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, JuMP.with_optimizer(Ipopt.Optimizer, tol=1e-6))
result_soc = run_opf(case, SOCWRPowerModel, JuMP.with_optimizer(Ipopt.Optimizer, tol=1e-6))
result_qc  = run_opf(case, QCWRPowerModel, JuMP.with_optimizer(Ipopt.Optimizer, 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 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: v0.3.4-27-g115de85, 115de853fd4103b712d051e902540e7fa2b627be

Ipopt.jl: v0.2.6, 959b9c67e396a6e2307fc022d26b0d95692ee6a4

NESTA: v0.7.0-1-gb10c1e1, b10c1e1ea0a4259f91a3efd50fbad72b22d2fb9f

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.)
nestacase3lmbd	3	3	5.8126e+03	1.22	1.32	<1	<1	<1
nestacase4gs	4	4	1.5643e+02	0.01	0.01	<1	<1	<1
nestacase5pjm	5	6	1.7552e+04	14.55	14.55	<1	<1	<1
nestacase6c	6	7	2.3206e+01	0.30	0.30	<1	<1	<1
nestacase6ww	6	11	3.1440e+03	0.62	0.63	<1	<1	<1
nestacase9wscc	9	9	5.2967e+03	0.01	0.01	<1	<1	<1
nestacase14ieee	14	20	2.4405e+02	0.11	0.11	<1	<1	<1
nestacase24ieee_rts	24	38	6.3352e+04	0.02	0.02	<1	<1	<1
nestacase29edin	29	99	2.9895e+04	0.10	0.12	<1	<1	<1
nestacase30as	30	41	8.0313e+02	0.06	0.06	<1	<1	<1
nestacase30fsr	30	41	5.7577e+02	0.39	0.39	<1	<1	<1
nestacase30ieee	30	41	2.0497e+02	15.65	15.89	<1	<1	<1
nestacase39epri	39	46	9.6506e+04	0.05	0.05	<1	<1	<1
nestacase57ieee	57	80	1.1433e+03	0.07	0.07	<1	<1	<1
nestacase73ieee_rts	73	120	1.8976e+05	0.04	0.04	<1	<1	<1
nestacase89pegase	89	210	5.8198e+03	0.17	0.17	<1	<1	<1
nestacase118ieee	118	186	3.7186e+03	1.57	1.83	<1	<1	<1
nestacase162ieee_dtc	162	284	4.2302e+03	3.96	4.03	<1	<1	<1
nestacase189edin	189	206	8.4929e+02	0.22	0.22	<1	<1	<1
nestacase240wecc	240	448	7.5136e+04	5.27	5.74	4	4	2
nestacase300ieee	300	411	1.6891e+04	1.18	1.18	<1	<1	<1
nestacase1354pegase	1354	1991	7.4069e+04	0.08	0.08	4	11	13
nestacase1397speir	1418	1919	3.8890e+03	0.69	0.94	4	6	2
nestacase1394sopeir	1418	1920	1.3668e+03	0.58	0.83	3	6	2
nestacase1460wpeir	1481	1988	4.6402e+03	0.65	0.89	4	7	3
nestacase1888rte	1888	2531	5.9805e+04	0.38	0.38	26	7	46
nestacase1951rte	1951	2596	8.1738e+04	0.07	0.08	16	9	10
nestacase2224edin	2224	3207	3.8128e+04	6.03	6.09	10	16	5
nestacase2383wpmp	2383	2896	1.8685e+06	0.99	1.05	10	11	6
nestacase2736spmp	2736	3504	1.3079e+06	0.29	0.30	8	12	5
nestacase2737sopmp	2737	3506	7.7763e+05	0.25	0.26	7	10	4
nestacase2746wopmp	2746	3514	1.2083e+06	0.36	0.37	7	11	4
nestacase2746wpmp	2746	3514	1.6318e+06	0.32	0.33	8	11	5
nestacase2848rte	2848	3776	5.3022e+04	0.08	0.08	61	10	48
nestacase2868rte	2868	3808	7.9795e+04	0.07	0.07	31	13	9
nestacase2869pegase	2869	4582	1.3400e+05	0.09	0.09	10	20	55
nestacase3012wpmp	3012	3572	2.6008e+06	0.98	1.03	12	16	9
nestacase3120spmp	3120	3693	2.1457e+06	0.54	0.55	12	17	6
nestacase3375wpmp	3375	4161	7.4357e+06	0.50	0.52	15	496	26
nestacase6468rte	6468	9000	8.6829e+04	0.23	0.23	99	64	464
nestacase6470rte	6470	9005	9.8348e+04	0.17	0.18	80	56	39
nestacase6495rte	6495	9019	1.0632e+05	0.49	0.49	55	53	37
nestacase6515rte	6515	9037	1.0987e+05	0.43	0.43	55	45	321
nestacase9241pegase	9241	16049	3.1591e+05	1.02	1.64	93	109	298
nestacase13659pegase	13659	20467	3.8612e+05	0.94	1.43	288	157	375

