Release v4.0

Grid Research for Good v4.0


GRG v4.0 is based on GRG v3.0, with more simplification on the JSON structure and the introduction of group blocks, DC lines, and time series constraints. External CSV files are now allowed for time series data, as well as improvements on the three winding transformers.

Technical Document

This document describes the Grid Research for Good (GRG) schema to represent static transmission networks. We aim to describe the model of the static network components, as well as the component hierarchical organization within a network. We also include the nominal unit to per-unit transformation (and vice versa) associated to each component. The schema to represent time series data, stochastic time series data, contingencies, group blocks, and time series constraints will also be discussed.

GRG Documentation

Schema

The JSON schema for the GRG v4.0 is released.

GRGv4.0_schema.txt

NESTA-GRG

The NESTA benchmarks in GRG format (v4.0) are also released. The release is stored in the Git repository below, together with benchmarks for prior GRG versions.

The WECC benchmark with time series data is also updated to GRGv4.0. The time series data is now stored in an external CSV file. Please refer to GRG Documentation PDF file for parsing information.

Repository link: https://gitlab.eecs.umich.edu/pvanhent/GRG-data-repository

Users can also directly download all the benchmarks via the following command:

git clone git@gitlab.eecs.umich.edu:pvanhent/GRG-data-repository.git [target directory]

Numerical Results

We show AC Optimal Power Flow (AC-OPF) results for our NESTA GDG benchmarks (middle & right column) and compare with the original objective value from the NESTA/LANL report (left column, accurate up to 5 significant figures). We test our benchmarks with two variants of AC-OPF model: one with thermal power limit constraints used by the original NESTA benchmark, and one with current limit constraints generated from the thermal limit parameters.

AC Optimal Power Flow
Data File Benchmark GDG (Thermal) GRG (Current)
nesta_case118_ieee 3,718.60 3,718.64 3,694.15
nesta_case1354_pegase 74,069.00 74,069.35 74,060.41
nesta_case13659_pegase 386,120.00 386,117.10 386,112.28
nesta_case1394sop_eir 1,366.80 1,366.81 1,358.53
nesta_case1397sp_eir 3,889.00 3,888.99 3,858.57
nesta_case1460wp_eir 4,640.20 4,640.18 4,272.88
nesta_case14_ieee 244.05 244.05 244.05
nesta_case162_ieee_dtc 4,230.20 4,230.23 4,070.70
nesta_case1888_rte 59,805.00 59,804.98 59,803.54
nesta_case189_edin 849.29 849.29 844.03
nesta_case1951_rte 81,738.00 81,737.68 81,736.16
nesta_case2224_edin 38,128.00 38,127.69 37,007.95
nesta_case2383wp_mp 1,868,500.00 1,868,511.77 1,858,584.74
nesta_case240_wecc 75,136.00 75,136.10 72,599.06
nesta_case24_ieee_rts 63,352.00 63,352.20 63,352.20
nesta_case2736sp_mp 1,307,900.00 1,307,883.12 1,307,831.17
nesta_case2737sop_mp 777,630.00 777,629.30 777,624.08
nesta_case2746wop_mp 1,208,300.00 1,208,279.81 1,208,279.81
nesta_case2746wp_mp 1,631,800.00 1,631,775.10 1,631,775.10
nesta_case2848_rte 53,022.00 53,021.83 53,021.62
nesta_case2868_rte 79,795.00 79,794.68 79,790.89
nesta_case2869_pegase 134,000.00 133,999.29 133,987.86
nesta_case29_edin 29,895.00 29,895.49 29,895.49
nesta_case300_ieee 16,891.00 16,891.28 16,660.38
nesta_case3012wp_mp 2,600,800.00 2,600,842.72 2,586,065.35
nesta_case30_as 803.13 803.13 803.13
nesta_case30_fsr 575.77 575.77 574.48
nesta_case30_ieee 204.97 204.97 192.11
nesta_case3120sp_mp 2,145,700.00 2,145,739.40 2,142,588.53
nesta_case3375wp_mp 7,435,700.00 7,435,697.48 7,413,407.32
nesta_case39_epri 96,506.00 96,505.52 96,505.52
nesta_case3_lmbd 5,812.60 5,812.64 5,731.70
nesta_case4_gs 156.43 156.43 156.43
nesta_case57_ieee 1,143.30 1,143.27 1,143.27
nesta_case5_pjm 17,552.00 17,551.89 14,997.04
nesta_case6468_rte 86,829.00 86,829.02 86,776.07
nesta_case6470_rte 98,348.00 98,347.83 98,308.69
nesta_case6495_rte 106,320.00 106,320.10 106,043.52
nesta_case6515_rte 109,870.00 109,865.40 109,642.33
nesta_case6_c 23.21 23.21 23.21
nesta_case6_ww 3,144.00 3,143.97 3,139.65
nesta_case73_ieee_rts 189,760.00 189,764.08 189,764.08
nesta_case89_pegase 5,819.80 5,819.81 5,817.60
nesta_case9241_pegase 315,910.00 315,912.16 315,894.24
nesta_case9_wscc 5,296.70 5,296.69 5,296.69

 

