Hi Arash,
It appears to me you may have omiited the generator data in your 4-bus case.
i tried your case with some simple definition of gen. data and it run for
both power flow and optimal power flow. generator data is as follows below
%% 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 2 0 100 -100 1.02 100 1 318 0 0 0 0 0 0 0 0 0 0 0 0;
];
Please find attached the case modeling and the results,
best regards
On 16 December 2013 10:48, Arash Alimardani <[email protected]>wrote:
> Hello all,
>
> I have the simplest OPF problem, but I can't get matpower to do it for me.
> I would appreciate if someone could help me.
>
> I have attached a figure of the system. Here is the description of the
> system:
>
> 4 buses including 1 generator and 3 load buses:
>
> mpc.bus = [
> 1 3 0 0 0 0 1 1.06 0 0 1 1.06 0.94;
> 2 1 0 0 0 0 1 1.045 -4.98 0 1 1.06
> 0.94;
> 3 1 0 0 0 0 1 1.01 -12.72 0 1 1.06
> 0.94;
> 4 1 .25 0 0 0 1 1.019 -10.33 0 1
> 1.06 0.94;
> ];
>
> as you can see the load of bus 4 is P=0.25, Q=0. All other loads are zero.
>
> As for branches:
>
> mpc.branch = [
> 1 2 1/3 0 0 9900 0 0 0 0 1 -360
> 360;
> 2 3 1/3 0 0 9900 0 0 0 0 1 -360
> 360;
> 3 4 1/3 0 0 9900 0 0 0 0 1 -360
> 360;
> ];
>
> As you can see, only a resistance with the value of 0.333 is the impedance
> of each line.
>
> The data is in per unit and:
> mpc.baseMVA = 1;
>
> And the cost of production:
> mpc.gencost = [
> 2 0 0 3 0.0430293 20 0;
> ];
>
>
> The solution which I have by solving it manually is:
> x0=[0;0;0;0;1;.833333;.666666;.5;.5;0];
>
> However, matpower doesn't converge to it even when I give it as the
> initial value (x0).
>
> Please, help me figure out the problem with my work.
>
> Regards,
> Arash Alimardani
>
--
*Fred Kanjelesa.*NCC-Trading/ZESCO
Zambia/Lusaka.
Mobile: +260967/955-880912
Extension: 5124
"I can do all things through Christ who strengthens me." *Philippians 4:13*
CASE MODEL
function mpc = case4gsARASH
%CASE4GS Power flow data for 4 bus, 2 gen case from Grainger & Stevenson.
% Please see CASEFORMAT for details on the case file format.
%
% This is the 4 bus example from pp. 337-338 of "Power System Analysis",
% by John Grainger, Jr., William Stevenson, McGraw-Hill, 1994.
% MATPOWER
% $Id: case4gs.m,v 1.4 2010/03/10 18:08:14 ray Exp $
%% 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 1.06 0 0 1 1.06 0.94;
2 1 0 0 0 0 1 1.045 -4.98 0 1 1.06 0.94;
3 1 0 0 0 0 1 1.01 -12.72 0 1 1.06 0.94;
4 1 0.25 0 0 0 1 1.019 -10.33 0 1 1.06
0.94;
];
%% 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 2 0 100 -100 1.02 100 1 318
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 = [
1 2 1/3 0 0 9900 0 0 0 0 1 -360 360;
2 3 1/3 0 0 9900 0 0 0 0 1 -360 360;
3 4 1/3 0 0 9900 0 0 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 0.0430293 20 0;
];
PF RESULTS
>> runpf(case4gsARASH);
MATPOWER Version 4.1, 14-Dec-2011 -- AC Power Flow (Newton)
Newton's method power flow converged in 4 iterations.
Converged in 0.02 seconds
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 4 Total Gen Capacity 318.0 -100.0 to 100.0
Generators 1 On-line Capacity 318.0 -100.0 to 100.0
Committed Gens 1 Generation (actual) 0.3 0.0
Loads 1 Load 0.3 0.0
Fixed 1 Fixed 0.3 0.0
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 3 Losses (I^2 * Z) 0.00 0.00
Transformers 0 Branch Charging (inj) - 0.0
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.018 p.u. @ bus 4 1.020 p.u. @ bus 1
Voltage Angle 0.00 deg @ bus 1 0.00 deg @ bus 3
P Losses (I^2*R) - 0.00 MW @ line 3-4
Q Losses (I^2*X) - 0.00 MVAr @ line 1-2
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ------- -------- -------- -------- -------- --------
1 1.020 0.000* 0.25 0.00 - -
2 1.019 0.000 - - - -
3 1.018 0.000 - - - -
4 1.018 0.000 - - 0.25 0.00
-------- -------- -------- --------
Total: 0.25 0.00 0.25 0.00
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 0.25 0.00 -0.25 -0.00 0.000 0.00
2 2 3 0.25 0.00 -0.25 -0.00 0.000 0.00
3 3 4 0.25 -0.00 -0.25 0.00 0.000 0.00
-------- --------
Total: 0.001 0.00
OPF RESULTS
>> runopf(case4gsARASH);
MATPOWER Version 4.1, 14-Dec-2011 -- AC Optimal Power Flow
MATLAB Interior Point Solver -- MIPS, Version 1.0, 07-Feb-2011
Converged!
Converged in 0.25 seconds
Objective Function Value = 5.02 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 4 Total Gen Capacity 318.0 -100.0 to 100.0
Generators 1 On-line Capacity 318.0 -100.0 to 100.0
Committed Gens 1 Generation (actual) 0.3 0.0
Loads 1 Load 0.3 0.0
Fixed 1 Fixed 0.3 0.0
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 3 Losses (I^2 * Z) 0.00 0.00
Transformers 0 Branch Charging (inj) - 0.0
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 1.000 p.u. @ bus 4 1.002 p.u. @ bus 1
Voltage Angle 0.00 deg @ bus 1 0.00 deg @ bus 1
P Losses (I^2*R) - 0.00 MW @ line 1-2
Q Losses (I^2*X) - 0.00 MVAr @ line 1-2
Lambda P 20.02 $/MWh @ bus 1 20.12 $/MWh @ bus 4
Lambda Q 0.00 $/MWh @ bus 1 0.00 $/MWh @ bus 1
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.002 0.000* 0.25 0.00 - - 20.018 -
2 1.001 0.000 - - - - 20.051 -
3 1.001 0.000 - - - - 20.085 -
4 1.000 0.000 - - 0.25 0.00 20.118 -
-------- -------- -------- --------
Total: 0.25 0.00 0.25 0.00
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 0.25 0.00 -0.25 0.00 0.000 0.00
2 2 3 0.25 0.00 -0.25 0.00 0.000 0.00
3 3 4 0.25 0.00 -0.25 0.00 0.000 0.00
-------- --------
Total: 0.001 0.00
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 1 0.004 0.00 0.25 318.00 -
>>
