PowerModels Experiment Results

This section presents results of running PowerModel.jl on collections of established power network test cases from NESTA. This provides validation of the PowerModel.jl as well as a results baseline for these test cases. All models were solved using IPOPT.

Experiment Design

This experiment consists of running the following PowerModels commands,

result_ac  = run_opf(case, ACPPowerModel, IpoptSolver(tol=1e-6))
result_soc = run_opf(case, SOCWRPowerModel, IpoptSolver(tol=1e-6))
result_qc  = run_opf(case, QCWRPowerModel, IpoptSolver(tol=1e-6))

for each case in the NESTA archive. If the value of result["status"] is :LocalOptimal then the values of result["objective"] and result["solve_time"] are reported, otherwise an err. or -- is displayed. A value of n.d. indicates that no data was available. The optimality gap is defined as,

soc_gap = 100*(result_ac["objective"] - result_soc["objective"])/result_ac["objective"]

It is important to note that the result["solve_time"] value in this experiment includes Julia's JIT time. Excluding the JIT time will reduce the runtime by 2-5 seconds.

Software Versions

PowerModels.jl: v0.3.1, 4488d66ae45c2ad523c1514a384ae4cb15242e2b

Ipopt.jl: v0.2.6, 959b9c67e396a6e2307fc022d26b0d95692ee6a4

NESTA: v0.7.0, ce1ecc76f5f6d3afec9fc5e9d23c82862d96667e

Hardware: Dual Intel 2.10GHz CPUs, 128GB RAM

Typical Operating Conditions (TYP)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case3_lmbd	3	3	5.8126e+03	1.22	1.32	5	2	2
nesta_case4_gs	4	4	1.5643e+02	0.01	0.01	5	2	2
nesta_case5_pjm	5	6	1.7552e+04	14.55	14.55	5	2	2
nesta_case6_c	6	7	2.3206e+01	0.30	0.30	5	2	2
nesta_case6_ww	6	11	3.1440e+03	0.62	0.63	5	3	2
nesta_case9_wscc	9	9	5.2967e+03	0.01	0.01	5	2	2
nesta_case14_ieee	14	20	2.4405e+02	0.11	0.11	5	2	2
nesta_case24_ieee_rts	24	38	6.3352e+04	0.02	0.02	5	3	3
nesta_case29_edin	29	99	2.9895e+04	0.10	0.12	5	3	3
nesta_case30_as	30	41	8.0313e+02	0.06	0.06	5	3	3
nesta_case30_fsr	30	41	5.7577e+02	0.39	0.39	5	3	3
nesta_case30_ieee	30	41	2.0497e+02	15.65	15.89	5	2	2
nesta_case39_epri	39	46	9.6506e+04	0.05	0.05	5	3	3
nesta_case57_ieee	57	80	1.1433e+03	0.07	0.07	5	3	2
nesta_case73_ieee_rts	73	120	1.8976e+05	0.04	0.04	5	3	3
nesta_case89_pegase	89	210	5.8198e+03	0.17	0.17	5	4	3
nesta_case118_ieee	118	186	3.7186e+03	1.57	1.83	5	3	3
nesta_case162_ieee_dtc	162	284	4.2302e+03	3.96	4.03	6	4	3
nesta_case189_edin	189	206	8.4929e+02	0.22	0.22	5	4	3
nesta_case240_wecc	240	448	7.5136e+04	5.27	5.74	9	12	5
nesta_case300_ieee	300	411	1.6891e+04	1.18	1.18	6	5	3
nesta_case1354_pegase	1354	1991	7.4069e+04	0.08	0.08	10	24	23
nesta_case1397sp_eir	1418	1919	3.8890e+03	0.69	0.94	10	20	8
nesta_case1394sop_eir	1418	1920	1.3668e+03	0.58	0.83	9	28	9
nesta_case1460wp_eir	1481	1988	4.6402e+03	0.65	0.89	9	20	10
nesta_case1888_rte	1888	2531	5.9805e+04	0.38	0.38	41	22	175
nesta_case1951_rte	1951	2596	8.1738e+04	0.07	0.08	25	26	26
nesta_case2224_edin	2224	3207	3.8128e+04	6.03	6.09	18	46	15
nesta_case2383wp_mp	2383	2896	1.8685e+06	0.99	1.05	18	33	18
nesta_case2736sp_mp	2736	3504	1.3079e+06	0.29	0.30	15	35	15
nesta_case2737sop_mp	2737	3506	7.7763e+05	0.25	0.26	13	31	12
nesta_case2746wop_mp	2746	3514	1.2083e+06	0.36	0.37	14	33	13
nesta_case2746wp_mp	2746	3514	1.6318e+06	0.32	0.33	16	33	15
nesta_case2848_rte	2848	3776	5.3022e+04	0.08	0.08	86	33	255
nesta_case2868_rte	2868	3808	7.9795e+04	0.07	0.07	46	44	24
nesta_case2869_pegase	2869	4582	1.3400e+05	0.09	0.09	17	53	48
nesta_case3012wp_mp	3012	3572	2.6008e+06	0.98	1.03	21	46	25
nesta_case3120sp_mp	3120	3693	2.1457e+06	0.54	0.55	20	45	18
nesta_case3375wp_mp	3375	4161	7.4357e+06	0.50	0.52	26	344	71
nesta_case6468_rte	6468	9000	8.6829e+04	0.23	0.23	121	202	590
nesta_case6470_rte	6470	9005	9.8348e+04	0.17	0.18	109	184	99
nesta_case6495_rte	6495	9019	1.0632e+05	0.49	0.49	74	173	90
nesta_case6515_rte	6515	9037	1.0987e+05	0.43	0.43	71	143	1240
nesta_case9241_pegase	9241	16049	3.1591e+05	n.d.	1.64	169	n.d.	586
nesta_case13659_pegase	13659	20467	3.8612e+05	n.d.	1.43	599	n.d.	5234