AC Optimal Power Flow
Data File (API cases) Benchmark GDG (Thermal) GRG (Current)
nesta_case118_ieee__api 10,270.00 10,269.82 6,492.73
nesta_case1354_pegase__api 52,449.00 52,448.51 52,273.15
nesta_case13659_pegase__api 302,840.00 302,835.64 301,161.94
nesta_case1394sop_eir__api 3,377.60 3,377.65 3,328.31
nesta_case1397sp_eir__api 6,665.80 6,665.77 6,580.64
nesta_case1460wp_eir__api 6,444.90 6,444.91 6,226.01
nesta_case14_ieee__api 325.13 325.13 321.16
nesta_case162_ieee_dtc__api 6,106.90 6,106.86 5,876.54
nesta_case1888_rte__api 58,546.00 58,545.61 57,738.38
nesta_case189_edin__api 1,914.10 1,914.15 1,867.59
nesta_case1951_rte__api 75,639.00 75,638.75 74,982.82
nesta_case2224_edin__api 44,435.00 44,435.05 43,046.93
nesta_case2383wp_mp__api 23,489.00 23,489.27 23,385.72
nesta_case240_wecc__api 142,670.00 142,673.71 142,111.23
nesta_case24_ieee_rts__api 6,426.70 6,426.65 6,181.44
nesta_case2736sp_mp__api 25,884.00 25,883.72 25,667.74
nesta_case2737sop_mp__api 21,675.00 21,675.00 21,615.15
nesta_case2746wop_mp__api 22,803.00 22,803.23 22,757.96
nesta_case2746wp_mp__api 25,964.00 25,963.78 25,882.39
nesta_case2848_rte__api 44,032.00 44,032.36 43,114.97
nesta_case2868_rte__api 75,506.00 75,505.75 74,869.27
nesta_case2869_pegase__api 98,415.00 98,414.80 97,620.17
nesta_case29_edin__api 295,290.00 295,291.22 294,170.93
nesta_case300_ieee__api 19,868.00 19,867.93 19,765.34
nesta_case3012wp_mp__api 28,334.00 28,334.12 28,131.82
nesta_case30_as__api 570.08 570.08 556.72
nesta_case30_fsr__api 366.56 366.56 211.00
nesta_case30_ieee__api 414.99 414.99 411.16
nesta_case3120sp_mp__api 23,715.00 23,715.33 23,281.05
nesta_case3375wp_mp__api 48,939.00 48,939.01 48,667.74
nesta_case39_epri__api 7,460.40 7,460.37 7,073.72
nesta_case3_lmbd__api 367.44 367.44 362.44
nesta_case4_gs__api 766.67 766.67 757.84
nesta_case57_ieee__api 1,430.70 1,430.65 1,430.65
nesta_case5_pjm__api 2,996.30 2,996.32 2,988.22
nesta_case6468_rte__api 68,149.00 68,149.04 67,410.90
nesta_case6470_rte__api 90,583.00 90,583.36 89,799.25
nesta_case6495_rte__api 88,944.00 88,943.88 87,655.97
nesta_case6515_rte__api 97,217.00 97,217.08 95,761.47
nesta_case6_c__api 813.87 813.87 811.16
nesta_case73_ieee_rts__api 19,995.00 19,995.00 18,634.13
nesta_case89_pegase__api 4,255.40 4,255.44 3,424.93
nesta_case9241_pegase__api 238,900.00 238,898.99 237,814.45
nesta_case9_wscc__api 656.23 656.23 631.06

 

AC Optimal Power Flow
Data File (SAD cases) Benchmark GDG (Thermal) GRG (Current)
nesta_case118_ieee__sad 4,106.70 4,106.72 4,091.77
nesta_case1354_pegase__sad 74,070.00 74,069.97 74,061.03
nesta_case13659_pegase__sad 386,140.00 386,141.87 386,136.46
nesta_case1394sop_eir__sad 1,449.30 1,449.32 1,449.32
nesta_case1397sp_eir__sad 4,237.80 4,237.82 4,147.82
nesta_case1460wp_eir__sad 5,337.00 5,336.98 5,334.61
nesta_case14_ieee__sad 244.05 244.05 244.05
nesta_case162_ieee_dtc__sad 4,253.50 4,253.51 4,156.91
nesta_case1888_rte__sad 59,806.00 59,857.78 59,855.52
nesta_case189_edin__sad 864.82 864.82 864.28
nesta_case1951_rte__sad 81,786.00 81,786.12 81,781.41
nesta_case2224_edin__sad 38,265.00 38,265.50 37,131.42
nesta_case2383wp_mp__sad 1,916,500.00 1,916,461.33 1,912,661.06
nesta_case240_wecc__sad 76,495.00 76,494.70 74,614.98
nesta_case24_ieee_rts__sad 76,943.00 76,943.24 76,941.01
nesta_case2736sp_mp__sad 1,329,400.00 1,329,426.24 1,329,408.38
nesta_case2737sop_mp__sad 792,660.00 792,664.66 792,647.96
nesta_case2746wop_mp__sad 1,234,400.00 1,234,397.25 1,234,397.25
nesta_case2746wp_mp__sad 1,667,400.00 1,667,370.34 1,667,341.37
nesta_case2848_rte__sad 53,031.00 53,031.15 53,030.70
nesta_case2868_rte__sad 79,818.00 79,818.39 79,814.14
nesta_case2869_pegase__sad 134,020.00 134,015.35 134,004.97
nesta_case29_edin__sad 41,258.00 41,258.45 41,258.45
nesta_case300_ieee__sad 16,894.00 16,893.92 16,824.92
nesta_case3012wp_mp__sad 2,621,300.00 2,621,317.35 2,604,327.49
nesta_case30_as__sad 897.49 897.49 897.46
nesta_case30_fsr__sad 576.79 576.79 574.48
nesta_case30_ieee__sad 204.97 204.97 192.11
nesta_case3120sp_mp__sad 2,175,500.00 2,175,503.10 2,174,889.27
nesta_case3375wp_mp__sad 7,435,700.00 7,435,697.48 7,413,407.32
nesta_case39_epri__sad 96,745.00 96,745.01 96,745.01
nesta_case3_lmbd__sad 5,959.30 5,959.33 5,736.05
nesta_case4_gs__sad 315.84 315.84 315.84
nesta_case57_ieee__sad 1,143.30 1,143.27 1,143.27
nesta_case5_pjm__sad 26,115.00 26,115.19 26,115.19
nesta_case6468_rte__sad 86,829.00 86,829.02 86,776.07
nesta_case6470_rte__sad 98,357.00 98,356.85 98,315.51
nesta_case6495_rte__sad 106,320.00 106,320.10 106,043.52
nesta_case6515_rte__sad 109,950.00 109,947.18 109,645.00
nesta_case6_c__sad 24.38 24.38 24.38
nesta_case6_ww__sad 3,146.30 3,146.27 3,139.87
nesta_case73_ieee_rts__sad 227,750.00 227,745.73 227,741.06
nesta_case89_pegase__sad 5,819.80 5,819.81 5,819.40
nesta_case9241_pegase__sad 315,920.00 315,918.17 315,900.62
nesta_case9_wscc__sad 5,528.30 5,528.26 5,528.26

