Introduction to PowerModelsITD

In this guide, we will go through a beginner guide that demonstrates the current capabilities of PowerModelsITD. This guide will showcase a non-comprehensive list of things you can do with PowerModelsITD.

Each example case shown in this guide will be divided into three main parts.

(1) Brief explanation of the test case and what we want to do/obtain.
(2) The Julia code needed to perform the specific case study (users can copy and paste this code directly).
(3) The console output obtained when the code is executed.

Important: All files used in this beginner guide are available in the /test/data folder of the repository.

Example Case #1: Solving a simple Integrated T&D Optimal Power Flow (OPFITD)

Test Case #1

In this example case, we want to solve the integrated T&D optimal power flow (opfitd) problem for a case where we have the PJM 5-bus system (case5_withload) as the transmission system and the IEEE 4 Node Test Feeder (case3_unbalanced.dss) as the distribution system. The boundary information that specifies the respective boundary buses for both the transmission and distribution systems can be found in case5_case3_unbal.json.

The formulation used to solve this optimization problem is the ACP-ACPU formulation.

Julia Code for Test Case #1

using PowerModelsITD
using Ipopt

silence!()  # Silences the console, so warning messages or information are not displayed

files_path = joinpath(dirname(pathof(PowerModelsITD)), "..")                    # file path for test cases files
pm_file = joinpath(files_path, "test/data/transmission/case5_withload.m")       # transmission system file
pmd_file = joinpath(files_path, "test/data/distribution/case3_unbalanced.dss")  # distribution system file
boundary_file = joinpath(files_path, "test/data/json/case5_case3_unbal.json")   # boundary file with info. about boundary buses
formulation = NLPowerModelITD{ACPPowerModel, ACPUPowerModel}                    # type of formulation to be used
data = parse_files(pm_file, pmd_file, boundary_file)                        # parse files into dictionary
result = solve_opfitd(data, formulation, Ipopt.Optimizer)                   # solve the opfitd

# Check the result
@info "Objective: $(result["objective"]) [\$/hr]"
@info "Termination Status of Solver: $(result["termination_status"])"
@info "Solve Time: $(result["solve_time"]) [seconds]"
@info "Solution Values for Transmission system: $(result["solution"]["it"]["pm"])"
@info "Solution Values for Distribution system(s): $(result["solution"]["it"]["pmd"])"
@info "Solution Values for Boundary(ies): $(result["solution"]["it"]["pmitd"])"

Console Output for Test Case #1

After running the corresponding code, the user should get the following output displayed on the console.

[ Main | Info ] : Objective: 17953.746512039743 [$/hr]
[ Main | Info ] : Termination Status of Solver: LOCALLY_SOLVED
[ Main | Info ] : Solve Time: 0.05849599838256836 [seconds]

[ Main | Info ] : Solution Values for Transmission system: Dict{String, Any}("baseMVA" => 100.0, "branch" => Dict{String, Any}("4" => Dict{String, Any}("qf" => -215.4572384567855, "qt" => 220.01471251650577, "pt" => 72.72770254777281, "pf" => -72.10324334974787), "1" => Dict{String, Any}("qf" => -91.9457671031378, "qt" => 113.04924896169344, "pt" => -235.96795359006418, "pf" => 238.13985616928193), "5" => Dict{String, Any}("qf" => 71.37529049674947, "qt" => -69.00868855761938, "pt" => 57.04309684079022, "pf" => -56.75055132454856), "2" => Dict{String, Any}("qf" => 40.82747127060588, "qt" => -27.51897757380047, "pt" => -190.17342809935752, "pf" => 191.55864094141782), "6" => Dict{String, Any}("qf" => 19.289482716290323, "qt" => 1.0554040857229503, "pt" => 239.9976806084548, "pf" => -237.90830207159405), "7" => Dict{String, Any}("qf" => 3.7979894950920543, "qt" => -4.367184067738672, "pt" => -8.068452673591816, "pf" => 8.071196939812054), "3" => Dict{String, Any}("qf" => 208.61829769507162, "qt" => -204.19918131371665, "pt" => 220.40004611863847, "pf" => -219.6984944935753)), "gen" => Dict{String, Any}("4" => Dict{String, Any}("qg" => 54.23181658487047, "pg" => 18.96136666983862), "1" => Dict{String, Any}("qg" => 30.00000079376986, "pg" => 40.00000096678977), "5" => Dict{String, Any}("qg" => -203.1437772279937, "pg" => 460.3977267270933), "2" => Dict{String, Any}("qg" => 127.50000106876985, "pg" => 170.00000165033464), "3" => Dict{String, Any}("qg" => 390.00000301325525, "pg" => 315.97715122322427)), "multinetwork" => false, "bus" => Dict{String, Any}("4" => Dict{String, Any}("va" => -9.820934169803595e-29, "vm" => 0.8999999900918129), "1" => Dict{String, Any}("va" => 3.9557118095964663, "vm" => 0.9178154479809132), "5" => Dict{String, Any}("va" => -0.8036120919989638, "vm" => 0.9400883479210898), "2" => Dict{String, Any}("va" => -0.6563318572164789, "vm" => 0.9416319858451535), "10" => Dict{String, Any}("va" => 5.018509000535593, "vm" => 0.904864159526407), "3" => Dict{String, Any}("va" => -0.3122279603896953, "vm" => 0.9670939985734723)), "per_unit" => false)