Congested Operating Conditions (API)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case3_lmbd__api	3	3	3.6744e+02	–	2.33	5	2	2
nesta_case4_gs__api	4	4	7.6667e+02	0.64	0.64	5	2	2
nesta_case5_pjm__api	5	6	2.9963e+03	0.27	0.27	5	2	2
nesta_case6_c__api	6	7	8.1387e+02	0.34	0.34	5	2	2
nesta_case9_wscc__api	9	9	6.5623e+02	0.01	0.01	5	2	2
nesta_case14_ieee__api	14	20	3.2513e+02	1.27	1.27	5	2	2
nesta_case24_ieee_rts__api	24	38	6.4267e+03	11.88	20.70	5	3	2
nesta_case29_edin__api	29	99	2.9529e+05	0.41	0.41	5	4	3
nesta_case30_as__api	30	41	5.7008e+02	4.64	4.64	5	2	2
nesta_case30_fsr__api	30	41	3.6656e+02	45.20	45.20	5	3	2
nesta_case30_ieee__api	30	41	4.1499e+02	0.93	0.93	5	2	2
nesta_case39_epri__api	39	46	7.4604e+03	2.98	3.00	5	3	2
nesta_case57_ieee__api	57	80	1.4307e+03	0.21	0.21	5	3	3
nesta_case73_ieee_rts__api	73	120	1.9995e+04	10.98	14.20	5	3	3
nesta_case89_pegase__api	89	210	4.2554e+03	19.83	19.88	6	4	3
nesta_case118_ieee__api	118	186	1.0270e+04	43.50	43.70	6	3	3
nesta_case162_ieee_dtc__api	162	284	6.1069e+03	1.25	1.34	6	4	3
nesta_case189_edin__api	189	206	1.9141e+03	1.70	1.70	6	4	3
nesta_case240_wecc__api	240	448	1.4267e+05	0.58	0.70	10	15	6
nesta_case300_ieee__api	300	411	1.9868e+04	0.64	0.71	6	5	3
nesta_case1354_pegase__api	1354	1991	5.2449e+04	0.36	0.36	12	25	10
nesta_case1397sp_eir__api	1418	1919	6.6658e+03	1.07	1.29	10	21	10
nesta_case1394sop_eir__api	1418	1920	3.3776e+03	0.37	0.39	12	32	9
nesta_case1460wp_eir__api	1481	1988	6.4449e+03	1.54	1.69	10	21	10
nesta_case1888_rte__api	1888	2531	5.8546e+04	0.71	0.71	16	43	16
nesta_case1951_rte__api	1951	2596	7.5639e+04	0.13	0.14	18	32	118
nesta_case2224_edin__api	2224	3207	4.4435e+04	2.41	2.42	19	45	15
nesta_case2383wp_mp__api	2383	2896	2.3489e+04	0.74	0.75	14	49	12
nesta_case2736sp_mp__api	2736	3504	2.5884e+04	2.18	2.19	15	33	14
nesta_case2737sop_mp__api	2737	3506	2.1675e+04	0.39	0.40	14	34	15
nesta_case2746wop_mp__api	2746	3514	2.2803e+04	0.49	0.49	14	34	14
nesta_case2746wp_mp__api	2746	3514	2.5964e+04	0.58	0.59	14	32	14
nesta_case2848_rte__api	2848	3776	4.4032e+04	0.23	0.23	37	55	20
nesta_case2868_rte__api	2868	3808	7.5506e+04	0.20	0.21	47	56	21
nesta_case2869_pegase__api	2869	4582	9.8415e+04	0.59	0.60	24	60	23
nesta_case3012wp_mp__api	3012	3572	2.8334e+04	1.04	1.07	16	38	17
nesta_case3120sp_mp__api	3120	3693	2.3715e+04	2.73	2.75	21	40	17
nesta_case3375wp_mp__api	3375	4161	4.8939e+04	0.68	0.69	22	341	102
nesta_case6468_rte__api	6468	9000	6.8149e+04	0.89	0.91	164	195	494
nesta_case6470_rte__api	6470	9005	9.0583e+04	0.80	0.82	80	168	58
nesta_case6495_rte__api	6495	9019	8.8944e+04	1.24	1.26	85	166	58
nesta_case6515_rte__api	6515	9037	9.7217e+04	1.07	1.10	93	166	63
nesta_case9241_pegase__api	9241	16049	2.3890e+05	n.d.	2.45	191	n.d.	138
nesta_case13659_pegase__api	13659	20467	3.0284e+05	n.d.	1.73	237	n.d.	257

