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Baseline Results

This section presents the results of running PowerModels.jl on the OPF benchmarks from the PGLib Archive. providing baseline results for these test cases. All models were solved using IPOPT.

Note that the displayed solve times are only approximate. These times do not include Julia's JIT time, around 2-5 seconds, and use the HSL ma27 solver in IPOPT. The default linear solver will increase the runtime by 2-6x.

Software Versions

PowerModels.jl: v0.7.2, 31e7627c4844fb8c54ff7206c0937cc907368e1e

Ipopt.jl: v0.3.0, ac35cedbdd602bb0f1c257a5e04b516df5119155

PGLib OPF: v18.08, dbfab62e1cffad0a59f6c128b040273ff8ee2f9b

Hardware: Dual Intel 2.10GHz CPUs, 128GB RAM

Typical Operating Conditions (TYP)

Case Name Nodes Edges DC ($/h) AC ($/h) QC Gap (%) SOC Gap (%) DC Time (sec.) AC Time (sec.) QC Time (sec.) SOC Time (sec.)
pglib_opf_case3_lmbd 3 3 5.6959e+03 5.8126e+03 1.22 1.32 <1 <1 <1 <1
pglib_opf_case5_pjm 5 6 1.7480e+04 1.7552e+04 14.55 14.55 <1 <1 <1 <1
pglib_opf_case14_ieee 14 20 5.9257e+03 6.2913e+03 0.11 0.11 <1 <1 <1 <1
pglib_opf_case24_ieee_rts 24 38 6.1001e+04 6.3352e+04 0.02 0.02 <1 <1 <1 <1
pglib_opf_case30_as 30 41 7.6760e+02 8.0313e+02 0.06 0.06 <1 <1 <1 <1
pglib_opf_case30_fsr 30 41 5.6521e+02 5.7577e+02 0.39 0.39 <1 <1 <1 <1
pglib_opf_case30_ieee 30 41 1.1081e+04 1.1974e+04 10.78 10.81 <1 <1 <1 <1
pglib_opf_case39_epri 39 46 1.4145e+05 1.4298e+05 0.49 0.49 <1 <1 <1 <1
pglib_opf_case57_ieee 57 80 3.5441e+04 3.9323e+04 0.46 0.46 <1 <1 <1 <1
pglib_opf_case73_ieee_rts 73 120 1.8300e+05 1.8976e+05 0.04 0.04 <1 <1 <1 <1
pglib_opf_case89_pegase 89 210 1.1224e+05 1.1633e+05 0.74 0.75 <1 <1 <1 <1
pglib_opf_case118_ieee 118 186 1.0962e+05 1.1580e+05 2.20 2.27 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc 162 284 1.1666e+05 1.2615e+05 7.54 7.67 <1 <1 <1 <1
pglib_opf_case179_goc 179 263 8.2381e+05 8.2627e+05 0.12 0.13 <1 <1 <1 <1
pglib_opf_case200_tamu 200 245 2.7480e+04 2.7558e+04 0.01 0.01 <1 <1 <1 <1
pglib_opf_case240_pserc 240 448 3.5056e+06 3.5700e+06 3.81 3.92 <1 4 4 2
pglib_opf_case300_ieee 300 411 5.9324e+05 6.6422e+05 2.56 2.60 <1 <1 <1 <1
