PowerModels Experiment Results

This section presents results of running PowerModels on collections of established power network test cases from the PGLib-OPF archive. This provides validation of PowerModels 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,

solver = optimizer_with_attributes(Ipopt.Optimizer, "tol" => 1e-6)
result_ac  = solve_opf(case,   ACPPowerModel, solver)
result_soc = solve_opf(case, SOCWRPowerModel, solver)
result_qc  = solve_opf(case,  QCRMPowerModel, solver)

for each case in the PGLib-OPF archive. If the value of result["termination_status"] is LOCALLY_SOLVED 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 does not include Julia's JIT time, about 2-5 seconds. The results were computed using the HSL ma57 solver in IPOPT. The default linear solver provided with Ipopt.jl will increase the runtime by 2-6x.

Software Versions

PowerModels.jl: v0.17

Ipopt.jl: v0.6

PGLib-OPF: v19.05

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.)
`case3_lmbd`	3	3	5.8126e+03	1.22	1.32	<1	<1	<1
`case5_pjm`	5	6	1.7552e+04	14.55	14.55	<1	<1	<1
`case14_ieee`	14	20	2.1781e+03	0.11	0.11	<1	<1	<1
`case24_ieee_rts`	24	38	6.3352e+04	0.02	0.02	<1	<1	<1
`case30_as`	30	41	8.0313e+02	0.06	0.06	<1	<1	<1
`case30_fsr`	30	41	5.7577e+02	0.39	0.39	<1	<1	<1
`case30_ieee`	30	41	8.2085e+03	18.81	18.84	<1	<1	<1
`case39_epri`	39	46	1.3842e+05	0.55	0.56	<1	<1	<1
`case57_ieee`	57	80	3.7589e+04	0.16	0.16	<1	<1	<1
`case73_ieee_rts`	73	120	1.8976e+05	0.04	0.04	<1	<1	<1
`case89_pegase`	89	210	1.0729e+05	0.75	0.75	<1	<1	<1
`case118_ieee`	118	186	9.7214e+04	0.79	0.91	<1	<1	<1
`case162_ieee_dtc`	162	284	1.0808e+05	5.84	5.95	<1	<1	<1
`case179_goc`	179	263	7.5427e+05	0.16	0.16	<1	<1	<1
`case200_tamu`	200	245	2.7558e+04	0.01	0.01	<1	<1	<1
`case240_pserc`	240	448	3.3297e+06	2.73	2.78	3	4	2
`case300_ieee`	300	411	5.6522e+05	2.58	2.63	<1	<1	<1
`case500_tamu`	500	597	7.2578e+04	5.39	5.39	<1	2	<1
`case588_sdet`	588	686	3.1314e+05	1.91	2.14	<1	2	<1
`case1354_pegase`	1354	1991	1.2588e+06	1.56	1.57	5	6	3
`case1888_rte`	1888	2531	1.4025e+06	2.05	2.05	9	8	31
`case1951_rte`	1951	2596	2.0856e+06	0.13	0.14	19	9	5
`case2000_tamu`	2000	3206	1.2285e+06	0.20	0.21	10	9	3
`case2316_sdet`	2316	3017	1.7753e+06	1.79	1.80	6	11	4
`case2383wp_k`	2383	2896	1.8682e+06	0.97	1.04	7	10	5
`case2736sp_k`	2736	3504	1.3080e+06	0.30	0.31	6	10	4
`case2737sop_k`	2737	3506	7.7773e+05	0.26	0.27	5	8	3
`case2746wop_k`	2746	3514	1.2083e+06	0.36	0.37	5	9	4
`case2746wp_k`	2746	3514	1.6317e+06	0.32	0.33	6	9	4
`case2848_rte`	2848	3776	1.2866e+06	0.12	0.13	17	13	7
`case2853_sdet`	2853	3921	2.0524e+06	0.87	0.91	9	12	6
`case2868_rte`	2868	3808	2.0096e+06	0.10	0.10	15	14	8
`case2869_pegase`	2869	4582	2.4628e+06	1.01	1.01	11	20	7
`case3012wp_k`	3012	3572	2.6008e+06	0.98	1.03	9	14	13
`case3120sp_k`	3120	3693	2.1480e+06	0.55	0.56	9	12	5
`case3375wp_k`	3374	4161	7.4382e+06	0.54	0.55	11	29	6
`case4661_sdet`	4661	5997	2.2513e+06	1.89	1.99	15	27	12
`case6468_rte`	6468	9000	2.0697e+06	1.12	1.13	64	87	27
`case6470_rte`	6470	9005	2.2376e+06	1.75	1.76	36	43	24
`case6495_rte`	6495	9019	3.0678e+06	15.09	15.11	69	65	25
`case6515_rte`	6515	9037	2.8255e+06	6.39	6.40	53	44	23
`case9241_pegase`	9241	16049	6.2431e+06	1.71	2.54	49	104	36
`case10000_tamu`	10000	12706	2.4859e+06	0.37	0.72	98	67	33
`case13659_pegase`	13659	20467	8.9480e+06	0.98	1.39	59	121	62