 

We also show results for the QC, SOCP, and SDP relaxation. We list the objective value and their optimality gap when comparing to the AC solution above. The optimality gap is computed by:

[ AC objective value – Relaxation objective value ] / [AC objective value],

and then converted to percentages (%).

QC Relaxation:

 

QC Optimal Power Flow
Data File GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee 3,654.67 1.72 3,645.81 1.31
nesta_case1354_pegase 74,009.18 0.08 74,003.68 0.08
nesta_case13659_pegase 380,505.99 1.45 382,393.97 0.96
nesta_case1394sop_eir 1,355.55 0.82 1,348.89 0.71
nesta_case1397sp_eir 3,852.70 0.93 3,829.68 0.75
nesta_case1460wp_eir 4,599.06 0.89 4,194.70 1.83
nesta_case14_ieee 243.78 0.11 243.78 0.11
nesta_case162_ieee_dtc 4,060.92 4.00 3,971.81 2.43
nesta_case1888_rte 59,577.85 0.38 59,573.51 0.38
nesta_case189_edin 847.50 0.21 842.13 0.23
nesta_case1951_rte 81,680.26 0.07 81,680.12 0.07
nesta_case2224_edin 35,827.97 6.03 35,711.01 3.50
nesta_case2383wp_mp 1,849,080.12 1.04 1,848,954.27 0.52
nesta_case240_wecc 71,128.10 5.33 70,674.61 2.65
nesta_case24_ieee_rts 63,344.57 0.01 63,344.57 0.01
nesta_case2736sp_mp 1,304,097.61 0.29 1,304,089.78 0.29
nesta_case2737sop_mp 775,703.23 0.25 775,706.95 0.25
nesta_case2746wop_mp 1,203,963.57 0.36 1,203,967.23 0.36
nesta_case2746wp_mp 1,626,575.01 0.32 1,626,516.55 0.32
nesta_case2848_rte 52,980.95 0.08 52,980.68 0.08
nesta_case2868_rte 79,744.80 0.06 79,741.48 0.06
nesta_case2869_pegase 133,878.64 0.09 133,872.45 0.09
nesta_case29_edin 29,860.82 0.12 29,860.49 0.12
nesta_case300_ieee 16,692.80 1.18 16,546.29 0.68
nesta_case3012wp_mp 2,574,744.36 1.00 2,573,678.36 0.48
nesta_case30_as 802.68 0.06 802.68 0.06
nesta_case30_fsr 573.55 0.39 573.54 0.16
nesta_case30_ieee 172.91 15.64 159.95 16.74
nesta_case3120sp_mp 2,134,198.26 0.54 2,132,596.30 0.47
nesta_case3375wp_mp 7,398,093.47 0.51 7,396,868.53 0.22
nesta_case39_epri 96,459.72 0.05 96,459.74 0.05
nesta_case3_lmbd 5,740.39 1.24 5,704.98 0.47
nesta_case4_gs 156.43 0.00 156.43 0.00
nesta_case57_ieee 1,142.53 0.06 1,142.53 0.06
nesta_case5_pjm 14,999.71 14.54 14,997.04 0.00
nesta_case6468_rte 86,631.45 0.23 86,622.01 0.18
nesta_case6470_rte 98,176.58 0.17 98,169.25 0.14
nesta_case6495_rte 105,803.53 0.49 105,788.55 0.24
nesta_case6515_rte 109,391.36 0.43 109,380.93 0.24
nesta_case6_c 23.14 0.30 23.14 0.30
nesta_case6_ww 3,124.67 0.61 3,124.16 0.49
nesta_case73_ieee_rts 189,706.06 0.03 189,706.15 0.03
nesta_case89_pegase 5,810.15 0.17 5,810.13 0.13
nesta_case9241_pegase 310,621.92 1.67 312,478.72 1.08
nesta_case9_wscc 5,296.67 0.00 5,296.67 0.00

 

