Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 9.654055e-18.

Hello

I am working with matpower and doing power flow analysis however when i run my code it doesnt converge. Please let me know what i might be doing wrong.

function mpc = model
%CASE33BW  Power flow data for 33 bus distribution system from Baran & Wu
%    Please see CASEFORMAT for details on the case file format.
%
%    Data from ...
%       M. E. Baran and F. F. Wu, "Network reconfiguration in distribution
%       systems for loss reduction and load balancing," in IEEE Transactions
%       on Power Delivery, vol. 4, no. 2, pp. 1401-1407, Apr 1989.
%       doi: 10.1109/61.25627
%       URL: http://doi.org/10.1109/61.25627

%% MATPOWER Case Format : Version 2
mpc.version = '2';

%%-----  Power Flow Data  -----%%
%% system MVA base
mpc.baseMVA = 8995;


%% bus data
%	bus_i	type	Pd	Qd	Gs	Bs	area	Vm	Va	baseKV	zone	Vmax	Vmin
mpc.bus = [  %% (Pd and Qd are specified in kW & kVAr here, converted to MW & MVAr below)
%bus_i type	Pd	Qd	   Gs	Bs area	Vm	Va baseKV  zone	Vmax Vmin
1	3	15.528	6.67704	0	0	1	1	0	0.23	1	1.1	0.9;
2	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
3	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
4	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
5	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
6	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
7	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
8	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
9	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
10	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
11	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
12	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
13	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
14	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
15	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
16	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
17	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
18	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
19	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
20	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
21	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
22	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
23	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
24	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
25	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
26	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
27	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
28	1	-0.944	-0.40592	0	0	1	1	0	0.23	1	1.1	0.9;
29	1	-0.624	-0.26832	0	0	1	1	0	0.23	1	1.1	0.9;
30	1	-0.764	-0.32852	0	0	1	1	0	0.23	1	1.1	0.9;
31	1	-0.86	-0.3698	0	0	1	1	0	0.23	1	1.1	0.9;
32	1	-0.884	-0.38012	0	0	1	1	0	0.23	1	1.1	0.9;
33	1	-0.12	-0.0516	0	0	1	1	0	0.23	1	1.1	0.9;
34	1	-1.264	-0.54352	0	0	1	1	0	0.23	1	1.1	0.9;
35	1	-2.056	-0.88408	0	0	1	1	0	0.23	1	1.1	0.9;
36	1	-1.904	-0.81872	0	0	1	1	0	0.23	1	1.1	0.9;
37	1	-0.224	-0.09632	0	0	1	1	0	0.23	1	1.1	0.9;
38	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
39	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
40	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
41	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
42	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
43	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
44	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
45	1	0	0	0	0	1	1	0	0.23	1	1.1	0.9;
46	1	-1.448	-0.62264	0	0	1	1	0	0.23	1	1.1	0.9;
47	1	-1.132	-0.48676	0	0	1	1	0	0.23	1	1.1	0.9;
48	1	-1.572	-0.67596	0	0	1	1	0	0.23	1	1.1	0.9;
49	1	-2.192	-0.94256	0	0	1	1	0	0.23	1	1.1	0.9;
50	1	-0.932	-0.40076	0	0	1	1	0	0.23	1	1.1	0.9;
51	1	1.392	0.59856	0	0	1	1	0	0.23	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
mpc.gen = [
	1	0	0	10	    -10	     1	100	      1	     0.02	      0	     0	  0	   0	   0	  0	       0	   0	     0	  0     	0	0;
];

%% branch data
%	fbus	tbus	r	x	b	rateA	rateB	rateC	ratio	angle	status	angmin	angmax
mpc.branch = [  %% (r and x specified in ohms here, converted to p.u. below)
									