pglib_opf_case500_tamu 500 597 7.0784e+04 7.2578e+04 5.39 5.39 <1 2 2 <1
pglib_opf_case588_sdet 588 686 3.7799e+05 3.8155e+05 1.68 1.87 <1 <1 2 <1
pglib_opf_case1354_pegase 1354 1991 1.3140e+06 1.3640e+06 2.40 2.41 <1 6 6 3
pglib_opf_case1888_rte 1888 2531 1.5111e+06 1.5654e+06 1.82 1.82 <1 15 9 5
pglib_opf_case1951_rte 1951 2596 2.3128e+06 2.3753e+06 0.12 0.13 <1 18 10 5
pglib_opf_case2000_tamu 2000 3206 1.2014e+06 1.2285e+06 0.20 0.21 <1 11 9 3
pglib_opf_case2316_sdet 2316 3017 2.2234e+06 2.2567e+06 2.22 2.22 <1 8 13 5
pglib_opf_case2383wp_k 2383 2896 1.8041e+06 1.8685e+06 0.99 1.05 <1 9 10 5
pglib_opf_case2736sp_k 2736 3504 1.2760e+06 1.3079e+06 0.29 0.30 <1 8 11 4
pglib_opf_case2737sop_k 2737 3506 7.6401e+05 7.7763e+05 0.25 0.26 <1 6 8 4
pglib_opf_case2746wop_k 2746 3514 1.1782e+06 1.2083e+06 0.36 0.37 <1 7 9 4
pglib_opf_case2746wp_k 2746 3514 1.5814e+06 1.6318e+06 0.32 0.33 <1 7 9 4
pglib_opf_case2848_rte 2848 3776 1.3636e+06 1.3847e+06 0.12 0.12 <1 21 14 7
pglib_opf_case2853_sdet 2853 3921 2.4498e+06 2.4694e+06 1.43 1.47 <1 11 13 9
pglib_opf_case2868_rte 2868 3808 2.2053e+06 2.2599e+06 0.11 0.11 <1 21 14 8
pglib_opf_case2869_pegase 2869 4582 2.5166e+06 2.6050e+06 1.07 1.08 <1 14 20 7
pglib_opf_case3012wp_k 3012 3572 2.5090e+06 2.6008e+06 0.98 1.03 <1 12 14 8
pglib_opf_case3120sp_k 3120 3693 2.0880e+06 2.1457e+06 0.54 0.55 <1 11 15 6
pglib_opf_case3375wp_k 3375 4161 7.3170e+06 7.4357e+06 0.50 0.52 <1 14 159 22
pglib_opf_case4661_sdet 4661 5997 2.7412e+06 2.7858e+06 2.26 2.35 <1 20 29 27
pglib_opf_case6468_rte 6468 9000 2.1619e+06 2.2623e+06 1.07 1.07 <1 97 66 27
pglib_opf_case6470_rte 6470 9005 2.4454e+06 2.5558e+06 1.95 1.96 2 45 64 24
pglib_opf_case6495_rte 6495 9019 2.8481e+06 3.4777e+06 16.73 16.75 2 86 49 24
pglib_opf_case6515_rte 6515 9037 2.8484e+06 3.1971e+06 7.86 7.87 2 70 63 23
pglib_opf_case9241_pegase 9241 16049 6.5179e+06 6.7747e+06 1.99 2.84 2 62 118 36
pglib_opf_case10000_tamu 10000 12706 2.4366e+06 2.4859e+06 0.37 0.72 2 89 123 38
pglib_opf_case13659_pegase 13659 20467 1.0565e+07 1.0781e+07 0.95 1.35 3 95 129 44

Congested Operating Conditions (API)

