 Test Case Archive of Optimal Power Flow (OPF) Problems with Local Optima

# Test Case Archive of Optimal Power Flow (OPF) Problems with Local Optima

## Test Cases

Following are the test cases for optimization techniques aimed at solving optimal power flow (OPF) problem. The deatils of all these test cases can be found in this paper. (Link)

Test Case nB nL nG Modifications # of Local Optima % Difference
WB2 2 1 1 - 2 3.18
WB3 3 2 1 - 2 0.21
WB5 5 6 2 - 2 14.34
LMBM3 3 3 3 - 5 69.94
case9mod 9 9 3 Lower bounds on reactive power
generation of all generators = -3 MVars,
demand scaled to 60%
4 50.80
case22loop 30 30 15 - 2 33.69
case39mod1 39 46 10 Voltage bounds tightened to ±5%
2 115.48
case39mod2 39 46 10 Voltage bounds tightened to ±5%,
only linear cost coefficients used
16 0.53
case118mod 118 186 54 Generators real and reactive power bounds
scaled by 7
3 50.97
case300mod 300 411 69 Lower bounds on reactive power
generation of all generators = -3 MVars,
demand scaled to 60%
7 2.52

nB:= Number of buses
nL:= Number of branches
nG:= Number of generators
% Difference:= 100*max[Global objective value-Local objective value]⁄Global Objective Value

Note: The modified test cases are adapted from the power systems test archive. (Link)

## Other cases with Local Optima

Some other test cases with local optima:

Test Case Modifications # of Local Optima % Difference
LMBM3_50 ±10% voltage bounds 2 100.00
WB5mod ±10% voltage bounds 3 117.32
case30loop ±5% voltage bounds 2 33.69
case30loopmod1 ±10% voltage bounds 3 132.90
case39mod3 Power generation bounds scaled by 4,
±5% voltage bounds
only linear objective coefficients considered
5 1.11
case39mod4 Real and reactive demand halved,
±5% voltage bounds
linear objective coefficients perturbed
3 51.08
case118mod2 Power generation bounds scaled by 4,
±10% voltage bounds
only linear objective coefficients considered
2 37.70
case300mod2 Power generation bounds scaled by 4,
±10% voltage bounds
only linear objective coefficients
2 0.07

## Data of Low Voltage Local Solutions

If voltage bounds are relaxed then it is possible to have local solutions of OPF problem. In these solutions, voltage at atleast one of the buses is very low. These solutions are ruled out once reasonable voltage bounds (5% or 10%) are applied. Following is the data of few low voltage local solutions which we have obtained. Note that by scaling up the demands, the voltage profile of local solution(s) improves. Brief discussion of these solutions can be found in a technical report (Link).

## Some useful Scripts

Send questions and requests to w.a.bukhsh@sms.ed.ac.uk

Last Updated: May 28, 2013