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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: v0.17.2

Ipopt.jl: v0.6.2

PGLib OPF: v20.07

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 2.0515e+03 2.1781e+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_ieee 30 41 7.4728e+03 8.2085e+03 18.81 18.84 <1 <1 <1 <1
pglib_opf_case39_epri 39 46 1.3689e+05 1.3842e+05 0.55 0.56 <1 <1 <1 <1
pglib_opf_case57_ieee 57 80 3.4773e+04 3.7589e+04 0.16 0.16 <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 1.0504e+05 1.0729e+05 0.75 0.75 <1 <1 <1 <1
pglib_opf_case118_ieee 118 186 9.3101e+04 9.7214e+04 0.79 0.91 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc 162 284 1.0146e+05 1.0808e+05 5.84 5.95 <1 <1 <1 <1
pglib_opf_case179_goc 179 263 7.5188e+05 7.5427e+05 0.16 0.16 <1 <1 <1 <1
pglib_opf_case200_activ 200 245 2.7480e+04 2.7558e+04 0.01 0.01 <1 <1 <1 <1
pglib_opf_case240_pserc 240 448 3.2714e+06 3.3297e+06 2.73 2.78 <1 3 4 2
pglib_opf_case300_ieee 300 411 5.1785e+05 5.6522e+05 2.58 2.63 <1 <1 <1 <1
pglib_opf_case500_goc 500 733 4.4055e+05 4.5495e+05 0.25 0.25 <1 <1 2 <1
pglib_opf_case588_sdet 588 686 3.1013e+05 3.1314e+05 1.91 2.14 <1 <1 2 <1
pglib_opf_case793_goc 793 913 2.5831e+05 2.6020e+05 1.32 1.33 <1 2 3 <1
pglib_opf_case1354_pegase 1354 1991 1.2182e+06 1.2588e+06 1.56 1.57 <1 4 6 3
pglib_opf_case1888_rte 1888 2531 1.3529e+06 1.4025e+06 2.05 2.05 <1 8 8 31
pglib_opf_case1951_rte 1951 2596 2.0316e+06 2.0856e+06 0.13 0.14 <1 18 9 5
pglib_opf_case2000_goc 2000 3639 9.4304e+05 9.7343e+05 0.31 0.31 <1 7 9 4
pglib_opf_case2312_goc 2312 3013 4.4033e+05 4.4133e+05 1.90 1.90 <1 6 10 3
pglib_opf_case2383wp_k 2383 2896 1.8041e+06 1.8682e+06 0.97 1.04 <1 7 10 5
pglib_opf_case2736sp_k 2736 3504 1.2760e+06 1.3080e+06 0.30 0.31 <1 6 11 4
pglib_opf_case2737sop_k 2737 3506 7.6401e+05 7.7773e+05 0.26 0.27 <1 5 9 3
pglib_opf_case2742_goc 2742 4673 2.5970e+05 2.7571e+05 1.33 1.35 <1 28 14 6
pglib_opf_case2746wop_k 2746 3514 1.1782e+06 1.2083e+06 0.36 0.37 <1 5 10 4
pglib_opf_case2746wp_k 2746 3514 1.5814e+06 1.6317e+06 0.32 0.33 <1 6 10 5
pglib_opf_case2848_rte 2848 3776 1.2677e+06 1.2866e+06 0.12 0.13 <1 16 13 7
pglib_opf_case2853_sdet 2853 3921 2.0370e+06 2.0524e+06 0.87 0.91 <1 9 12 6
pglib_opf_case2868_rte 2868 3808 1.9667e+06 2.0096e+06 0.10 0.10 <1 14 13 8
pglib_opf_case2869_pegase 2869 4582 2.3864e+06 2.4628e+06 1.01 1.01 <1 12 20 7
pglib_opf_case3012wp_k 3012 3572 2.5090e+06 2.6008e+06 0.98 1.03 <1 9 14 12
pglib_opf_case3022_goc 3022 4135 5.9922e+05 6.0138e+05 2.76 2.77 <1 10 14 5
pglib_opf_case3120sp_k 3120 3693 2.0880e+06 2.1480e+06 0.55 0.56 <1 9 12 5