Congested Operating Conditions (API)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
`case3_lmbd__api`	3	3	1.1242e+04	5.63	9.32	<1	<1	<1
`case5_pjm__api`	5	6	7.6377e+04	4.09	4.09	<1	<1	<1
`case14_ieee__api`	14	20	5.9994e+03	5.13	5.13	<1	<1	<1
`case24_ieee_rts__api`	24	38	1.3495e+05	13.01	17.87	<1	<1	<1
`case30_as__api`	30	41	4.9962e+03	44.61	44.61	<1	<1	<1
`case30_fsr__api`	30	41	7.0115e+02	2.76	2.76	<1	<1	<1
`case30_ieee__api`	30	41	1.8044e+04	5.46	5.46	<1	<1	<1
`case39_epri__api`	39	46	2.4975e+05	1.72	1.74	<1	<1	<1
`case57_ieee__api`	57	80	4.9297e+04	0.09	0.09	<1	<1	<1
`case73_ieee_rts__api`	73	120	4.2273e+05	11.07	12.89	<1	<1	<1
`case89_pegase__api`	89	210	1.3428e+05	13.45	13.47	<1	<1	<1
`case118_ieee__api`	118	186	2.4205e+05	28.70	28.81	<1	<1	<1
`case162_ieee_dtc__api`	162	284	1.2100e+05	4.33	4.36	<1	<1	<1
`case179_goc__api`	179	263	1.9321e+06	5.93	9.88	<1	2	<1
`case200_tamu__api`	200	245	3.6763e+04	0.03	0.03	<1	<1	<1
`case240_pserc__api`	240	448	4.7681e+06	0.69	0.74	4	5	2
`case300_ieee__api`	300	411	6.5015e+05	0.84	0.89	<1	<1	<1
`case500_tamu__api`	500	597	4.2776e+04	2.92	2.92	<1	2	<1
`case588_sdet__api`	588	686	3.9476e+05	1.39	1.61	<1	2	<1
`case1354_pegase__api`	1354	1991	1.4867e+06	0.65	0.66	5	7	3
`case1888_rte__api`	1888	2531	1.9539e+06	0.22	0.23	8	15	6
`case1951_rte__api`	1951	2596	2.4168e+06	0.53	0.55	9	9	5
`case2000_tamu__api`	2000	3206	1.2850e+06	2.66	2.71	13	10	3
`case2316_sdet__api`	2316	3017	2.1890e+06	1.79	1.80	8	11	4
`case2383wp_k__api`	2383	2896	2.7913e+05	0.01	0.01	2	3	<1
`case2736sp_k__api`	2736	3504	6.5394e+05	10.83	10.84	7	9	3
`case2737sop_k__api`	2737	3506	3.6920e+05	6.41	6.41	6	4	2
`case2746wop_k__api`	2746	3514	5.1166e+05	0.01	0.01	2	3	2
`case2746wp_k__api`	2746	3514	5.8183e+05	0.01	0.00	3	5	2
`case2848_rte__api`	2848	3776	1.4760e+06	0.25	0.25	28	13	6
`case2853_sdet__api`	2853	3921	2.4579e+06	1.92	1.96	10	13	6
`case2868_rte__api`	2868	3808	2.3405e+06	0.18	0.19	26	15	6
`case2869_pegase__api`	2869	4582	2.9342e+06	1.32	1.33	13	19	8
`case3012wp_k__api`	3012	3572	7.2887e+05	0.00	0.00	4	5	2
`case3120sp_k__api`	3120	3693	9.8428e+05	23.54	23.60	12	13	4
`case3375wp_k__api`	3374	4161	5.8478e+06	9.35	–	11	22	347
`case4661_sdet__api`	4661	5997	2.6951e+06	2.54	2.64	17	27	50
`case6468_rte__api`	6468	9000	2.3135e+06	0.80	0.82	76	55	190
`case6470_rte__api`	6470	9005	2.6065e+06	1.19	1.20	55	38	68
`case6495_rte__api`	6495	9019	3.0265e+06	2.97	3.01	55	46	23
`case6515_rte__api`	6515	9037	3.1363e+06	1.91	1.95	63	46	22
`case9241_pegase__api`	9241	16049	7.0264e+06	1.80	–	118	262	1617
`case10000_tamu__api`	10000	12706	1.8713e+06	5.53	6.18	108	117	34
`case13659_pegase__api`	13659	20467	9.2971e+06	1.18	1.83	65	164	76