Congested Operating Conditions (API)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nestacase3lmbd__api	3	3	3.6744e+02	1.79	3.26	<1	<1	<1
nestacase4gs__api	4	4	7.6667e+02	0.64	0.64	<1	<1	<1
nestacase5pjm__api	5	6	2.9963e+03	0.27	0.27	<1	<1	<1
nestacase6c__api	6	7	8.1387e+02	0.34	0.34	<1	<1	<1
nestacase9wscc__api	9	9	6.5623e+02	0.01	0.01	<1	<1	<1
nestacase14ieee__api	14	20	3.2513e+02	1.27	1.27	<1	<1	<1
nestacase24ieee_rts__api	24	38	6.4267e+03	11.88	20.70	<1	<1	<1
nestacase29edin__api	29	99	2.9529e+05	0.41	0.41	<1	<1	<1
nestacase30as__api	30	41	5.7008e+02	4.64	4.64	<1	<1	<1
nestacase30fsr__api	30	41	3.6656e+02	45.20	45.20	<1	<1	<1
nestacase30ieee__api	30	41	4.1499e+02	0.93	0.93	<1	<1	<1
nestacase39epri__api	39	46	7.4604e+03	2.98	3.00	<1	<1	<1
nestacase57ieee__api	57	80	1.4307e+03	0.21	0.21	<1	<1	<1
nestacase73ieee_rts__api	73	120	1.9995e+04	10.98	14.20	<1	<1	<1
nestacase89pegase__api	89	210	4.2554e+03	19.83	19.88	<1	<1	<1
nestacase118ieee__api	118	186	1.0270e+04	43.50	43.70	<1	<1	<1
nestacase162ieee_dtc__api	162	284	6.1069e+03	1.25	1.34	<1	<1	<1
nestacase189edin__api	189	206	1.9141e+03	1.70	1.70	<1	<1	<1
nestacase240wecc__api	240	448	1.4267e+05	0.58	0.70	4	6	2
nestacase300ieee__api	300	411	1.9868e+04	0.64	0.71	<1	<1	<1
nestacase1354pegase__api	1354	1991	5.2449e+04	0.36	0.36	6	9	4
nestacase1397speir__api	1418	1919	6.6658e+03	1.07	1.29	5	5	3
nestacase1394sopeir__api	1418	1920	3.3776e+03	0.37	0.39	6	6	3
nestacase1460wpeir__api	1481	1988	6.4449e+03	1.54	1.69	4	7	3
nestacase1888rte__api	1888	2531	5.8546e+04	0.71	0.71	9	14	6
nestacase1951rte__api	1951	2596	7.5639e+04	0.13	0.14	11	12	41
nestacase2224edin__api	2224	3207	4.4435e+04	2.41	2.42	11	15	5
nestacase2383wpmp__api	2383	2896	2.3489e+04	0.74	0.75	7	9	4
nestacase2736spmp__api	2736	3504	2.5884e+04	2.18	2.19	8	11	5
nestacase2737sopmp__api	2737	3506	2.1675e+04	0.39	0.40	8	11	5
nestacase2746wopmp__api	2746	3514	2.2803e+04	0.49	0.49	8	11	4
nestacase2746wpmp__api	2746	3514	2.5964e+04	0.58	0.59	7	10	4
nestacase2848rte__api	2848	3776	4.4032e+04	0.23	0.23	25	18	10
nestacase2868rte__api	2868	3808	7.5506e+04	0.20	0.21	32	22	8
nestacase2869pegase__api	2869	4582	9.8415e+04	0.59	0.60	15	22	9
nestacase3012wpmp__api	3012	3572	2.8334e+04	1.04	1.07	9	12	6
nestacase3120spmp__api	3120	3693	2.3715e+04	2.73	2.75	12	14	5
nestacase3375wpmp__api	3375	4161	4.8939e+04	0.68	0.69	13	57	51
nestacase6468rte__api	6468	9000	6.8149e+04	0.89	0.91	124	59	246
nestacase6470rte__api	6470	9005	9.0583e+04	0.80	0.82	63	50	22
nestacase6495rte__api	6495	9019	8.8944e+04	1.24	1.26	64	47	24
nestacase6515rte__api	6515	9037	9.7217e+04	1.07	1.10	72	51	25
nestacase9241pegase__api	9241	16049	2.3890e+05	1.67	2.45	88	108	42
nestacase13659pegase__api	13659	20467	3.0285e+05	1.13	1.74	155	148	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.)