[ Main | Info ] : Solution Values for Distribution system(s): Dict{String, Any}("line" => Dict{String, Any}("3bus_unbal.quad" => Dict{String, Any}("qf" => [1344.7785535214057, 1503.9392726830868, 1502.43791779139], "qt" => [-1333.3300000000002, -1500.0000000000002, -1500.0000000000002], "pt" => [-3333.3323371531164, -2333.3323371935803, -2333.3323371900296], "pf" => [3351.5305232165006, 2340.3516279866967, 2344.8964126191295]), "3bus_unbal.ohline" => Dict{String, Any}("qf" => [1354.6163225169614, 1507.2344513630765, 1504.4700979169072], "qt" => [-1344.7785535214057, -1503.9392726830868, -1502.43791779139], "pt" => [-3351.5305232165006, -2340.3516279866967, -2344.8964126191295], "pf" => [3367.110727286094, 2346.3597337552624, 2354.8245890269895])), "settings" => Dict{String, Any}("sbase" => 100000.0), "transformer" => Dict{String, Any}("3bus_unbal.subxf" => Dict{String, Any}("q" => [[1354.7952022418647, 1507.3400640138161, 1504.5761375753734], [-1354.6163225169614, -1507.2344513630765, -1504.4700979169072]], "p" => [[3367.1286152278885, 2346.3702946258413, 2354.835193007617], [-3367.110727286094, -2346.3597337552624, -2354.8245890269895]])), "generator" => Dict{String, Any}("3bus_unbal.gen1" => Dict{String, Any}("qg_bus" => [-0.0, -0.0, -0.0], "qg" => [-0.0, -0.0, -0.0], "pg" => [666.6676628468832, 666.6676628064197, 666.6676628099706], "pg_bus" => [666.6676628468832, 666.6676628064197, 666.6676628099706])), "load" => Dict{String, Any}("3bus_unbal.l2" => Dict{String, Any}("qd_bus" => [1500.0000000000002], "pd_bus" => [3000.0000000000005], "qd" => [1500.0000000000002], "pd" => [3000.0000000000005]), "3bus_unbal.l3" => Dict{String, Any}("qd_bus" => [1500.0000000000002], "pd_bus" => [3000.0000000000005], "qd" => [1500.0000000000002], "pd" => [3000.0000000000005]), "3bus_unbal.l1" => Dict{String, Any}("qd_bus" => [1333.3300000000002], "pd_bus" => [4000.0], "qd" => [1333.3300000000002], "pd" => [4000.0])), "bus" => Dict{String, Any}("3bus_unbal.loadbus" => Dict{String, Any}("va" => [-0.9542852429015141, -120.82463162589393, 119.31695673367102], "vm" => [7.406969380817659, 7.446613395025093, 7.431619824571949]), "3bus_unbal.substation" => Dict{String, Any}("va" => [-0.8089341499650244, -120.8072185671511, 119.19279637320398], "vm" => [7.489646348633082, 7.489651704574486, 7.489663202448464]), "3bus_unbal.primary" => Dict{String, Any}("va" => [-0.8772138344778904, -120.81603057758366, 119.24896754768255], "vm" => [7.4514218741879255, 7.4697354940559455, 7.462765580863505]), "3bus_unbal.sourcebus" => Dict{String, Any}("va" => [-0.8064197613818459, -120.80551025323088, 119.19451148306055], "vm" => [124.83030630100751, 124.83048117738736, 124.8306695534823])), "per_unit" => false)