pglib_opf_case3375wp_k 3374 4161 7.3170e+06 7.4382e+06 0.54 0.55 <1 11 28 6
pglib_opf_case3970_goc 3970 6641 9.3422e+05 9.6099e+05 0.34 0.34 2 18 23 12
pglib_opf_case4020_goc 4020 6988 7.9506e+05 8.2225e+05 1.22 1.23 <1 21 33 13
pglib_opf_case4601_goc 4601 7199 7.9381e+05 8.2624e+05 0.53 0.54 2 22 28 14
pglib_opf_case4619_goc 4619 8150 4.5744e+05 4.7670e+05 0.88 0.91 2 19 32 23
pglib_opf_case4661_sdet 4661 5997 2.2163e+06 2.2513e+06 1.89 1.99 <1 15 27 11
pglib_opf_case4837_goc 4837 7765 8.5040e+05 8.7226e+05 0.47 0.47 <1 20 28 11
pglib_opf_case4917_goc 4917 6726 1.3837e+06 1.3878e+06 2.50 2.50 <1 17 26 9
pglib_opf_case6468_rte 6468 9000 1.9828e+06 2.0697e+06 1.12 1.13 <1 63 84 27
pglib_opf_case6470_rte 6470 9005 2.1361e+06 2.2376e+06 1.75 1.76 2 33 43 23
pglib_opf_case6495_rte 6495 9019 2.5618e+06 3.0678e+06 15.09 15.11 2 67 63 24
pglib_opf_case6515_rte 6515 9037 2.5593e+06 2.8255e+06 6.39 6.40 2 54 43 22
pglib_opf_case9241_pegase 9241 16049 6.0287e+06 6.2431e+06 1.71 2.54 2 48 103 36
pglib_opf_case9591_goc 9591 15915 1.0309e+06 1.0617e+06 0.61 0.62 3 60 120 43
pglib_opf_case10000_goc 10000 13193 1.3461e+06 1.3540e+06 1.51 1.54 2 47 98 26
pglib_opf_case10480_goc 10480 18559 2.2158e+06 2.3146e+06 1.15 1.23 3 65 115 42
pglib_opf_case13659_pegase 13659 20467 8.7699e+06 8.9480e+06 0.98 1.39 3 54 120 61
pglib_opf_case19402_goc 19402 34704 1.8978e+06 1.9778e+06 1.18 1.19 8 139 345 110
pglib_opf_case24464_goc 24464 37816 2.5128e+06 2.6295e+06 0.95 0.97 6 118 341 98
pglib_opf_case30000_goc 30000 35393 1.0921e+06 1.1423e+06 2.88 2.89 9 258 494 119

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 1.1236e+04 5.60 9.27 <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 4.7976e+03 5.9994e+03 5.13 5.13 <1 <1 <1 <1
pglib_opf_case24_ieee_rts__api 24 38 1.2336e+05 1.3494e+05 13.01 17.88 <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_ieee__api 30 41 1.6147e+04 1.8044e+04 5.46 5.46 <1 <1 <1 <1
pglib_opf_case39_epri__api 39 46 2.4462e+05 2.4967e+05 1.70 1.72 <1 <1 <1 <1
pglib_opf_case57_ieee__api 57 80 4.7421e+04 4.9290e+04 0.08 0.08 <1 <1 <1 <1
pglib_opf_case73_ieee_rts__api 73 120 3.6236e+05 4.2263e+05 11.05 12.87 <1 <1 <1 <1
pglib_opf_case89_pegase__api 89 210 1.1729e+05 1.3017e+05 23.07 23.11 <1 <1 <1 <1
pglib_opf_case118_ieee__api 118 186 2.2448e+05 2.4224e+05 29.74 29.97 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc__api 162 284 1.1166e+05 1.2099e+05 4.33 4.36 <1 <1 <1 <1
pglib_opf_case179_goc__api 179 263 1.8900e+06 1.9320e+06 5.93 9.88 <1 <1 2 <1
pglib_opf_case200_activ__api 200 245 3.5008e+04 3.5701e+04 0.03 0.03 <1 <1 <1 <1