Small Angle Difference Conditions (SAD)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case3_lmbd__sad	3	3	5.9593e+03	1.00	3.75	5	2	2
nesta_case4_gs__sad	4	4	3.1584e+02	1.50	4.50	5	2	2
nesta_case5_pjm__sad	5	6	2.6115e+04	0.99	3.61	5	2	2
nesta_case6_c__sad	6	7	2.4376e+01	0.43	1.32	5	2	2
nesta_case6_ww__sad	6	11	3.1463e+03	0.18	0.70	5	3	2
nesta_case9_wscc__sad	9	9	5.5283e+03	0.51	1.55	5	2	2
nesta_case14_ieee__sad	14	20	2.4405e+02	0.05	0.07	5	2	2
nesta_case24_ieee_rts__sad	24	38	7.6943e+04	2.66	9.35	5	3	3
nesta_case29_edin__sad	29	99	4.1258e+04	16.46	25.90	5	3	3
nesta_case30_as__sad	30	41	8.9749e+02	2.29	7.87	5	3	2
nesta_case30_fsr__sad	30	41	5.7679e+02	0.41	0.47	5	3	3
nesta_case30_ieee__sad	30	41	2.0497e+02	4.17	6.57	5	3	2
nesta_case39_epri__sad	39	46	9.6745e+04	0.01	0.03	5	3	3
nesta_case57_ieee__sad	57	80	1.1433e+03	0.05	0.07	5	3	3
nesta_case73_ieee_rts__sad	73	120	2.2775e+05	2.28	6.53	5	3	3
nesta_case89_pegase__sad	89	210	5.8198e+03	0.13	0.14	5	3	3
nesta_case118_ieee__sad	118	186	4.1067e+03	4.46	8.23	5	3	3
nesta_case162_ieee_dtc__sad	162	284	4.2535e+03	4.31	4.56	6	4	3
nesta_case189_edin__sad	189	206	8.6482e+02	0.80	0.80	5	4	3
nesta_case240_wecc__sad	240	448	7.6495e+04	5.17	7.41	10	11	5
nesta_case300_ieee__sad	300	411	1.6894e+04	1.10	1.17	6	5	3
nesta_case1354_pegase__sad	1354	1991	7.4070e+04	0.07	0.08	10	19	16
nesta_case1397sp_eir__sad	1418	1919	4.2378e+03	7.23	7.37	11	35	9
nesta_case1394sop_eir__sad	1418	1920	1.4493e+03	3.30	4.32	10	26	9
nesta_case1460wp_eir__sad	1481	1988	5.3370e+03	0.72	0.92	10	19	9
nesta_case1888_rte__sad	1888	2531	5.9806e+04	0.37	0.38	46	26	178
nesta_case1951_rte__sad	1951	2596	8.1786e+04	0.11	0.13	28	27	215
nesta_case2224_edin__sad	2224	3207	3.8265e+04	5.45	6.04	20	45	14
nesta_case2383wp_mp__sad	2383	2896	1.9165e+06	2.13	3.12	19	33	18
nesta_case2736sp_mp__sad	2736	3504	1.3294e+06	1.52	1.80	19	35	16
nesta_case2737sop_mp__sad	2737	3506	7.9266e+05	1.92	2.10	17	34	13
nesta_case2746wop_mp__sad	2746	3514	1.2344e+06	1.99	2.37	16	28	14
nesta_case2746wp_mp__sad	2746	3514	1.6674e+06	1.66	2.21	17	32	17
nesta_case2848_rte__sad	2848	3776	5.3031e+04	0.08	0.09	92	41	26
nesta_case2868_rte__sad	2868	3808	7.9818e+04	0.08	0.10	92	45	26
nesta_case2869_pegase__sad	2869	4582	1.3402e+05	0.09	0.10	19	67	123
nesta_case3012wp_mp__sad	3012	3572	2.6213e+06	1.40	1.61	23	50	20
nesta_case3120sp_mp__sad	3120	3693	2.1755e+06	1.40	1.59	24	51	20
nesta_case3375wp_mp__sad	3375	4161	7.4357e+06	0.47	0.52	24	129	260
nesta_case6468_rte__sad	6468	9000	8.6829e+04	0.21	0.21	155	209	518
nesta_case6470_rte__sad	6470	9005	9.8357e+04	0.16	0.17	109	139	594
nesta_case6495_rte__sad	6495	9019	1.0632e+05	0.48	0.49	71	187	92
nesta_case6515_rte__sad	6515	9037	1.0995e+05	0.49	0.51	79	149	115
nesta_case9241_pegase__sad	9241	16049	3.1592e+05	n.d.	0.82	153	n.d.	840
nesta_case13659_pegase__sad	13659	20467	3.8614e+05	n.d.	0.71	505	n.d.	1749

