rdzman
commented
1 year ago The first thing I always try with a non-convergent OPF is to turn on soft limits to see whether there are limits that cause the problem to be infeasible. For example ...
>> mpc = loadcase('case10ba');
>> mpc = toggle_softlims(mpc, 'on');
>> runopf(mpc)
MATPOWER Version 8.0b1, 30-May-2023
Optimal Power Flow -- AC-polar-power formulation
MATPOWER Interior Point Solver -- MIPS, Version 1.5, 12-Dec-2022
(using built-in linear solver)
Converged!
OPF successful
Converged in 0.09 seconds
Objective Function Value = 8486.44 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 10 Total Gen Capacity 10.0 -10.0 to 10.0
Generators 1 On-line Capacity 10.0 -10.0 to 10.0
Committed Gens 1 Generation (actual) 13.1 5.1
Loads 9 Load 12.4 4.2
Fixed 9 Fixed 12.4 4.2
Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0
Shunts 0 Shunt (inj) -0.0 0.0
Branches 9 Losses (I^2 * Z) 0.69 0.91
Transformers 0 Branch Charging (inj) - 0.0
Inter-ties 0 Total Inter-tie Flow 0.0 0.0
Areas 1
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 0.900 p.u. @ bus 10 1.052 p.u. @ bus 1
Voltage Angle -5.31 deg @ bus 10 0.00 deg @ bus 1
P Losses (I^2*R) - 0.17 MW @ line 5-6
Q Losses (I^2*X) - 0.25 MVAr @ line 3-4
Lambda P 1020.00 $/MWh @ bus 1 4718.22 $/MWh @ bus 10
Lambda Q 0.00 $/MWh @ bus 1 2288.90 $/MWh @ bus 10
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.052 0.000* 13.06 5.10 - - 1020.000 -
2 1.045 -0.469 - - 1.84 0.46 1048.579 76.626
3 1.040 -1.137 - - 0.98 0.34 1054.762 186.716
4 1.017 -2.087 - - 1.79 0.45 1232.417 419.363
5 1.003 -2.374 - - 1.60 1.84 1393.630 542.449
6 0.974 -3.324 - - 1.61 0.60 1856.170 871.113
7 0.965 -3.691 - - 0.78 0.11 2063.8321016.374
8 0.948 -4.116 - - 1.15 0.06 2522.1981232.536
9 0.920 -4.803 - - 0.98 0.13 3577.2001736.707
10 0.900 -5.313 - - 1.64 0.20 4718.2242288.896
-------- -------- -------- --------
Total: 13.06 5.10 12.37 4.19
================================================================================
| 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 13.06 5.10 -13.01 -4.96 0.041 0.14
2 2 3 11.17 4.50 -11.17 -4.35 0.004 0.15
3 3 4 10.19 4.01 -10.03 -3.76 0.156 0.25
4 4 5 8.24 3.31 -8.14 -3.22 0.101 0.09
5 5 6 6.55 1.38 -6.38 -1.24 0.167 0.15
6 6 7 4.77 0.64 -4.73 -0.60 0.042 0.04
7 7 8 3.95 0.49 -3.88 -0.45 0.066 0.04
8 8 9 2.73 0.39 -2.65 -0.35 0.077 0.04
9 9 10 1.67 0.22 -1.64 -0.20 0.034 0.02
-------- --------
Total: 0.687 0.91
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 1.000 1.052 1.000 99999.999
10 82415.957 0.900 0.900 1.100 -
================================================================================
| Generation Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
1 1 - 0.00 13.06 10.00 1000.000
================================================================================
| Soft Voltage Upper Bounds |
================================================================================
Bus Voltage Limit Overload mu
# Mag(pu) (pu) (pu) ($/pu)
----- ------- ------- ------- ---------
1 1.052 1.000 0.052 99999.999
--------
Total: 0.05
================================================================================
| Soft Voltage Lower Bounds |
================================================================================
----------------------------------------
Bus Voltage Limit Overload mu
# Mag(pu) (pu) (pu) ($/pu)
----- ------- ------- ------- ---------
10 0.900 0.900 0.000 82415.957
--------
Total: 0.00
================================================================================
| Soft Generator Active Power Upper Bounds |
================================================================================
Gen Bus Generation Limit Overload mu
# # P (MW) (MW) (MW) ($/MW)
----- ----- -------- ------- ------- ---------
1 1 13.06 10.00 3.06 1000.000
--------
Total: 3.06
================================================================================
| Soft Generator Active Power Lower Bounds |
================================================================================
No violations.
================================================================================
| Soft Generator Reactive Power Upper Bounds |
================================================================================
No violations.
================================================================================
| Soft Generator Reactive Power Lower Bounds |
================================================================================
No violations.You can also use the checklimits() function in the extras directory to check for constraint violations in a power flow solution.
>> r = runpf('case10ba', mpoption('out.all', 0));
MATPOWER Version 8.0b1, 30-May-2023
Power Flow -- AC-polar-power formulation
Newton's method converged in 4 iterations.
PF successful
>> checklimits(r);
No Branch Flow Emergency Rating Violations
No Branch Flow Short Term Rating Violations
No Branch Flow Normal Rating Violations
Generator Active Limit Violations
No Pmin Violations
Pmax Violations
gen bus Pmin Pg Pmax violation % violation
-------- -------- ---------- ---------- ---------- ---------- ----------
1 1 0.0 13.2 10.0 3.15 31.5
Generator Reactive Limit Violations
No Qmin Violations
No Qmax Violations
Bus Voltage Limit Violations
Vmin Violations
bus Vmin Vm Vmax violation % violation
-------- ---------- ---------- ---------- ---------- ----------
10 0.90 0.84 1.10 0.06 5.68
9 0.90 0.86 1.10 0.04 3.76
8 0.90 0.89 1.10 0.01 1.00
No Vmax Violations
Dear all,
I have encountered a significant difficulty of OPF obtaining a feasible solution with several Matpower cases of distribution grids no matter how small in size. For example all the following cases: 'case136ma' 'case10ba' 'case118zh' 'case16am' 'case17me' 'case70da' 'case85' 'case94pi' 'case9target'
cannot converge to a feasible solution. All solvers, IPOPT, MIPS, FMINCON, fail. I activated special options to help IPOPT to converge. These are
expect_infeasible_problem yesandstart_with_resto yes. I also tried several barrier update strategies to no avail. Also tried the optionopf.start=1,2,3. The really weird thing is that foropf.start=3, the initial guess is usually feasible if alsopf.alg=YSUM or ISUM. But IPOPT or any other optimizer although it starts with a feasible solution, it quickly diverges and cannot get back the feasible region. I understand that power flow using the simple Newton algorithm does not converge. This is clear. Is this also the reason why OPF cannot converge, despite the sophisticated linesearches (filter or Merit-based) and 1-norm feasibility restoration algorithms?Any idea how to remedy this behavior?
Best regards!