[ Main | Info ] : Solution Values for Boundary(ies): Dict{String, Any}("multinetwork" => false, "boundary" => Dict{String, Any}("(100001, 5, voltage_source.3bus_unbal.source)" => Dict{String, Any}("pbound_fr" => [8068.452673591816], "qbound_fr" => [4367.184067738673]), "(100001, voltage_source.3bus_unbal.source, 5)" => Dict{String, Any}("pbound_to" => [-3367.1850486607445, -2346.4026604158908, -2354.8649645151804], "qbound_to" => [-1355.0096276913357, -1507.4706735124998, -1504.7037665348369])))

Example Case #2: Solving a Multinetwork (Time-series) Multisystem (Multiple Distribution Systems) OPFITD

Test Case #2

In this example case, we want to solve the integrated T&D optimal power flow (opfitd) problem for a Multinetwork case where we have the PJM 5-bus system (case5_with2loads) as the transmission system and two copies of the IEEE 4 Node Test Feeder (case3_unbalanced_withoutgen_mn.dss) as the distribution systems, where each distribution system has load profiles for their respective loads for four timesteps. The boundary information that specifies the respective boundary buses for both the transmission and distribution systems can be found in case5_case3x2.json.

The formulation used to solve this optimization problem is the ACP-ACPU formulation.

Julia Code for Test Case #2

using PowerModelsITD
using Ipopt

silence!()  # Silences the console, so warning messages or information are not displayed

files_path = joinpath(dirname(pathof(PowerModelsITD)), "..")                                    # file path for test cases files
pm_file = joinpath(files_path, "test/data/transmission/case5_with2loads.m")                     # transmission system file
pmd_file = joinpath(files_path, "test/data/distribution/case3_unbalanced_withoutgen_mn.dss")    # distribution system file
boundary_file = joinpath(files_path, "test/data/json/case5_case3x2.json")                       # boundary file with info. about boundary buses
pmd_files = [pmd_file, pmd_file]                                                                # vector of distrib. systems (in this case a copy of the same)
formulation = NLPowerModelITD{ACPPowerModel, ACPUPowerModel}                                    # type of formulation to be used
result = solve_mn_opfitd(pm_file, pmd_files, boundary_file, formulation, Ipopt.Optimizer; auto_rename=true)  # solve the multinetwork opfitd

# Check the result
@info "Objective: $(result["objective"]) [\$/hr]"
@info "Termination Status of Solver: $(result["termination_status"])"
@info "Solve Time: $(result["solve_time"]) [seconds]"
@info "Solution Values for Transmission system: $(result["solution"]["it"]["pm"])"
@info "Solution Values for Distribution system(s): $(result["solution"]["it"]["pmd"])"
@info "Solution Values for Boundary(ies): $(result["solution"]["it"]["pmitd"])"

Console Output for Test Case #2

After running the corresponding code, the user should get the following output displayed on the console.

[ Main | Info ] : Objective: 71583.37023067646 [$/hr]
[ Main | Info ] : Termination Status of Solver: LOCALLY_SOLVED
[ Main | Info ] : Solve Time: 0.5699648857116699 [seconds]