QC Optimal Power Flow
Data File (API cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__api 5,774.30 43.77 5,633.90 13.23
nesta_case1354_pegase__api 52,258.07 0.36 52,202.87 0.13
nesta_case13659_pegase__api 297,535.23 1.75 297,658.52 1.16
nesta_case1394sop_eir__api 3,364.43 0.39 3,315.22 0.39
nesta_case1397sp_eir__api 6,588.37 1.16 6,535.89 0.68
nesta_case1460wp_eir__api 6,339.41 1.64 6,191.29 0.56
nesta_case14_ieee__api 321.02 1.26 320.56 0.19
nesta_case162_ieee_dtc__api 6,026.33 1.32 5,841.46 0.60
nesta_case1888_rte__api 58,132.89 0.70 57,022.76 1.24
nesta_case189_edin__api 1,881.73 1.69 1,853.87 0.73
nesta_case1951_rte__api 75,538.41 0.13 74,886.44 0.13
nesta_case2224_edin__api 43,365.60 2.41 42,780.07 0.62
nesta_case2383wp_mp__api 23,315.07 0.74 23,293.47 0.39
nesta_case240_wecc__api 141,847.95 0.58 141,567.42 0.38
nesta_case24_ieee_rts__api 5,548.11 13.67 5,441.51 11.97
nesta_case2736sp_mp__api 25,319.25 2.18 25,298.94 1.44
nesta_case2737sop_mp__api 21,590.79 0.39 21,555.25 0.28
nesta_case2746wop_mp__api 22,692.81 0.48 22,681.58 0.34
nesta_case2746wp_mp__api 25,813.16 0.58 25,744.74 0.53
nesta_case2848_rte__api 43,932.88 0.23 43,019.45 0.22
nesta_case2868_rte__api 75,355.77 0.20 74,731.50 0.18
nesta_case2869_pegase__api 97,832.11 0.59 97,285.27 0.34
nesta_case29_edin__api 294,077.08 0.41 294,042.55 0.04
nesta_case300_ieee__api 19,742.71 0.63 19,662.96 0.52
nesta_case3012wp_mp__api 28,032.43 1.06 27,932.96 0.71
nesta_case30_as__api 543.69 4.63 541.58 2.72
nesta_case30_fsr__api 200.88 45.20 200.59 4.94
nesta_case30_ieee__api 411.17 0.92 410.19 0.23
nesta_case3120sp_mp__api 23,065.18 2.74 23,023.55 1.11
nesta_case3375wp_mp__api 48,604.15 0.68 48,469.22 0.41
nesta_case39_epri__api 7,238.77 2.97 6,920.08 2.17
nesta_case3_lmbd__api 360.87 1.79 360.37 0.57
nesta_case4_gs__api 761.83 0.63 753.90 0.52
nesta_case57_ieee__api 1,427.70 0.21 1,427.70 0.21
nesta_case5_pjm__api 2,988.29 0.27 2,988.22 0.00
nesta_case6468_rte__api 67,539.98 0.89 67,100.25 0.46
nesta_case6470_rte__api 89,856.53 0.80 89,530.37 0.30
nesta_case6495_rte__api 87,839.28 1.24 87,041.73 0.70
nesta_case6515_rte__api 96,168.36 1.08 95,327.37 0.45
nesta_case6_c__api 811.13 0.34 811.12 0.00
nesta_case73_ieee_rts__api 17,630.42 11.83 17,639.33 5.34
nesta_case89_pegase__api 3,411.61 19.83 3,410.86 0.41
nesta_case9241_pegase__api 232,986.28 2.47 234,125.37 1.55
nesta_case9_wscc__api 656.22 0.00 630.71 0.06

 

QC Optimal Power Flow
Data File (SAD cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__sad 3,915.53 4.66 3,899.15 4.71
nesta_case1354_pegase__sad 74,018.14 0.07 74,013.10 0.06
nesta_case13659_pegase__sad 383,410.12 0.71 383,410.12 0.71
nesta_case1394sop_eir__sad 1,388.31 4.21 1,399.11 3.46
nesta_case1397sp_eir__sad 3,924.62 7.39 3,925.70 5.36
nesta_case1460wp_eir__sad 5,283.48 1.00 5,289.12 0.85
nesta_case14_ieee__sad 243.93 0.05 243.93 0.05
nesta_case162_ieee_dtc__sad 4,066.24 4.40 3,975.84 4.36
nesta_case1888_rte__sad 59,585.45 0.45 59,581.22 0.46
nesta_case189_edin__sad 856.32 0.98 856.31 0.92
nesta_case1951_rte__sad 81,696.23 0.11 81,696.40 0.10
nesta_case2224_edin__sad 36,153.57 5.52 35,946.30 3.19
nesta_case2383wp_mp__sad 1,874,201.33 2.21 1,875,144.25 1.96
nesta_case240_wecc__sad 72,379.90 5.38 71,989.23 3.52
nesta_case24_ieee_rts__sad 74,691.07 2.93 74,659.77 2.96
nesta_case2736sp_mp__sad 1,309,104.03 1.53 1,309,092.85 1.53
nesta_case2737sop_mp__sad 777,430.71 1.92 777,434.23 1.92
nesta_case2746wop_mp__sad 1,209,692.28 2.00 1,209,686.38 2.00
nesta_case2746wp_mp__sad 1,639,472.96 1.67 1,639,368.32 1.68
nesta_case2848_rte__sad 52,991.32 0.08 52,991.05 0.07
nesta_case2868_rte__sad 79,758.82 0.07 79,755.48 0.07
nesta_case2869_pegase__sad 133,894.03 0.09 133,888.43 0.09
nesta_case29_edin__sad 34,424.47 16.56 34,424.47 16.56
nesta_case300_ieee__sad 16,708.18 1.10 16,667.63 0.93
nesta_case3012wp_mp__sad 2,583,656.25 1.44 2,583,464.20 0.80
nesta_case30_as__sad 876.72 2.31 876.72 2.31
nesta_case30_fsr__sad 574.44 0.41 574.31 0.03
nesta_case30_ieee__sad 196.43 4.17 183.87 4.29
nesta_case3120sp_mp__sad 2,144,445.09 1.43 2,143,972.54 1.42
nesta_case3375wp_mp__sad 7,400,306.26 0.48 7,399,388.82 0.19
nesta_case39_epri__sad 96,699.56 0.05 96,699.56 0.05
nesta_case3_lmbd__sad 5,874.07 1.43 5,721.31 0.26
nesta_case4_gs__sad 311.01 1.53 311.01 1.53
nesta_case57_ieee__sad 1,142.74 0.05 1,142.74 0.05
nesta_case5_pjm__sad 25,856.71 0.99 25,844.35 1.04
nesta_case6468_rte__sad 86,639.43 0.22 86,630.28 0.17
nesta_case6470_rte__sad 98,198.73 0.16 98,192.17 0.13
nesta_case6495_rte__sad 105,815.76 0.47 105,799.39 0.23
nesta_case6515_rte__sad 109,407.96 0.49 109,394.39 0.23
nesta_case6_c__sad 24.27 0.42 24.27 0.42
nesta_case6_ww__sad 3,139.40 0.22 3,136.45 0.11
nesta_case73_ieee_rts__sad 221,967.31 2.54 221,936.68 2.55
nesta_case89_pegase__sad 5,811.76 0.14 5,811.64 0.13
nesta_case9241_pegase__sad 313,344.79 0.81 313,318.29 0.82
nesta_case9_wscc__sad 5,498.50 0.54 5,498.50 0.54