Case Name Nodes Edges DC ($/h) AC ($/h) QC Gap (%) SOC Gap (%) DC Time (sec.) AC Time (sec.) QC Time (sec.) SOC Time (sec.)
pglib_opf_case3_lmbd__api 3 3 1.0444e+04 1.1242e+04 5.63 9.32 <1 <1 <1 <1
pglib_opf_case5_pjm__api 5 6 7.5433e+04 7.6377e+04 4.09 4.09 <1 <1 <1 <1
pglib_opf_case14_ieee__api 14 20 1.1586e+04 1.3311e+04 1.77 1.77 <1 <1 <1 <1
pglib_opf_case24_ieee_rts__api 24 38 1.2336e+05 1.3495e+05 13.01 17.87 <1 <1 <1 <1
pglib_opf_case30_as__api 30 41 3.0921e+03 4.9962e+03 44.61 44.61 <1 <1 <1 <1
pglib_opf_case30_fsr__api 30 41 6.7254e+02 7.0115e+02 2.76 2.76 <1 <1 <1 <1
pglib_opf_case30_ieee__api 30 41 2.1698e+04 2.4032e+04 3.73 3.73 <1 <1 <1 <1
pglib_opf_case39_epri__api 39 46 2.5216e+05 2.5721e+05 1.57 1.60 <1 <1 <1 <1
pglib_opf_case57_ieee__api 57 80 5.7032e+04 5.9274e+04 0.08 0.08 <1 <1 <1 <1
pglib_opf_case73_ieee_rts__api 73 120 3.6238e+05 4.2273e+05 11.07 12.89 <1 <1 <1 <1
pglib_opf_case89_pegase__api 89 210 1.2974e+05 1.4198e+05 8.13 8.14 <1 <1 <1 <1
pglib_opf_case118_ieee__api 118 186 2.9247e+05 3.1642e+05 28.63 28.70 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc__api 162 284 1.3016e+05 1.4351e+05 5.44 5.49 <1 <1 <1 <1
pglib_opf_case179_goc__api 179 263 2.0801e+06 2.1326e+06 7.18 12.02 <1 2 2 <1
pglib_opf_case200_tamu__api 200 245 3.7111e+04 3.7694e+04 0.02 0.02 <1 <1 <1 <1
pglib_opf_case240_pserc__api 240 448 5.3109e+06 5.3917e+06 0.80 0.83 <1 5 6 2
pglib_opf_case300_ieee__api 300 411 7.3994e+05 7.7549e+05 0.88 0.95 <1 <1 2 <1
pglib_opf_case500_tamu__api 500 597 3.8864e+04 4.0343e+04 0.08 0.08 <1 2 2 <1
pglib_opf_case588_sdet__api 588 686 4.9162e+05 4.9964e+05 0.93 1.17 <1 2 2 <1
pglib_opf_case1354_pegase__api 1354 1991 1.6604e+06 1.7187e+06 0.85 0.86 <1 6 10 3
pglib_opf_case1888_rte__api 1888 2531 2.2014e+06 2.2625e+06 0.29 0.29 <1 10 17 6
pglib_opf_case1951_rte__api 1951 2596 2.7694e+06 2.8658e+06 0.44 0.47 <1 11 9 5