Small Angle Difference Conditions (SAD)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
`case3_lmbd__sad`	3	3	5.9593e+03	1.42	3.75	<1	<1	<1
`case5_pjm__sad`	5	6	2.6115e+04	0.99	3.62	<1	<1	<1
`case14_ieee__sad`	14	20	2.7773e+03	21.50	21.54	<1	<1	<1
`case24_ieee_rts__sad`	24	38	7.6943e+04	2.93	9.56	<1	<1	<1
`case30_as__sad`	30	41	8.9749e+02	2.32	7.88	<1	<1	<1
`case30_fsr__sad`	30	41	5.7679e+02	0.41	0.47	<1	<1	<1
`case30_ieee__sad`	30	41	8.2085e+03	5.93	9.70	<1	<1	<1
`case39_epri__sad`	39	46	1.4835e+05	0.21	0.66	<1	<1	<1
`case57_ieee__sad`	57	80	3.8664e+04	0.35	0.71	<1	<1	<1
`case73_ieee_rts__sad`	73	120	2.2775e+05	2.54	6.75	<1	<1	<1
`case89_pegase__sad`	89	210	1.0729e+05	0.71	0.73	<1	<1	<1
`case118_ieee__sad`	118	186	1.0522e+05	6.84	8.22	<1	<1	<1
`case162_ieee_dtc__sad`	162	284	1.0870e+05	6.25	6.48	<1	<1	<1
`case179_goc__sad`	179	263	7.6254e+05	1.01	1.12	<1	<1	<1
`case200_tamu__sad`	200	245	2.7558e+04	0.01	0.01	<1	<1	<1
`case240_pserc__sad`	240	448	3.4071e+06	4.41	4.98	4	4	2
`case300_ieee__sad`	300	411	5.6571e+05	2.43	2.61	<1	<1	<1
`case500_tamu__sad`	500	597	7.9234e+04	7.90	7.92	<1	2	<1
`case588_sdet__sad`	588	686	3.2986e+05	6.10	6.81	<1	2	<1
`case1354_pegase__sad`	1354	1991	1.2588e+06	1.53	1.57	5	6	3
`case1888_rte__sad`	1888	2531	1.4139e+06	2.81	2.82	9	8	24
`case1951_rte__sad`	1951	2596	2.0928e+06	0.44	0.48	17	9	5
`case2000_tamu__sad`	2000	3206	1.2303e+06	0.33	0.35	10	9	3
`case2316_sdet__sad`	2316	3017	1.7753e+06	1.76	1.80	6	10	5
`case2383wp_k__sad`	2383	2896	1.9127e+06	1.98	2.93	8	10	5
`case2736sp_k__sad`	2736	3504	1.3273e+06	1.36	1.63	8	10	5
`case2737sop_k__sad`	2737	3506	7.9153e+05	1.76	1.95	7	9	4
`case2746wop_k__sad`	2746	3514	1.2343e+06	2.01	2.37	7	8	4
`case2746wp_k__sad`	2746	3514	1.6676e+06	1.67	2.22	8	9	5
`case2848_rte__sad`	2848	3776	1.2890e+06	0.24	0.26	17	13	6
`case2853_sdet__sad`	2853	3921	2.0701e+06	1.69	1.74	9	11	6
`case2868_rte__sad`	2868	3808	2.0224e+06	0.61	0.64	18	13	6
`case2869_pegase__sad`	2869	4582	2.4689e+06	1.02	1.13	11	20	7
`case3012wp_k__sad`	3012	3572	2.6213e+06	1.41	1.62	10	14	6
`case3120sp_k__sad`	3120	3693	2.1782e+06	1.51	1.65	11	14	6
`case3375wp_k__sad`	3374	4161	7.4382e+06	0.50	0.55	11	18	6
`case4661_sdet__sad`	4661	5997	2.2610e+06	1.79	1.96	16	27	12
`case6468_rte__sad`	6468	9000	2.0697e+06	1.10	1.12	63	75	31
`case6470_rte__sad`	6470	9005	2.2416e+06	1.87	1.91	37	42	22
`case6495_rte__sad`	6495	9019	3.0678e+06	14.99	15.11	70	56	25
`case6515_rte__sad`	6515	9037	2.8826e+06	8.22	8.26	61	46	22
`case9241_pegase__sad`	9241	16049	6.3195e+06	2.42	2.48	59	91	35
`case10000_tamu__sad`	10000	12706	2.4859e+06	0.36	0.72	59	68	36
`case13659_pegase__sad`	13659	20467	9.0433e+06	1.64	1.69	57	125	43