
 
];
\%% branch data
%       fbus    tbus    r       x       b       rateA   rateB   rateC   ratio   
angle   status  
mpc.branch = [
        1       2        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        2       3        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        3       4        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        3       5        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        5       6        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        6       7        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;
        6       8        0.06   0.02    0       1000       1000       1000      
 0       0       1      ;     
    8       9        0.06   0.02    0   1000       1000       1000       0      
 0       1      ; 
    9       10       0.06   0.02    0   1000       1000       1000       0      
 0       1      ; 
    9       11       0.06   0.02    0   1000       1000       1000       0      
 0       1      ; 
];
\%% generator cost data
%       1       startup shutdown        n       x1      y1      ...     xn      
yn
%       2       startup shutdown        n       c(n-1)  ...     c0
mpc.gencost = [
        2       0       0       2       80  0   ;
];

Fwd: Singular in radial networks

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