pglib_opf_case240_pserc__api 240 448 4.5760e+06 4.6406e+06 0.64 0.67 <1 4 5 2
pglib_opf_case300_ieee__api 300 411 6.6114e+05 6.8499e+05 0.83 0.85 <1 <1 <1 <1
pglib_opf_case500_goc__api 500 733 6.5084e+05 6.9241e+05 3.44 3.44 <1 2 2 <1
pglib_opf_case588_sdet__api 588 686 3.8834e+05 3.9476e+05 1.39 1.61 <1 <1 2 <1
pglib_opf_case793_goc__api 793 913 3.1086e+05 3.1885e+05 13.21 13.43 <1 2 3 <1
pglib_opf_case1354_pegase__api 1354 1991 1.4558e+06 1.4983e+06 0.54 0.55 <1 4 7 3
pglib_opf_case1888_rte__api 1888 2531 1.9019e+06 1.9539e+06 0.22 0.23 <1 7 15 6
pglib_opf_case1951_rte__api 1951 2596 2.3361e+06 2.4108e+06 0.51 0.57 <1 8 9 5
pglib_opf_case2000_goc__api 2000 3639 1.3934e+06 1.4686e+06 2.07 2.07 <1 8 8 4
pglib_opf_case2312_goc__api 2312 3013 5.3368e+05 5.7152e+05 13.08 13.09 <1 11 10 3
pglib_opf_case2383wp_k__api 2383 2896 2.7913e+05 2.7913e+05 0.01 0.01 <1 2 3 <1
pglib_opf_case2736sp_k__api 2736 3504 6.1114e+05 6.5394e+05 10.83 10.84 <1 7 9 3
pglib_opf_case2737sop_k__api 2737 3506 3.4557e+05 3.6715e+05 5.88 5.88 <1 6 4 2
pglib_opf_case2742_goc__api 2742 4673 5.2504e+05 6.4219e+05 24.40 24.45 <1 22 16 5
pglib_opf_case2746wop_k__api 2746 3514 5.1166e+05 5.1166e+05 0.01 0.01 <1 2 3 2
pglib_opf_case2746wp_k__api 2746 3514 5.8183e+05 5.8183e+05 0.01 0.00 <1 4 5 2
pglib_opf_case2848_rte__api 2848 3776 1.4624e+06 1.4970e+06 0.25 0.25 <1 26 18 7
pglib_opf_case2853_sdet__api 2853 3921 2.4300e+06 2.4578e+06 1.92 1.96 <1 10 13 6
pglib_opf_case2868_rte__api 2868 3808 2.2344e+06 2.2946e+06 0.17 0.18 <1 23 15 6
pglib_opf_case2869_pegase__api 2869 4582 2.8484e+06 2.9296e+06 0.99 1.00 <1 13 21 8
pglib_opf_case3012wp_k__api 3012 3572 7.2887e+05 7.2887e+05 0.00 0.00 <1 4 5 2
pglib_opf_case3022_goc__api 3022 4135 6.3985e+05 6.5189e+05 9.80 9.82 <1 9 14 4
pglib_opf_case3120sp_k__api 3120 3693 8.8346e+05 9.3692e+05 23.90 23.96 <1 12 15 4
pglib_opf_case3375wp_k__api 3374 4161 5.7582e+06 5.8478e+06 9.35 -- <1 11 21 352
pglib_opf_case3970_goc__api 3970 6641 1.0784e+06 1.4557e+06 34.53 34.58 2 37 22 9
pglib_opf_case4020_goc__api 4020 6988 1.0853e+06 1.2979e+06 17.56 17.58 2 39 28 9
pglib_opf_case4601_goc__api 4601 7199 7.1860e+05 7.9253e+05 20.39 20.51 2 29 25 10
pglib_opf_case4619_goc__api 4619 8150 9.5405e+05 1.0299e+06 8.24 8.30 3 28 32 14
pglib_opf_case4661_sdet__api 4661 5997 2.6410e+06 2.6953e+06 2.54 2.64 <1 16 27 105
pglib_opf_case4837_goc__api 4837 7765 1.0693e+06 1.1578e+06 8.10 8.15 2 36 35 12
pglib_opf_case4917_goc__api 4917 6726 1.5417e+06 1.5479e+06 8.52 8.54 <1 16 26 8
pglib_opf_case6468_rte__api 6468 9000 2.2215e+06 2.3135e+06 0.80 0.82 <1 81 56 178