 

SOCP relaxation:

 

SOCP Optimal Power Flow
Data File GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee 3,650.77 1.83 3,640.81 1.44
nesta_case1354_pegase 74,012.27 0.08 74,005.33 0.07
nesta_case13659_pegase 380,489.43 1.46 382,443.66 0.95
nesta_case1394sop_eir 1,355.59 0.82 1,348.93 0.71
nesta_case1397sp_eir 3,852.77 0.93 3,829.73 0.75
nesta_case1460wp_eir 4,599.08 0.89 4,194.66 1.83
nesta_case14_ieee 243.78 0.11 243.78 0.11
nesta_case162_ieee_dtc 4,059.93 4.03 3,970.73 2.46
nesta_case1888_rte 59,578.12 0.38 59,573.77 0.38
nesta_case189_edin 847.50 0.21 842.13 0.23
nesta_case1951_rte 81,680.36 0.07 81,680.19 0.07
nesta_case2224_edin 35,806.24 6.09 35,709.05 3.51
nesta_case2383wp_mp 1,848,900.95 1.05 1,848,858.21 0.52
nesta_case240_wecc 70,828.43 5.73 70,259.04 3.22
nesta_case24_ieee_rts 63,344.57 0.01 63,344.57 0.01
nesta_case2736sp_mp 1,303,975.55 0.30 1,303,964.92 0.30
nesta_case2737sop_mp 775,673.19 0.25 775,676.57 0.25
nesta_case2746wop_mp 1,203,843.00 0.37 1,203,846.72 0.37
nesta_case2746wp_mp 1,626,473.64 0.32 1,626,414.56 0.33
nesta_case2848_rte 52,981.22 0.08 52,980.93 0.08
nesta_case2868_rte 79,745.37 0.06 79,742.03 0.06
nesta_case2869_pegase 133,879.80 0.09 133,873.51 0.09
nesta_case29_edin 29,860.91 0.12 29,859.48 0.12
nesta_case300_ieee 16,692.03 1.18 16,545.53 0.69
nesta_case3012wp_mp 2,574,258.10 1.02 2,573,280.16 0.49
nesta_case30_as 802.68 0.06 802.68 0.06
nesta_case30_fsr 573.55 0.39 573.54 0.16
nesta_case30_ieee 172.41 15.88 159.64 16.90
nesta_case3120sp_mp 2,134,006.04 0.55 2,132,319.29 0.48
nesta_case3375wp_mp 7,397,372.55 0.52 7,396,243.45 0.23
nesta_case39_epri 96,459.72 0.05 96,459.73 0.05
nesta_case3_lmbd 5,736.17 1.32 5,701.59 0.53
nesta_case4_gs 156.43 0.00 156.43 0.00
nesta_case57_ieee 1,142.53 0.06 1,142.53 0.06
nesta_case5_pjm 14,999.71 14.54 14,997.04 0.00
nesta_case6468_rte 86,635.38 0.22 86,625.01 0.17
nesta_case6470_rte 98,181.06 0.17 98,173.36 0.14
nesta_case6495_rte 105,807.46 0.48 105,791.97 0.24
nesta_case6515_rte 109,395.61 0.43 109,384.76 0.23
nesta_case6_c 23.14 0.30 23.14 0.30
nesta_case6_ww 3,124.28 0.63 3,124.11 0.49
nesta_case73_ieee_rts 189,706.06 0.03 189,706.15 0.03
nesta_case89_pegase 5,810.16 0.17 5,810.14 0.13
nesta_case9241_pegase 310,624.76 1.67 312,533.41 1.06
nesta_case9_wscc 5,296.67 0.00 5,296.67 0.00

 