nestacase3lmbd__sad	3	3	5.9593e+03	1.42	3.75	<1	<1	<1
nestacase4gs__sad	4	4	3.1584e+02	1.53	4.53	<1	<1	<1
nestacase5pjm__sad	5	6	2.6115e+04	0.99	3.62	<1	<1	<1
nestacase6c__sad	6	7	2.4376e+01	0.43	1.32	<1	<1	<1
nestacase6ww__sad	6	11	3.1463e+03	0.18	0.70	<1	<1	<1
nestacase9wscc__sad	9	9	5.5283e+03	0.54	1.57	<1	<1	<1
nestacase14ieee__sad	14	20	2.4405e+02	0.05	0.08	<1	<1	<1
nestacase24ieee_rts__sad	24	38	7.6943e+04	2.93	9.56	<1	<1	<1
nestacase29edin__sad	29	99	4.1258e+04	16.57	25.91	<1	<1	<1
nestacase30as__sad	30	41	8.9749e+02	2.32	7.88	<1	<1	<1
nestacase30fsr__sad	30	41	5.7679e+02	0.41	0.47	<1	<1	<1
nestacase30ieee__sad	30	41	2.0497e+02	4.17	6.79	<1	<1	<1
nestacase39epri__sad	39	46	9.6745e+04	0.05	0.08	<1	<1	<1
nestacase57ieee__sad	57	80	1.1433e+03	0.05	0.07	<1	<1	<1
nestacase73ieee_rts__sad	73	120	2.2775e+05	2.54	6.75	<1	<1	<1
nestacase89pegase__sad	89	210	5.8198e+03	0.14	0.15	<1	<1	<1
nestacase118ieee__sad	118	186	4.1067e+03	4.62	8.29	<1	<1	<1
nestacase162ieee_dtc__sad	162	284	4.2535e+03	4.31	4.56	<1	<1	<1
nestacase189edin__sad	189	206	8.6482e+02	0.99	0.99	<1	<1	<1
nestacase240wecc__sad	240	448	7.6495e+04	5.29	7.41	4	4	2
nestacase300ieee__sad	300	411	1.6894e+04	1.10	1.18	<1	<1	<1
nestacase1354pegase__sad	1354	1991	7.4070e+04	0.07	0.08	4	7	6
nestacase1397speir__sad	1418	1919	4.2378e+03	7.27	7.42	5	8	3
nestacase1394sopeir__sad	1418	1920	1.4493e+03	3.33	4.34	4	5	3
nestacase1460wpeir__sad	1481	1988	5.3370e+03	0.84	1.03	4	6	3
nestacase1888rte__sad	1888	2531	5.9806e+04	0.37	0.38	28	8	101
nestacase1951rte__sad	1951	2596	8.1786e+04	0.11	0.13	17	10	9
nestacase2224edin__sad	2224	3207	3.8265e+04	5.52	6.10	11	15	5
nestacase2383wpmp__sad	2383	2896	1.9165e+06	2.16	3.13	12	11	6
nestacase2736spmp__sad	2736	3504	1.3294e+06	1.53	1.80	11	12	5
nestacase2737sopmp__sad	2737	3506	7.9266e+05	1.92	2.10	10	11	4
nestacase2746wopmp__sad	2746	3514	1.2344e+06	2.00	2.37	9	9	4
nestacase2746wpmp__sad	2746	3514	1.6674e+06	1.68	2.21	9	11	6
nestacase2848rte__sad	2848	3776	5.3031e+04	0.08	0.09	59	13	10
nestacase2868rte__sad	2868	3808	7.9818e+04	0.08	0.10	42	13	10
nestacase2869pegase__sad	2869	4582	1.3402e+05	0.09	0.10	11	25	19
nestacase3012wpmp__sad	3012	3572	2.6213e+06	1.41	1.62	14	17	7
nestacase3120spmp__sad	3120	3693	2.1755e+06	1.42	1.61	16	17	7
nestacase3375wpmp__sad	3375	4161	7.4357e+06	0.47	0.52	16	30	43
nestacase6468rte__sad	6468	9000	8.6829e+04	0.22	0.23	127	59	118
nestacase6470rte__sad	6470	9005	9.8357e+04	0.16	0.18	74	42	38
nestacase6495rte__sad	6495	9019	1.0632e+05	0.48	0.49	60	60	39
nestacase6515rte__sad	6515	9037	1.0995e+05	0.49	0.51	52	46	36
nestacase9241pegase__sad	9241	16049	3.1592e+05	0.80	0.82	87	100	649
nestacase13659pegase__sad	13659	20467	3.8614e+05	0.70	0.71	193	127	139