[ Main | Info ] : Solution Values for Transmission system: Dict{String, Any}("multinetwork" => true, "nw" => Dict{String, Any}("4" => Dict{String, Any}("baseMVA" => 100.0, "branch" => Dict{String, Any}("3" => Dict{String, Any}("qf" => 209.7124512609962, "qt" => -205.25808038279263, "pt" => 220.4516503859562, "pf" => -219.74655219293345), "4" => Dict{String, Any}("qf" => -214.48170261865238, "qt" => 218.94452403011204, "pt" => 70.63553676891648, "pf" => -70.02040086637558), "1" => Dict{String, Any}("qf" => -93.26577989474518, "qt" => 114.45283104138902, "pt" => -235.99842638945864, "pf" => 238.17872276993856), "5" => Dict{String, Any}("qf" => 72.445478971592, "qt" => -70.00150166186677, "pt" => 57.688800117737046, "pf" => -57.388497698913255), "2" => Dict{String, Any}("qf" => 41.053330496054876, "qt" => -27.739129989384807, "pt" => -190.18204403801204, "pf" => 191.56783204014675), "6" => Dict{String, Any}("qf" => 19.29122822256867, "qt" => 1.0536848339377651, "pt" => 239.99768816280888, "pf" => -237.90830703516832), "7" => Dict{String, Any}("qf" => 1.418871577263358, "qt" => -2.003521254092567, "pt" => -6.017516284814005, "pf" => 6.018827255834227), "8" => Dict{String, Any}("qf" => 0.7049338049713338, "qt" => -1.2985975532566612, "pt" => -3.008593331044258, "pf" => 3.008930510206021)), "gen" => Dict{String, Any}("4" => Dict{String, Any}("qg" => 53.02059657131708, "pg" => 19.598449044556656), "1" => Dict{String, Any}("qg" => 30.00000079365296, "pg" => 40.00000096679825), "5" => Dict{String, Any}("qg" => -204.20439554885485, "pg" => 460.449338548765), "2" => Dict{String, Any}("qg" => 127.50000106865294, "pg" => 170.0000016503536), "3" => Dict{String, Any}("qg" => 390.00000300170404, "pg" => 313.2470390700032)), "bus" => Dict{String, Any}("4" => Dict{String, Any}("va" => -4.8091331437638894e-29, "vm" => 0.8999999900913073), "1" => Dict{String, Any}("va" => 3.955108495412184, "vm" => 0.9178896115768673), "5" => Dict{String, Any}("va" => -0.7695989397082574, "vm" => 0.9413800134626195), "2" => Dict{String, Any}("va" => -0.6574104691903474, "vm" => 0.9421095463639055), "6" => Dict{String, Any}("va" => -0.8254740984569308, "vm" => 0.9409689065117178), "10" => Dict{String, Any}("va" => 5.018515926892925, "vm" => 0.9048635910623162), "3" => Dict{String, Any}("va" => -0.3270759541168204, "vm" => 0.967421494353026))), "1" => Dict{String, Any}("baseMVA" => 100.0, "branch" => Dict{String, Any}("3" => Dict{String, Any}("qf" => 209.71245126093345, "qt" => -205.25808038273263, "pt" => 220.4516503861189, "pf" => -219.74655219309614), "4" => Dict{String, Any}("qf" => -214.4817026186947, "qt" => 218.94452403016115, "pt" => 70.6355367692654, "pf" => -70.02040086672375), "1" => Dict{String, Any}("qf" => -93.26577989466723, "qt" => 114.45283104133719, "pt" => -235.9984263896544, "pf" => 238.17872277013694), "5" => Dict{String, Any}("qf" => 72.44547897154284, "qt" => -70.001501661815, "pt" => 57.68880011784228, "pf" => -57.38849769901818), "2" => Dict{String, Any}("qf" => 41.05333049603968, "qt" => -27.73912998937486, "pt" => -190.1820440379769, "pf" => 191.56783204011106), "6" => Dict{String, Any}("qf" => 19.291228222568602, "qt" => 1.0536848339378524, "pt" => 239.99768816280888, "pf" => -237.90830703516832), "7" => Dict{String, Any}("qf" => 1.4188715773575376, "qt" => -2.003521254185469, "pt" => -6.017516285357827, "pf" => 6.0188272563781675), "8" => Dict{String, Any}("qf" => 0.7049338050415234, "qt" => -1.2985975533248926, "pt" => -3.0085933319508262, "pf" => 3.0089305111127547)), "gen" => Dict{String, Any}("4" => Dict{String, Any}("qg" => 53.02059657137874, "pg" => 19.598449044697038), "1" => Dict{String, Any}("qg" => 30.00000079365296, "pg" => 40.00000096679825), "5" => Dict{String, Any}("qg" => -204.2043955487948, "pg" => 460.44933854892776), "2" => Dict{String, Any}("qg" => 127.50000106865294, "pg" => 170.0000016503536), "3" => Dict{String, Any}("qg" => 390.00000300170404, "pg" => 313.24703907024724)), "bus" => Dict{String, Any}("4" => Dict{String, Any}("va" => 1.2906268155608688e-29, "vm" => 0.8999999900913073), "1" => Dict{String, Any}("va" => 3.9551084954114852, "vm" => 0.9178896115768619), "5" => Dict{String, Any}("va" => -0.7695989397229616, "vm" => 