pglib_opf_case6470_rte__api 6470 9005 2.4983e+06 2.6065e+06 1.19 1.20 2 52 37 80
pglib_opf_case6495_rte__api 6495 9019 2.8138e+06 2.9750e+06 1.99 2.04 2 54 65 22
pglib_opf_case6515_rte__api 6515 9037 2.8952e+06 3.0617e+06 1.87 1.89 <1 59 46 21
pglib_opf_case9241_pegase__api 9241 16049 6.7974e+06 7.0112e+06 1.84 2.67 2 64 196 806
pglib_opf_case9591_goc__api 9591 15915 1.3274e+06 1.4259e+06 13.79 13.84 5 145 115 26
pglib_opf_case10000_goc__api 10000 13193 2.2110e+06 2.3728e+06 7.60 7.65 4 52 71 27
pglib_opf_case10480_goc__api 10480 18559 2.6217e+06 2.7627e+06 4.72 4.78 4 77 95 35
pglib_opf_case13659_pegase__api 13659 20467 9.0372e+06 9.2842e+06 1.19 1.85 3 55 135 76
pglib_opf_case19402_goc__api 19402 34704 2.2861e+06 2.3987e+06 4.71 4.75 9 195 271 100
pglib_opf_case24464_goc__api 24464 37816 2.3433e+06 2.4723e+06 3.93 4.00 7 137 291 151
pglib_opf_case30000_goc__api 30000 35393 1.3219e+06 1.3530e+06 24.74 24.79 15 439 608 119

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. 2.6109e+04 0.99 3.62 <1 <1 <1 <1
pglib_opf_case14_ieee__sad 14 20 inf. 2.7768e+03 21.48 21.53 <1 <1 <1 <1
pglib_opf_case24_ieee_rts__sad 24 38 7.8122e+04 7.6918e+04 2.93 9.55 <1 <1 <1 <1
pglib_opf_case30_as__sad 30 41 inf. 8.9735e+02 2.31 7.88 <1 <1 <1 <1
pglib_opf_case30_ieee__sad 30 41 inf. 8.2085e+03 5.94 9.70 <1 <1 <1 <1
pglib_opf_case39_epri__sad 39 46 1.5067e+05 1.4834e+05 0.21 0.67 <1 <1 <1 <1
pglib_opf_case57_ieee__sad 57 80 inf. 3.8663e+04 0.35 0.71 <1 <1 <1 <1
pglib_opf_case73_ieee_rts__sad 73 120 2.3268e+05 2.2760e+05 2.54 6.73 <1 <1 <1 <1
pglib_opf_case89_pegase__sad 89 210 inf. 1.0729e+05 0.71 0.73 <1 <1 <1 <1
pglib_opf_case118_ieee__sad 118 186 inf. 1.0516e+05 6.79 8.17 <1 <1 <1 <1
pglib_opf_case162_ieee_dtc__sad 162 284 1.0629e+05 1.0869e+05 6.25 6.48 <1 <1 <1 <1
pglib_opf_case179_goc__sad 179 263 inf. 7.6253e+05 1.01 1.12 <1 <1 <1 <1
pglib_opf_case200_activ__sad 200 245 inf. 2.7558e+04 0.01 0.01 <1 <1 <1 <1
pglib_opf_case240_pserc__sad 240 448 inf. 3.4054e+06 4.37 4.93 <1 4 4 2
pglib_opf_case300_ieee__sad 300 411 5.2729e+05 5.6570e+05 2.43 2.61 <1 <1 <1 <1
pglib_opf_case500_goc__sad 500 733 inf. 4.8740e+05 6.45 6.67 <1 <1 2 <1
pglib_opf_case588_sdet__sad 588 686 inf. 3.2936e+05 5.98 6.67 <1 <1 2 <1
pglib_opf_case793_goc__sad 793 913 inf. 2.8580e+05 6.26 7.97 <1 2 3 <1
pglib_opf_case1354_pegase__sad 1354 1991 inf. 1.2588e+06 1.53 1.57 <1 4 6 3
pglib_opf_case1888_rte__sad 1888 2531 1.3532e+06 1.4139e+06 2.81 2.82 <1 9 8 19
pglib_opf_case1951_rte__sad 1951 2596 inf. 2.0924e+06 0.42 0.46 2 17 9 5
pglib_opf_case2000_goc__sad 2000 3639 inf. 9.9288e+05 1.35 1.52 2 7 11 4
pglib_opf_case2312_goc__sad 2312 3013 inf. 4.6235e+05 3.40 3.93 2 7 10 4