								
1	2	0.000428	0.000272	1.130832	0.0805	0.0805	0.0805	0	0	1	-360	360
2	3	0.001712	0.001088	4.523328	0.0805	0.0805	0.0805	0	0	1	-360	360
17	4	0.001177	0.000748	3.109788	0.0805	0.0805	0.0805	0	0	1	-360	360
3	5	0.001284	0.000816	3.392496	0.0805	0.0805	0.0805	0	0	1	-360	360
5	6	0.000749	0.000476	1.978956	0.0805	0.0805	0.0805	0	0	1	-360	360
6	7	0.000321	0.000204	0.848124	0.0805	0.0805	0.0805	0	0	1	-360	360
7	8	0.000428	0.000272	1.130832    0.0805	0.0805	0.0805	0	0	1	-360	360
4	9	0.001605	0.00102  	4.24062	    0.0805	0.0805	0.0805	0	0	1	-360	360
8	10	0.001375	0.000748	2.59149	    0.06555	0.06555	0.06555	0	0	1	-360	360
10	11	0.0015	    0.000816	2.82708	0.06555	0.06555	0.06555	    0	0	1	-360	360
11	12	0.000625	0.00034	    1.17795	0.06555	0.06555	0.06555  	0	0	1	-360	360
9	13	0.000875	0.000476	1.64913	0.06555	0.06555	0.06555  	0	0	1	-360	360
12	14	0.00175	    0.000952	3.29826	0.06555	0.06555	0.06555  	0	0	1	-360	360
13	15	0.000625	0.00034	    1.17795	0.06555	0.06555	0.06555  	0	0	1	-360	360
15	16	0.001	    0.000544	1.88472	0.06555	0.06555	0.06555	    0	0	1	-360	360
14	17	0.00075  	0.000408	1.41354	0.06555	0.06555	0.06555 	0	0	1	-360	360
17	18	0.001	    0.000544	1.88472	0.06555	0.06555	0.06555	    0	0	1	-360	360
18	19	0.001125	0.000612	2.12031	0.06555	0.06555	0.06555	    0	0	1	-360	360
16	20	0.00175  	0.000952	3.29826	0.06555	0.06555	0.06555	    0	0	1	-360	360
19	21	0.001	    0.000544	1.88472	0.06555	0.06555	0.06555	    0	0	1	-360	360
20	22	0.00075	    0.000408	1.41354	0.06555	0.06555	0.06555	    0	0	1	-360	360
21	23	0.001875	0.00102  	3.53385	0.06555	0.06555	0.06555	    0	0	1	-360	360
23	24	0.000375	0.000204	0.70677	0.06555	0.06555	0.06555	    0	0	1	-360	360
24	25	0.00075	    0.000408	1.41354	0.06555	0.06555	0.06555	    0	0	1	-360	360
22	26	0.000375	0.000204	0.70677	   0.06555	0.06555	0.06555	0	0	1	-360	360
26	27	0.000875	0.000476	1.64913	   0.06555	0.06555	0.06555	0	0	1	-360	360
3	28	0.01064    	0.00148  	3.392496	0.0368	0.0368	0.0368	0	0	1	-360	360
5	29	0.00798	    0.00111	    2.544372	0.0368	0.0368	0.0368	0	0	1	-360	360
6	30	0.007448	0.001036	2.3747472	0.0368	0.0368	0.0368	0	0	1	-360	360
7	31	0.005852	0.000814	1.8658728	0.0368	0.0368	0.0368	0	0	1	-360	360
8	32	0.013832	0.001924	4.4102448	0.0368	0.0368	0.0368	0	0	1	-360	360
9	33	0.017024	0.002368	5.4279936	0.0368	0.0368	0.0368	0	0	1	-360	360
10	34	0.019684	0.002738	6.2761176	0.0368	0.0368	0.0368	0	0	1	-360	360
11	35	0.018088	0.002516	5.7672432	0.0368	0.0368	0.0368	0	0	1	-360	360
12	36	0.017024	0.002368	5.4279936	0.0368	0.0368	0.0368	0	0	1	-360	360
13	37	0.009044	0.001258	2.8836216	0.0368	0.0368	0.0368	0	0	1	-360	360
14	38	0.0133	    0.00185	    4.24062	    0.0368	0.0368	0.0368	0	0	1	-360	360
15	39	0.015428	0.002146	4.9191192	0.0368	0.0368	0.0368	0	0	1	-360	360
16	40	0.009044	0.001258	2.8836216	0.0368	0.0368	0.0368	0	0	1	-360	360
17	41	0.001064	0.000148	0.3392496	0.0368	0.0368	0.0368	0	0	1	-360	360
18	42	0.011172	0.001554	3.5621208	0.0368	0.0368	0.0368	0	0	1	-360	360
19	43	0.004256	0.000592	1.3569984	0.0368	0.0368	0.0368	0	0	1	-360	360
20	44	0.001596	0.000222	0.5088744	0.0368	0.0368	0.0368	0	0	1	-360	360
21	45	0.019152	0.002664	6.1064928	0.0368	0.0368	0.0368	0	0	1	-360	360
22	46	0.017024	0.002368	5.4279936	0.0368	0.0368	0.0368	0	0	1	-360	360
23	47	0.017024	0.002368	5.4279936	0.0368	0.0368	0.0368	0	0	1	-360	360
24	48	0.009576	0.001332	3.0532464	0.0368	0.0368	0.0368	0	0	1	-360	360
25	49	0.019152	0.002664	6.1064928	0.0368	0.0368	0.0368	0	0	1	-360	360
26	50	0.012236	0.001702	3.9013704	0.0368	0.0368	0.0368	0	0	1	-360	360
27	51	0.005852	0.000814	1.8658728	0.0368	0.0368	0.0368	0	0	1	-360	360





];

%%-----  OPF Data  -----%%
%% generator cost data
%	1	startup	shutdown	n	x1	y1	...	xn	yn
%	2	startup	shutdown	n	c(n-1)	...	c0
mpc.gencost = [
	2	0	0	3	0	20	0;
];


%% convert branch impedances from Ohms to p.u.
[PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
    VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
[F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
    TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
    ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
Vbase = mpc.bus(1, BASE_KV) * 1e3;      %% in Volts
Sbase = mpc.baseMVA * 1e6;              %% in VA
mpc.branch(:, [BR_R BR_X]) = mpc.branch(:, [BR_R BR_X]) / (Vbase^2 / Sbase);

%% convert loads from kW to MW
mpc.bus(:, [PD, QD]) = mpc.bus(:, [PD, QD]) / 1e3;

Answer 1

[Shiva Kalyan Diwakaruni]

Hi,

The error "Matrix is close to singular or badly sclaed.Results may be inaccurate" are generally a result of using double-precision arithmetic;

The best way to increase precision of numeric calculations is to use the "vpa" function from the Symbolic Math Toolbox. The "vpa" function uses variable-precision floating-point arithmetic (VPA) to evaluate each element of the symbolic input to this function to a specified number of significant digits. Please refer to the below links

https://www.mathworks.com/help/symbolic/increase-precision-of-numeric-calculations.html

Hope it helps