Optimization-Based Exploration of the Feasible Power Flow Space for OPF Data Collection
Julia
Optimization-Based Exploration of the Feasible Power Flow Space for Rapid Data Collection
Test functions statement
Following is a subset of the functions which were experimentally tested in this paper. In the following, $\Gamma$ is the set of all previously collected data points, $G$ is the set of dispatchable generator buses, and $N$ is the set of all buses. Lower case variables are decision variables (e.g., $p_{i}$), while upper case variables are numerical data points (e.g., $P_{i,j}$). In our tests, we also attempted to normalize all variables using statistical metrics from the exhaustive set. This normalization aimed at scaling all variable distances between zero and one. However, this strategy is omitted from this paper, since it did not present significant improvements in the numerical study.
This section shows in tables the multi-dimensional Hausdorff distances after 301 iterations computed after the euclidean distance of two variables is calculated. This numerical study considers two combinations: the complex power distance and the active power with the voltage magnitude distance.
The N dimension Hausdorff distance algorithm is applied to all the functions listed above in five test systems of the IEEE library: 3-bus, 5-bus, 14-bus, 30-bus, and 57-bus.
The solver chosen for this task is the Ipopt, an interior point optimizer. It is an open-source software for large-scale non-linear optimization. This optimizer works swiftly with the data of this report. However, there are some functions which are not capable of optimizing. Hence the results stated as "DNF" mean that the function could not be solved with the used software. It might be solvable with a more powerful and more expensive optimizer, but they will not qualify for the post-analysis in this report.
Furthermore, the "DNF" status encloses a wide range of different errors. From maximum iterations exceeded to an error in the step computation, to steps size becomes too small. The reasons they cannot be solved will not be considered, and they will just be labelled as "DNF".
Complex power values
The following table shows the values of the complex power Hausdorff distance.
F
IEEE3
IEEE5
IEEE 14
IEEE 30
IEEE 57
1
0,627106
6,569731
0,494571
0,335585
4,477464
2
DNF
DNF
DNF
DNF
DNF
3
0,480737
3,4464
DNF
0,250789
2,424641
4
0,511438
3,320618
0,222556
0,23554
1,925264
5
0,473523
3,336494
DNF
0,245588
DNF
6
0,737029
DNF
0,269667
0,32102
DNF
7
0,737029
DNF
0,384685
0,335581
DNF
8
0,847258
3,033554
0,251332
0,2223
DNF
9
0,627106
7,335899
0,428832
0,309139
3,572925
10
0,983041
DNF
0,466129
0,374483
DNF
11
0,479627
4,209596
0,237468
DNF
DNF
12
0,649108
3,321969
DNF
0,250216
1,610526
13
0,607738
3,25027
DNF
0,224168
1,493927
14
DNF
DNF
DNF
DNF
DNF
15
DNF
DNF
DNF
0,283906
DNF
16
DNF
DNF
DNF
DNF
DNF
17
0,459662
3,554565
0,257766
0,234971
2,340729
18
0,51359
3,253236
0,218473
0,223962
1,86068
19
0,474246
3,47093
0,248185
0,224916
DNF
20
DNF
DNF
DNF
DNF
4,477464
21
DNF
DNF
DNF
0,32102
4,477464
22
0,737029
DNF
0,428832
0,335585
DNF
23
DNF
DNF
0,528889
0,335585
DNF
24-25
DNF
DNF
DNF
DNF
DNF
26
0,734689
4,434955
0,377998
0,301497
1,9555
27
0,731707
4,48439
0,31687
0,303438
2,024717
28
0,710965
4,43401
0,342646
0,271446
1,912997
29
DNF
DNF
DNF
DNF
DNF
30
0,737253
4,504636
0,417803
0,418933
2,581535
31
0,737448
4,400133
0,428267
0,421751
2,698014
32
0,737264
4,311681
0,437301
0,419949
2,797347
33
0,382181
4,192798
0,368557
0,294004
1,883026
34
0,431283
3,811446
0,304908
0,292869
1,813766
35
0,737029
DNF
0,428844
0,32102
DNF
36
0,457824
3,626734
0,211565
0,27462
1,791248
37
0,460138
3,280765
0,2183
0,23497
1,808853
38
0,799807
3,121847
0,249082
DNF
1,390772
39-40
DNF
DNF
DNF
DNF
DNF
Active power and voltage magnitude values
The following table compares a multi-dimensional profile with the euclidean distances of voltage magnitude and active power generation.