pglib_opf_case2383wp_k__sad 2383 2896 inf. 1.9112e+06 1.93 2.86 2 8 10 5
pglib_opf_case2736sp_k__sad 2736 3504 inf. 1.3266e+06 1.32 1.58 2 7 11 5
pglib_opf_case2737sop_k__sad 2737 3506 inf. 7.9095e+05 1.70 1.88 2 7 10 4
pglib_opf_case2742_goc__sad 2742 4673 2.5970e+05 2.7571e+05 1.34 1.36 <1 28 15 5
pglib_opf_case2746wop_k__sad 2746 3514 inf. 1.2337e+06 1.97 2.32 2 7 8 4
pglib_opf_case2746wp_k__sad 2746 3514 inf. 1.6669e+06 1.65 2.19 2 7 9 5
pglib_opf_case2848_rte__sad 2848 3776 inf. 1.2890e+06 0.23 0.25 2 16 13 6
pglib_opf_case2853_sdet__sad 2853 3921 inf. 2.0692e+06 1.65 1.70 3 9 11 6
pglib_opf_case2868_rte__sad 2868 3808 inf. 2.0213e+06 0.56 0.59 2 16 14 6
pglib_opf_case2869_pegase__sad 2869 4582 inf. 2.4687e+06 1.02 1.12 3 11 20 7
pglib_opf_case3012wp_k__sad 3012 3572 inf. 2.6195e+06 1.35 1.56 2 10 15 14
pglib_opf_case3022_goc__sad 3022 4135 5.9922e+05 6.0143e+05 2.76 2.77 <1 9 13 5
pglib_opf_case3120sp_k__sad 3120 3693 inf. 2.1749e+06 1.38 1.52 3 11 18 6
pglib_opf_case3375wp_k__sad 3374 4161 7.3196e+06 7.4382e+06 0.50 0.55 <1 11 68 7
pglib_opf_case3970_goc__sad 3970 6641 inf. 9.6555e+05 0.63 0.76 5 20 24 12
pglib_opf_case4020_goc__sad 4020 6988 inf. 8.8969e+05 8.45 8.66 4 28 32 13
pglib_opf_case4601_goc__sad 4601 7199 1.1956e+06 8.7818e+05 6.25 6.37 3 29 28 14
pglib_opf_case4619_goc__sad 4619 8150 inf. 4.8435e+05 1.95 2.00 5 22 31 15
pglib_opf_case4661_sdet__sad 4661 5997 inf. 2.2610e+06 1.79 1.96 2 15 27 12
pglib_opf_case4837_goc__sad 4837 7765 inf. 8.7712e+05 0.73 0.85 6 22 27 11
pglib_opf_case4917_goc__sad 4917 6726 1.3843e+06 1.3890e+06 2.45 2.52 <1 17 24 9
pglib_opf_case6468_rte__sad 6468 9000 1.9828e+06 2.0697e+06 1.10 1.12 <1 63 69 30
pglib_opf_case6470_rte__sad 6470 9005 2.1391e+06 2.2416e+06 1.87 1.91 2 35 41 22
pglib_opf_case6495_rte__sad 6495 9019 2.5618e+06 3.0678e+06 14.99 15.11 2 69 56 23
pglib_opf_case6515_rte__sad 6515 9037 2.5595e+06 2.8698e+06 7.82 7.85 2 57 46 21
pglib_opf_case9241_pegase__sad 9241 16049 inf. 6.3185e+06 2.40 2.47 7 52 90 36
pglib_opf_case9591_goc__sad 9591 15915 inf. 1.1674e+06 9.35 9.56 11 83 112 42
pglib_opf_case10000_goc__sad 10000 13193 inf. 1.4902e+06 5.35 6.77 13 44 67 26
pglib_opf_case10480_goc__sad 10480 18559 inf. 2.3147e+06 1.14 1.23 25 65 107 41
pglib_opf_case13659_pegase__sad 13659 20467 inf. 9.0422e+06 1.63 1.68 16 62 125 43
pglib_opf_case19402_goc__sad 19402 34704 1.9102e+06 1.9838e+06 1.44 1.49 10 162 321 108
pglib_opf_case24464_goc__sad 24464 37816 2.5549e+06 2.6540e+06 1.77 1.84 10 145 312 101
pglib_opf_case30000_goc__sad 30000 35393 1.2702e+06 1.2866e+06 10.14 11.84 10 336 481 120