pglib_opf_case2000_tamu__api 2000 3206 1.2563e+06 1.2883e+06 2.47 2.49 <1 18 11 3
pglib_opf_case2316_sdet__api 2316 3017 2.7281e+06 2.7745e+06 1.96 1.96 <1 9 12 4
pglib_opf_case2383wp_k__api 2383 2896 2.7913e+05 2.7913e+05 0.01 0.01 <1 3 3 <1
pglib_opf_case2736sp_k__api 2736 3504 5.8612e+05 6.2604e+05 12.97 12.98 <1 9 10 3
pglib_opf_case2737sop_k__api 2737 3506 3.4557e+05 3.5871e+05 3.67 3.67 <1 8 4 2
pglib_opf_case2746wop_k__api 2746 3514 5.1166e+05 5.1166e+05 0.01 0.01 <1 4 4 2
pglib_opf_case2746wp_k__api 2746 3514 5.8183e+05 5.8183e+05 0.01 0.00 <1 5 5 2
pglib_opf_case2848_rte__api 2848 3776 1.6698e+06 1.7094e+06 0.22 0.22 <1 32 15 8
pglib_opf_case2853_sdet__api 2853 3921 2.9598e+06 2.9950e+06 2.31 2.36 <1 14 15 7
pglib_opf_case2868_rte__api 2868 3808 2.6809e+06 2.7669e+06 0.18 0.19 <1 33 22 6
pglib_opf_case2869_pegase__api 2869 4582 3.1794e+06 3.2878e+06 1.32 1.32 <1 15 20 8
pglib_opf_case3012wp_k__api 3012 3572 7.2887e+05 7.2887e+05 0.00 0.00 <1 5 6 2
pglib_opf_case3120sp_k__api 3120 3693 9.0936e+05 9.6963e+05 24.15 24.18 <1 15 14 4
pglib_opf_case3375wp_k__api 3375 4161 5.7641e+06 5.8861e+06 9.46 -- <1 14 20 248
pglib_opf_case4661_sdet__api 4661 5997 3.2725e+06 3.3429e+06 2.17 2.27 <1 21 32 134
pglib_opf_case6468_rte__api 6468 9000 2.6154e+06 2.7179e+06 0.41 0.42 <1 78 62 31
pglib_opf_case6470_rte__api 6470 9005 3.0479e+06 3.1769e+06 0.77 0.78 2 56 41 22
pglib_opf_case6495_rte__api 6495 9019 3.5653e+06 3.8236e+06 4.13 4.18 2 66 64 26
pglib_opf_case6515_rte__api 6515 9037 3.4761e+06 3.7086e+06 2.76 2.83 2 72 53 190
pglib_opf_case9241_pegase__api 9241 16049 7.8361e+06 8.1143e+06 2.17 3.04 2 161 112 840
pglib_opf_case10000_tamu__api 10000 12706 1.7660e+06 1.8164e+06 7.26 7.93 5 137 124 37
pglib_opf_case13659_pegase__api 13659 20467 1.0956e+07 1.1280e+07 1.23 1.92 3 79 121 57