SOCP Optimal Power Flow
Data File (API cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__api 5,782.24 43.70 5,624.44 13.37
nesta_case1354_pegase__api 52,260.18 0.36 52,204.71 0.13
nesta_case13659_pegase__api 297,352.36 1.81 297,694.76 1.15
nesta_case1394sop_eir__api 3,364.65 0.38 3,315.44 0.39
nesta_case1397sp_eir__api 6,579.87 1.29 6,527.65 0.81
nesta_case1460wp_eir__api 6,336.50 1.68 6,187.66 0.62
nesta_case14_ieee__api 321.02 1.26 320.56 0.19
nesta_case162_ieee_dtc__api 6,025.40 1.33 5,839.98 0.62
nesta_case1888_rte__api 58,130.57 0.71 57,019.90 1.24
nesta_case189_edin__api 1,881.73 1.69 1,853.87 0.73
nesta_case1951_rte__api 75,538.72 0.13 74,884.66 0.13
nesta_case2224_edin__api 43,362.98 2.41 42,779.59 0.62
nesta_case2383wp_mp__api 23,314.63 0.74 23,292.64 0.40
nesta_case240_wecc__api 141,682.88 0.69 141,489.31 0.44
nesta_case24_ieee_rts__api 5,096.93 20.69 5,080.18 17.82
nesta_case2736sp_mp__api 25,317.73 2.19 25,296.56 1.45
nesta_case2737sop_mp__api 21,589.69 0.39 21,554.20 0.28
nesta_case2746wop_mp__api 22,692.16 0.49 22,680.65 0.34
nesta_case2746wp_mp__api 25,811.59 0.59 25,742.34 0.54
nesta_case2848_rte__api 43,933.10 0.23 43,019.17 0.22
nesta_case2868_rte__api 75,352.94 0.20 74,728.80 0.19
nesta_case2869_pegase__api 97,832.77 0.59 97,283.19 0.35
nesta_case29_edin__api 294,087.98 0.41 294,030.96 0.05
nesta_case300_ieee__api 19,726.95 0.71 19,652.02 0.57
nesta_case3012wp_mp__api 28,031.61 1.07 27,932.34 0.71
nesta_case30_as__api 543.69 4.63 541.58 2.72
nesta_case30_fsr__api 200.88 45.20 200.59 4.94
nesta_case30_ieee__api 411.17 0.92 410.19 0.23
nesta_case3120sp_mp__api 23,064.93 2.74 23,022.95 1.11
nesta_case3375wp_mp__api 48,602.96 0.69 48,467.77 0.41
nesta_case39_epri__api 7,237.22 2.99 6,918.86 2.19
nesta_case3_lmbd__api 355.47 3.26 355.25 1.98
nesta_case4_gs__api 761.83 0.63 753.90 0.52
nesta_case57_ieee__api 1,427.70 0.21 1,427.70 0.21
nesta_case5_pjm__api 2,988.29 0.27 2,988.22 0.00
nesta_case6468_rte__api 67,538.33 0.90 67,095.69 0.47
nesta_case6470_rte__api 89,852.12 0.81 89,523.52 0.31
nesta_case6495_rte__api 87,831.28 1.25 87,026.81 0.72
nesta_case6515_rte__api 96,157.47 1.09 95,313.19 0.47
nesta_case6_c__api 811.13 0.34 811.12 0.00
nesta_case73_ieee_rts__api 17,157.37 14.19 16,957.62 9.00
nesta_case89_pegase__api 3,409.78 19.87 3,409.16 0.46
nesta_case9241_pegase__api 232,912.52 2.51 234,162.30 1.54
nesta_case9_wscc__api 656.22 0.00 630.71 0.06

 

SOCP Optimal Power Flow
Data File (SAD cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__sad 3,759.66 8.45 3,754.88 8.23
nesta_case1354_pegase__sad 74,012.65 0.08 74,005.81 0.07
nesta_case13659_pegase__sad 380,498.92 1.46 382,456.27 0.95
nesta_case1394sop_eir__sad 1,385.37 4.41 1,397.20 3.60
nesta_case1397sp_eir__sad 3,918.92 7.53 3,924.81 5.38
nesta_case1460wp_eir__sad 5,279.23 1.08 5,287.94 0.87
nesta_case14_ieee__sad 243.88 0.07 243.88 0.07
nesta_case162_ieee_dtc__sad 4,059.96 4.55 3,971.29 4.47
nesta_case1888_rte__sad 59,578.37 0.47 59,574.03 0.47
nesta_case189_edin__sad 856.31 0.98 856.30 0.92
nesta_case1951_rte__sad 81,680.47 0.13 81,680.28 0.12
nesta_case2224_edin__sad 35,934.48 6.09 35,860.66 3.42
nesta_case2383wp_mp__sad 1,856,507.17 3.13 1,856,799.86 2.92
nesta_case240_wecc__sad 70,828.61 7.41 70,609.63 5.37
nesta_case24_ieee_rts__sad 69,594.57 9.55 69,594.57 9.55
nesta_case2736sp_mp__sad 1,305,597.01 1.79 1,305,597.12 1.79
nesta_case2737sop_mp__sad 776,067.54 2.09 776,070.74 2.09
nesta_case2746wop_mp__sad 1,205,202.78 2.37 1,205,203.87 2.36
nesta_case2746wp_mp__sad 1,630,560.61 2.21 1,630,466.59 2.21
nesta_case2848_rte__sad 52,983.58 0.09 52,983.27 0.09
nesta_case2868_rte__sad 79,745.58 0.09 79,742.24 0.09
nesta_case2869_pegase__sad 133,883.14 0.10 133,878.09 0.09
nesta_case29_edin__sad 30,568.69 25.91 30,568.69 25.91
nesta_case300_ieee__sad 16,693.10 1.19 16,653.51 1.02
nesta_case3012wp_mp__sad 2,578,856.32 1.62 2,578,000.77 1.01
nesta_case30_as__sad 825.93 7.97 826.63 7.89
nesta_case30_fsr__sad 574.08 0.47 574.05 0.08
nesta_case30_ieee__sad 191.07 6.78 180.39 6.10
nesta_case3120sp_mp__sad 2,140,476.97 1.61 2,139,307.76 1.64
nesta_case3375wp_mp__sad 7,397,567.04 0.51 7,396,735.75 0.22
nesta_case39_epri__sad 96,662.73 0.09 96,664.71 0.08
nesta_case3_lmbd__sad 5,736.17 3.74 5,701.90 0.60
nesta_case4_gs__sad 301.56 4.52 301.56 4.52
nesta_case57_ieee__sad 1,142.56 0.06 1,142.56 0.06
nesta_case5_pjm__sad 25,171.09 3.62 25,154.93 3.68
nesta_case6468_rte__sad 86,638.88 0.22 86,628.76 0.17
nesta_case6470_rte__sad 98,189.61 0.17 98,183.89 0.13
nesta_case6495_rte__sad 105,807.46 0.48 105,792.22 0.24
nesta_case6515_rte__sad 109,395.61 0.50 109,385.17 0.24
nesta_case6_c__sad 24.06 1.31 24.06 1.31
nesta_case6_ww__sad 3,124.28 0.70 3,124.11 0.50
nesta_case73_ieee_rts__sad 212,380.25 6.75 212,380.30 6.74
nesta_case89_pegase__sad 5,810.18 0.17 5,810.17 0.16
nesta_case9241_pegase__sad 310,628.00 1.67 312,542.17 1.06
nesta_case9_wscc__sad 5,441.72 1.57 5,441.72 1.57