Radial Topologies (RAD)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nestacase9kds__rad	9	8	inf.	–	–	<1	<1	<1
nestacase9l_kds__rad	9	8	inf.	–	–	<1	<1	<1
nestacase30fsr_kds__rad	30	29	6.1904e+02	1.74	1.74	<1	<1	<1
nestacase30fsrlkds__rad	30	29	4.4584e+02	2.25	2.25	<1	<1	<1
nestacase30kds__rad	30	29	4.7943e+03	11.47	11.47	<1	<1	<1
nestacase30l_kds__rad	30	29	4.5623e+03	33.47	33.47	<1	<1	<1
nestacase57kds__rad	57	56	1.2101e+04	13.58	13.58	<1	<1	<1
nestacase57l_kds__rad	57	56	1.0173e+04	17.43	17.43	<1	<1	<1

Non-Convex Optimization Cases (NCO)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nestacase5bgm__nco	5	6	1.0823e+03	10.29	10.74	<1	<1	<1
nestacase9bgm__nco	9	9	3.0878e+03	10.85	10.85	<1	<1	<1
nestacase9na_cao__nco	9	9	-2.1243e+02	-15.05	-18.12	<1	<1	<1
nestacase9nb_cao__nco	9	9	-2.4742e+02	-15.62	-19.31	<1	<1	<1
nestacase14s_cao__nco	14	20	9.6704e+03	3.83	3.83	<1	<1	<1
nestacase391_bgm__nco	39	46	1.1221e+04	3.73	3.74	<1	<1	<1

Utility Cases (UTL)

Case Name	Nodes	Edges	AC ($/h)	QC Gap (%)	SOC Gap (%)	AC Time (sec.)	QC Time (sec.)	SOC Time (sec.)
nestacase3cc__utl	3	3	2.0756e+02	1.55	1.62	<1	<1	<1
nestacase3cgs__utl	3	3	1.0171e+02	1.69	1.69	<1	<1	<1
nestacase3ch__utl	3	5	9.8740e+01	100.01	100.01	<1	<1	<1
nestacase5lmbd__utl	5	7	2.3989e+03	0.01	0.01	<1	<1	<1
nestacase7lmbd__utl	7	9	1.0344e+02	0.16	0.16	<1	<1	<1
nestacase22bgm__utl	22	22	4.5388e+03	0.00	0.01	<1	<1	<1
nestacase30test__utl	30	44	6.1510e+02	7.05	7.05	<1	<1	<1