Small Angle Difference Conditions (SAD)

Case Name Nodes Edges DC ($/h) AC ($/h) QC Gap (%) SOC Gap (%) DC Time (sec.) AC Time (sec.) QC Time (sec.) SOC Time (sec.)
pglib_opf_case3_lmbd__sad 3 3 5.8560e+03 5.9593e+03 1.42 3.75 <1 <1 <1 <1
pglib_opf_case5_pjm__sad 5 6 inf. 2.6115e+04 0.99 3.62 <1 <1 <1 <1
pglib_opf_case14_ieee__sad 14 20 inf. 6.7834e+03 7.16 7.21 <1 <1 <1 <1
pglib_opf_case24_ieee_rts__sad 24 38 7.8163e+04 7.6943e+04 2.93 9.56 <1 <1 <1 <1
pglib_opf_case30_as__sad 30 41 inf. 8.9749e+02 2.32 7.88 <1 <1 <1 <1
pglib_opf_case30_fsr__sad 30 41 inf. 5.7679e+02 0.41 0.47 <1 <1 <1 <1
pglib_opf_case30_ieee__sad 30 41 inf. 1.1974e+04 3.42 5.65 <1 <1 <1 <1
pglib_opf_case39_epri__sad 39 46 1.5470e+05 1.5246e+05 0.20 0.60 <1 <1 <1 <1
pglib_opf_case57_ieee__sad 57 80 inf. 4.5208e+04 0.83 1.79 <1 <1 <1 <1
pglib_opf_case73_ieee_rts__sad 73 120 2.3291e+05 2.2775e+05 2.54 6.75 <1 <1 <1 <1
pglib_opf_case89_pegase__sad 89 210 inf. 1.1657e+05 0.82 0.86 <1 <1 <1 <1
pglib_opf_case118_ieee__sad 118 186 inf. 1.2924e+05 9.48 11.53 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc__sad 162 284 1.2549e+05 1.2704e+05 8.02 8.32 <1 <1 <1 <1
pglib_opf_case179_goc__sad 179 263 inf. 8.3560e+05 1.05 1.13 <1 <1 <1 <1
pglib_opf_case200_tamu__sad 200 245 inf. 2.7558e+04 0.01 0.01 <1 <1 <1 <1
pglib_opf_case240_pserc__sad 240 448 inf. 3.6565e+06 5.24 6.19 <1 4 4 2
pglib_opf_case300_ieee__sad 300 411 6.0726e+05 6.6431e+05 2.36 2.52 <1 <1 <1 <1
pglib_opf_case500_tamu__sad 500 597 inf. 7.9234e+04 7.90 7.92 <1 2 2 <1
pglib_opf_case588_sdet__sad 588 686 inf. 4.0427e+05 6.26 6.93 <1 2 2 <1
pglib_opf_case1354_pegase__sad 1354 1991 inf. 1.3646e+06 2.37 2.45 <1 6 6 3
pglib_opf_case1888_rte__sad 1888 2531 1.5123e+06 1.5806e+06 2.73 2.74 <1 16 9 5
pglib_opf_case1951_rte__sad 1951 2596 inf. 2.3830e+06 0.41 0.45 2 25 9 5
pglib_opf_case2000_tamu__sad 2000 3206 inf. 1.2303e+06 0.33 0.35 2 12 10 3
pglib_opf_case2316_sdet__sad 2316 3017 inf. 2.2567e+06 2.18 2.22 <1 8 11 5
pglib_opf_case2383wp_k__sad 2383 2896 inf. 1.9165e+06 2.16 3.13 2 11 10 6
pglib_opf_case2736sp_k__sad 2736 3504 inf. 1.3294e+06 1.53 1.80 2 10 10 5
pglib_opf_case2737sop_k__sad 2737 3506 inf. 7.9268e+05 1.93 2.10 2 9 9 4
pglib_opf_case2746wop_k__sad 2746 3514 inf. 1.2344e+06 2.00 2.37 2 8 8 4
pglib_opf_case2746wp_k__sad 2746 3514 inf. 1.6674e+06 1.68 2.21 2 9 9 5
pglib_opf_case2848_rte__sad 2848 3776 inf. 1.3880e+06 0.28 0.30 2 22 14 6
pglib_opf_case2853_sdet__sad 2853 3921 inf. 2.4945e+06 2.39 2.46 4 11 13 8
pglib_opf_case2868_rte__sad 2868 3808 inf. 2.2718e+06 0.54 0.58 2 21 14 6
pglib_opf_case2869_pegase__sad 2869 4582 inf. 2.6204e+06 1.41 1.50 4 15 26 8
pglib_opf_case3012wp_k__sad 3012 3572 inf. 2.6213e+06 1.41 1.62 3 13 14 6
pglib_opf_case3120sp_k__sad 3120 3693 inf. 2.1755e+06 1.42 1.61 4 15 16 7
pglib_opf_case3375wp_k__sad 3375 4161 7.3197e+06 7.4357e+06 0.47 0.52 <1 14 52 60
pglib_opf_case4661_sdet__sad 4661 5997 inf. 2.8017e+06 2.31 2.51 3 21 27 78
pglib_opf_case6468_rte__sad 6468 9000 2.1619e+06 2.2623e+06 1.05 1.06 <1 91 95 28
pglib_opf_case6470_rte__sad 6470 9005 2.4483e+06 2.5597e+06 2.03 2.08 2 46 46 22
pglib_opf_case6495_rte__sad 6495 9019 2.8482e+06 3.4777e+06 16.63 16.75 2 83 54 23
pglib_opf_case6515_rte__sad 6515 9037 2.8486e+06 3.2679e+06 9.82 9.87 2 75 52 22
pglib_opf_case9241_pegase__sad 9241 16049 inf. 6.9198e+06 3.52 3.59 11 66 109 36
pglib_opf_case10000_tamu__sad 10000 12706 2.4366e+06 2.4859e+06 0.36 0.72 2 79 92 36
pglib_opf_case13659_pegase__sad 13659 20467 inf. 1.0903e+07 1.72 1.75 13 85 138 73