 

SDP relaxation:

 

SDP Optimal Power Flow
Data File GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee 3,662.40 1.51 3,651.12 1.16
nesta_case1354_pegase 74,015.55 0.07 74,008.53 0.07
nesta_case13659_pegase N/A N/A N/A N/A
nesta_case1394sop_eir 1,356.06 0.79 1,349.51 0.66
nesta_case1397sp_eir 3,854.30 0.89 3,831.15 0.71
nesta_case1460wp_eir 4,600.98 0.84 4,196.65 1.78
nesta_case14_ieee 244.05 0.00 244.05 0.00
nesta_case162_ieee_dtc 4,060.07 4.02 3,970.85 2.45
nesta_case1888_rte 59,581.08 0.37 59,576.84 0.38
nesta_case189_edin 847.89 0.17 842.26 0.21
nesta_case1951_rte 81,681.96 0.07 81,681.73 0.07
nesta_case2224_edin 35,812.44 6.07 35,710.03 3.51
nesta_case2383wp_mp 1,848,921.56 1.05 1,848,879.26 0.52
nesta_case240_wecc 70,853.87 5.70 70,265.39 3.21
nesta_case24_ieee_rts 63,344.59 0.01 63,344.59 0.01
nesta_case2736sp_mp 1,303,979.59 0.30 1,303,968.95 0.30
nesta_case2737sop_mp 775,675.03 0.25 775,678.41 0.25
nesta_case2746wop_mp 1,203,844.60 0.37 1,203,848.32 0.37
nesta_case2746wp_mp 1,626,478.45 0.32 1,626,419.35 0.33
nesta_case2848_rte 52,982.49 0.07 52,982.21 0.07
nesta_case2868_rte 79,748.09 0.06 79,744.72 0.06
nesta_case2869_pegase 133,884.82 0.09 133,878.40 0.08
nesta_case29_edin 29,870.69 0.08 29,870.69 0.08
nesta_case300_ieee 16,734.79 0.93 16,574.35 0.52
nesta_case3012wp_mp 2,574,301.66 1.02 2,573,287.32 0.49
nesta_case30_as 803.11 0.00 803.11 0.00
nesta_case30_fsr 573.64 0.37 573.59 0.15
nesta_case30_ieee 204.85 0.06 191.99 0.06
nesta_case3120sp_mp 2,134,014.15 0.55 2,132,327.27 0.48
nesta_case3375wp_mp 7,397,571.01 0.51 7,396,301.83 0.23
nesta_case39_epri 96,459.87 0.05 96,459.88 0.05
nesta_case3_lmbd 5,789.91 0.39 5,731.65 0.00
nesta_case4_gs 156.43 0.00 156.43 0.00
nesta_case57_ieee 1,142.55 0.06 1,142.55 0.06
nesta_case5_pjm 16,635.70 5.22 14,997.04 0.00
nesta_case6468_rte 86,638.56 0.22 86,628.20 0.17
nesta_case6470_rte 98,185.04 0.17 98,177.36 0.13
nesta_case6495_rte 105,813.11 0.48 105,797.64 0.23
nesta_case6515_rte 109,400.76 0.42 109,389.96 0.23
nesta_case6_c 23.21 0.00 23.21 0.00
nesta_case6_ww 3,124.54 0.62 3,124.35 0.49
nesta_case73_ieee_rts 189,706.07 0.03 189,706.17 0.03
nesta_case89_pegase 5,810.18 0.17 5,810.15 0.13
nesta_case9241_pegase 310,642.68 1.67 312,547.86 1.06
nesta_case9_wscc 5,296.68 0.00 5,296.68 0.00

 

SDP Optimal Power Flow
Data File (API cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__api 5,804.60 43.48 5,632.06 13.26
nesta_case1354_pegase__api 52,268.85 0.34 52,208.60 0.12
nesta_case13659_pegase__api 297,376.97 1.80 297,716.09 1.14
nesta_case1394sop_eir__api 3,366.10 0.34 3,316.84 0.34
nesta_case1397sp_eir__api 6,609.61 0.84 6,556.33 0.37
nesta_case1460wp_eir__api 6,348.74 1.49 6,195.08 0.50
nesta_case14_ieee__api 324.97 0.05 321.16 0.00
nesta_case162_ieee_dtc__api 6,025.67 1.33 5,840.22 0.62
nesta_case1888_rte__api 58,135.48 0.70 57,025.92 1.23
nesta_case189_edin__api 1,891.30 1.19 1,853.98 0.73
nesta_case1951_rte__api 75,542.35 0.13 74,887.49 0.13
nesta_case2224_edin__api 43,373.29 2.39 42,783.07 0.61
nesta_case2383wp_mp__api 23,316.09 0.74 23,294.23 0.39
nesta_case240_wecc__api 141,686.62 0.69 141,493.26 0.43
nesta_case24_ieee_rts__api 5,096.93 20.69 5,080.18 17.82
nesta_case2736sp_mp__api 25,317.76 2.19 25,296.61 1.45
nesta_case2737sop_mp__api 21,589.74 0.39 21,554.26 0.28
nesta_case2746wop_mp__api 22,692.19 0.49 22,680.66 0.34
nesta_case2746wp_mp__api 25,811.64 0.59 25,742.39 0.54
nesta_case2848_rte__api 43,936.50 0.22 43,026.07 0.21
nesta_case2868_rte__api 75,363.27 0.19 74,740.34 0.17
nesta_case2869_pegase__api 97,847.14 0.58 97,296.91 0.33
nesta_case29_edin__api 294,094.37 0.41 294,037.73 0.05
nesta_case300_ieee__api 19,745.83 0.61 19,664.48 0.51
nesta_case3012wp_mp__api 28,033.69 1.06 27,932.68 0.71
nesta_case30_as__api 548.41 3.80 546.55 1.83
nesta_case30_fsr__api 208.26 43.19 205.47 2.62
nesta_case30_ieee__api 413.62 0.33 411.14 0.00
nesta_case3120sp_mp__api 23,073.31 2.71 23,027.05 1.09
nesta_case3375wp_mp__api 48,609.71 0.67 48,469.41 0.41
nesta_case39_epri__api 7,237.23 2.99 6,918.92 2.19
nesta_case3_lmbd__api 362.98 1.21 362.44 0.00
nesta_case4_gs__api 766.57 0.01 757.82 0.00
nesta_case57_ieee__api 1,428.03 0.18 1,428.03 0.18
nesta_case5_pjm__api 2,996.16 0.01 2,988.22 0.00
nesta_case6468_rte__api 67,547.84 0.88 67,105.54 0.45
nesta_case6470_rte__api 89,866.66 0.79 89,538.71 0.29
nesta_case6495_rte__api 87,851.45 1.23 87,042.54 0.70
nesta_case6515_rte__api 96,183.25 1.06 95,329.24 0.45
nesta_case6_c__api 813.83 0.00 811.16 0.00
nesta_case73_ieee_rts__api 17,157.38 14.19 16,957.62 9.00
nesta_case89_pegase__api 3,410.40 19.86 3,409.16 0.46
nesta_case9241_pegase__api 232,943.04 2.49 234,187.53 1.53
nesta_case9_wscc__api 656.23 0.00 631.06 0.00