Radial Topologies (RAD)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case9_kds__rad	9	8	inf.	–	–	5	2	2
nesta_case9_l_kds__rad	9	8	inf.	–	–	5	2	2
nesta_case30_fsr_kds__rad	30	29	6.1904e+02	1.74	1.74	5	3	2
nesta_case30_fsr_l_kds__rad	30	29	4.4584e+02	2.25	2.25	5	3	2
nesta_case30_kds__rad	30	29	4.7943e+03	11.47	11.47	5	3	2
nesta_case30_l_kds__rad	30	29	4.5623e+03	33.47	33.47	5	2	2
nesta_case57_kds__rad	57	56	1.2101e+04	13.58	13.58	5	3	3
nesta_case57_l_kds__rad	57	56	1.0173e+04	17.43	17.43	5	3	2

Non-Convex Optimization Cases (NCO)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case5_bgm__nco	5	6	1.0823e+03	9.59	10.06	5	2	2
nesta_case9_bgm__nco	9	9	3.0878e+03	10.85	10.85	5	2	2
nesta_case9_na_cao__nco	9	9	-2.1243e+02	-15.05	-18.12	5	2	2
nesta_case9_nb_cao__nco	9	9	-2.4742e+02	-15.62	-19.31	5	2	2
nesta_case14_s_cao__nco	14	20	9.6704e+03	3.83	3.83	5	2	3
nesta_case39_1_bgm__nco	39	46	1.1221e+04	3.73	3.74	5	3	3

Utility Cases (UTL)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nesta_case3_cc__utl	3	3	2.0756e+02	1.55	1.62	5	2	2
nesta_case3_cgs__utl	3	3	1.0171e+02	1.69	1.69	5	2	2
nesta_case3_ch__utl	3	5	9.8740e+01	100.01	100.01	5	2	2
nesta_case5_lmbd__utl	5	7	2.3989e+03	0.01	0.01	5	2	2
nesta_case7_lmbd__utl	7	9	1.0344e+02	0.16	0.16	5	2	2
nesta_case22_bgm__utl	22	22	4.5388e+03	0.00	0.01	5	2	2
nesta_case30_test__utl	30	44	6.1510e+02	7.05	7.05	5	3	2