The results of using PowerModelsADAv0.1.1 on 9 test cases from PGLib-OPF is shown here. We benchmark three distributed algorithms with 5 power flow formulations.
We run the three distributed algorithms on a high-performance computing service with a 16-core CPU and 16GB of RAM. We produced the results shown here using Julia v1.8, and Ipopt solver.
We report the results that achieved the $l_2$-norm of the mismatches less than 0.01 (radians and per unit) within 10,000 iterations and the absolute value of the relative error less than 1% of the central solution from PowerModels.jl.
We tune the ADAs parameters by selecting large values and gradually reducing the values until reaching a good solution. For the ADMM and APP, we started with $\alpha = 10^6$ and divided by 10 for the next run, while for the ATC we started with $\alpha =1.2$ and subtracted 0.099 for the next run.
| Algorithm | | ADMM | | ATC | | APP | |
|---|
| Case name | Area | Time | Itr. | Time | Itr. | Time | Itr. |
| 14_ieee | 2 | 1.13 | 14 | 1.70 | 28 | 5.36 | 31 |
| 24_ieee_rts | 4 | 21.02 | 97 | 7.82 | 67 | 37.84 | 207 |
| 30_ieee | 3 | 2.18 | 24 | 3.89 | 43 | 2.33 | 25 |
| 30pwl | 3 | 7.40 | 24 | 4.08 | 36 | 10.73 | 49 |
| 39_epri | 3 | 20.14 | 89 | 239.80 | 1261 | 179.63 | 873 |
| 73_ieee_rts | 3 | 14.37 | 61 | 18.61 | 58 | 23.02 | 83 |
| 179_goc | 3 | 31.42 | 66 | 62.06 | 81 | 76.82 | 166 |
| 300_ieee | 4 | 21.51 | 66 | 651.26 | 920 | 28.16 | 77 |
| 588_sdet | 8 | 295.05 | 871 | 3133.82 | 1971 | 437.17 | 1283 |
| Algorithm | | ADMM | | ATC | | APP | |
|---|
| Case name | Area | Time | Itr. | Time | Itr. | Time | Itr. |
| 14_ieee | 2 | 1.04 | 14 | 1.75 | 28 | 2.80 | 33 |
| 24_ieee_rts | 4 | 11.45 | 95 | 8.19 | 66 | 23.70 | 206 |
| 30_ieee | 3 | 3.20 | 22 | 3.53 | 40 | 3.36 | 24 |
| 30pwl | 3 | 1.07 | 10 | 6.82 | 59 | 6.13 | 48 |
| 39_epri | 3 | 11.40 | 86 | 323.25 | 1243 | 12.12 | 95 |
| 73_ieee_rts | 3 | 10.38 | 60 | 21.85 | 58 | 19.76 | 116 |
| 179_goc | 3 | 47.25 | 122 | 63.58 | 83 | 64.74 | 170 |
| 300_ieee | 4 | 17.89 | 44 | 1088.83 | 900 | 33.34 | 94 |
| 588_sdet | 8 | 401.70 | 1031 | 3838.72 | 1977 | 473.00 | 1181 |
| Algorithm | | ADMM | | ATC | | APP | |
|---|
| Case name | Area | Time | Itr. | Time | Itr. | Time | Itr. |
| 14_ieee | 2 | 1.24 | 15 | 0.79 | 45 | 1.24 | 21 |
| 24_ieee_rts | 4 | 12.02 | 174 | 2.61 | 60 | 14.05 | 199 |
| 30_ieee | 3 | 1.41 | 21 | 0.35 | 45 | 1.44 | 20 |
| 30pwl | 3 | 1.53 | 18 | 0.34 | 42 | 1.38 | 20 |
| 39_epri | 3 | 4.90 | 69 | 6.181 | 69 | 4.51 | 64 |
| 73_ieee_rts | 3 | 6.81 | 75 | 4.88 | 55 | 6.77 | 79 |
| 179_goc | 3 | 4.56 | 37 | 3.24 | 27 | 5.21 | 44 |
| 300_ieee | 4 | 3.60 | 26 | 11.31 | 58 | 6.03 | 36 |
| 588_sdet | 8 | 106.01 | 656 | 18.535 | 655 | 185.20 | 1156 |
| Algorithm | | ADMM | | ATC | | APP | |
|---|
| Case name | Area | Time | Itr. | Time | Itr. | Time | Itr. |
| 14_ieee | 2 | 1.29 | 12 | 2.16 | 39 | 0.98 | 12 |
| 24_ieee_rts | 4 | 3.85 | 39 | 4.18 | 32 | 4.94 | 51 |
| 30_ieee | 3 | 1.32 | 12 | 3.96 | 33 | 1.46 | 13 |
| 30pwl | 3 | 1.30 | 11 | 4.53 | 29 | 1.42 | 13 |
| 39_epri | 3 | 5.34 | 41 | 8.53 | 47 | 16.12 | 119 |
| 73_ieee_rts | 3 | 0.51 | 3 | 8.03 | 23 | 0.45 | 3 |
| 179_goc | 3 | 7.56 | 16 | 20.87 | 23 | 3.54 | 8 |
| 300_ieee | 4 | 5.64 | 11 | 51.75 | 42 | 7.18 | 14 |
| 588_sdet | 8 | 87.89 | 131 | 145.32 | 53 | 85.91 | 130 |
| Algorithm | | ADMM | | ATC | | APP | |
|---|
| Case name | Area | Time | Itr. | Time | Itr. | Time | Itr. |
| 14_ieee | 2 | 2.09 | 15 | 4.37 | 24 | 4.47 | 15 |
| 24_ieee_rts | 4 | 15.53 | 55 | 22.07 | 50 | 19.10 | 66 |
| 30_ieee | 3 | 11.05 | 32 | 12.66 | 33 | 9.89 | 30 |
| 30pwl | 3 | 1.73 | 9 | 11.25 | 29 | 2.68 | 14 |
| 39_epri | 3 | 31.80 | 85 | 82.02 | 104 | 36.31 | 101 |
| 73_ieee_rts | 3 | 2.59 | 7 | 1268.75 | 1009 | 2.81 | 7 |
| 179_goc | 3 | 49.63 | 24 | 118.34 | 24 | 77.16 | 39 |
| 300_ieee | 4 | 18.52 | 11 | 602.90 | 60 | 57.31 | 27 |
| 588_sdet | 8 | 321.28 | 177 | 500.23 | 56 | 316.85 | 177 |