 

SDP Optimal Power Flow
Data File (SAD cases) GDG (Thermal) Opt. Gap (%) GDG (Current) Opt. Gap (%)
nesta_case118_ieee__sad 3,771.76 8.16 3,764.91 7.99
nesta_case1354_pegase__sad 74,015.68 0.07 74,008.85 0.07
nesta_case13659_pegase__sad N/A N/A N/A N/A
nesta_case1394sop_eir__sad 1,387.12 4.29 1,399.61 3.43
nesta_case1397sp_eir__sad 3,920.42 7.49 3,926.16 5.34
nesta_case1460wp_eir__sad 5,281.05 1.05 5,289.71 0.84
nesta_case14_ieee__sad 244.05 0.00 244.05 0.00
nesta_case162_ieee_dtc__sad 4,060.10 4.55 3,971.41 4.46
nesta_case1888_rte__sad 59,581.36 0.46 59,577.12 0.47
nesta_case189_edin__sad 856.84 0.92 856.43 0.91
nesta_case1951_rte__sad 81,682.07 0.13 81,681.83 0.12
nesta_case2224_edin__sad 35,939.91 6.08 35,861.17 3.42
nesta_case2383wp_mp__sad 1,856,530.67 3.13 1,856,829.13 2.92
nesta_case240_wecc__sad 70,854.06 7.37 70,628.23 5.34
nesta_case24_ieee_rts__sad 69,809.12 9.27 69,809.12 9.27
nesta_case2736sp_mp__sad 1,305,601.28 1.79 1,305,601.38 1.79
nesta_case2737sop_mp__sad 776,069.43 2.09 776,072.64 2.09
nesta_case2746wop_mp__sad 1,205,204.32 2.36 1,205,205.41 2.36
nesta_case2746wp_mp__sad 1,630,583.84 2.21 1,630,489.37 2.21
nesta_case2848_rte__sad 52,984.81 0.09 52,984.50 0.09
nesta_case2868_rte__sad 79,748.26 0.09 79,744.89 0.09
nesta_case2869_pegase__sad 133,888.54 0.09 133,883.32 0.09
nesta_case29_edin__sad 30,668.03 25.67 30,663.07 25.68
nesta_case300_ieee__sad 16,737.30 0.93 16,692.08 0.79
nesta_case3012wp_mp__sad 2,578,889.17 1.62 2,578,007.72 1.01
nesta_case30_as__sad 893.50 0.44 893.61 0.43
nesta_case30_fsr__sad 575.94 0.15 574.10 0.07
nesta_case30_ieee__sad 204.85 0.06 191.99 0.06
nesta_case3120sp_mp__sad 2,140,486.02 1.61 2,139,316.61 1.64
nesta_case3375wp_mp__sad 7,397,768.91 0.51 7,396,804.47 0.22
nesta_case39_epri__sad 96,663.05 0.08 96,665.01 0.08
nesta_case3_lmbd__sad 5,848.58 1.86 5,735.99 0.00
nesta_case4_gs__sad 315.68 0.05 315.68 0.05
nesta_case57_ieee__sad 1,142.59 0.06 1,142.59 0.06
nesta_case5_pjm__sad 26,105.10 0.04 26,105.10 0.04
nesta_case6468_rte__sad 86,641.96 0.22 86,631.85 0.17
nesta_case6470_rte__sad 98,193.50 0.17 98,187.79 0.13
nesta_case6495_rte__sad 105,813.11 0.48 105,797.88 0.23
nesta_case6515_rte__sad 109,400.76 0.50 109,390.37 0.23
nesta_case6_c__sad 24.37 0.01 24.37 0.01
nesta_case6_ww__sad 3,124.54 0.69 3,124.35 0.49
nesta_case73_ieee_rts__sad 212,381.50 6.75 212,381.54 6.74
nesta_case89_pegase__sad 5,810.20 0.17 5,810.17 0.16
nesta_case9241_pegase__sad 310,645.79 1.67 312,556.67 1.06
nesta_case9_wscc__sad 5,526.96 0.02 5,526.96 0.02