0.9413800134625423), "2" => Dict{String, Any}("va" => -0.6574104691947822, "vm" => 0.9421095463638751), "6" => Dict{String, Any}("va" => -0.8254740984889308, "vm" => 0.9409689065115902), "10" => Dict{String, Any}("va" => 5.018515926892924, "vm" => 0.9048635910623162), "3" => Dict{String, Any}("va" => -0.3270759541189024, "vm" => 0.9674214943530053))), "2" => Dict{String, Any}("baseMVA" => 100.0, "branch" => Dict{String, Any}("3" => Dict{String, Any}("qf" => 209.71245126094163, "qt" => -205.25808038273715, "pt" => 220.45165038612856, "pf" => -219.74655219310594), "4" => Dict{String, Any}("qf" => -214.4817026186913, "qt" => 218.94452403015868, "pt" => 70.63553676925657, "pf" => -70.02040086671512), "1" => Dict{String, Any}("qf" => -93.26577989467265, "qt" => 114.45283104134505, "pt" => -235.99842638966595, "pf" => 238.1787227701487), "5" => Dict{String, Any}("qf" => 72.44547897154538, "qt" => -70.00150166181722, "pt" => 57.688800117857696, "pf" => -57.38849769903358), "2" => Dict{String, Any}("qf" => 41.053330496036935, "qt" => -27.739129989371886, "pt" => -190.18204403797492, "pf" => 191.56783204010912), "6" => Dict{String, Any}("qf" => 19.291228222572368, "qt" => 1.0536848339335343, "pt" => 239.99768816280888, "pf" => -237.90830703516826), "7" => Dict{String, Any}("qf" => 1.4188715773462648, "qt" => -2.0035212541732794, "pt" => -6.017516285360724, "pf" => 6.0188272563810745), "8" => Dict{String, Any}("qf" => 0.7049338050293561, "qt" => -1.2985975533139513, "pt" => -3.008593331590926, "pf" => 3.008930510752742)), "gen" => Dict{String, Any}("4" => Dict{String, Any}("qg" => 53.02059657138327, "pg" => 19.59844904471449), "1" => Dict{String, Any}("qg" => 30.00000079365296, "pg" => 40.00000096679825), "5" => Dict{String, Any}("qg" => -204.2043955488037, "pg" => 460.4493385489374), "2" => Dict{String, Any}("qg" => 127.50000106865294, "pg" => 170.0000016503536), "3" => Dict{String, Any}("qg" => 390.00000300170404, "pg" => 313.24703907022297)), "bus" => Dict{String, Any}("4" => Dict{String, Any}("va" => -8.850496391421805e-29, "vm" => 0.8999999900913073), "1" => Dict{String, Any}("va" => 3.9551084954114537, "vm" => 0.9178896115768609), "5" => Dict{String, Any}("va" => -0.7695989397233032, "vm" => 0.9413800134625466), "2" => Dict{String, Any}("va" => -0.6574104691950458, "vm" => 0.9421095463638758), "6" => Dict{String, Any}("va" => -0.8254740984823784, "vm" => 0.9409689065116095), "10" => Dict{String, Any}("va" => 5.018515926892941, "vm" => 0.9048635910623148), "3" => Dict{String, Any}("va" => -0.3270759541192233, "vm" => 0.9674214943530055))), "3" => Dict{String, Any}("baseMVA" => 100.0, "branch" => Dict{String, Any}("3" => Dict{String, Any}("qf" => 209.7124512609906, "qt" => -205.2580803827864, "pt" => 220.45165038608707, "pf" => -219.7465521930642), "4" => Dict{String, Any}("qf" => -214.48170261865874, "qt" => 218.94452403012218, "pt" => 70.63553676895856, "pf" => -70.0204008664175), "1" => Dict{String, Any}("qf" => -93.26577989472547, "qt" => 114.45283104139405, "pt" => -235.9984263896151, "pf" => 238.17872277009747), "5" => Dict{String, Any}("qf" => 72.44547897158185, "qt" => -70.00150166185058, "pt" => 57.6888001178973, "pf" => -57.38849769907291), "2" => Dict{String, Any}("qf" => 41.05333049604079, "qt" => -27.739129989375172, "pt" => -190.1820440379844, "pf" => 191.56783204011862), "6" => Dict{String, Any}("qf" => 19.291228222579896, "qt" => 1.0536848339270362, "pt" => 239.99768816280894, "pf" => -237.90830703516818), "7" => Dict{String, Any}("qf" => 1.4188715772646756, "qt" => -2.0035212540928145, "pt" => -6.017516285012341, "pf" => 6.018827256032563), "8" => Dict{String, Any}("qf" => 0.7049338050059494, "qt" => -1.298597553290569, "pt" => -3.008593331239918, "pf" => 3.0089305104016915)), "gen" => Dict{String, Any}("4" => Dict{String, Any}("qg" => 53.02059657135414, "pg" => 19.598449044744708), "1" => Dict{String, Any}("qg" => 30.00000079365296, "pg" => 40.00000096679825), "5" => Dict{String, Any}("qg" => -204.20439554885937, "pg" => 460.44933854889604), "2" => Dict{String, Any}("qg" => 127.50000106865294, "pg" => 170.0000016503536), "3" => Dict{String, Any}("qg" => 390.00000300170404, "pg" => 313.24703906988566)), "bus" => Dict{String, Any}("4" => Dict{String, Any}("va" => 4.6922476467138066e-29, "vm" => 0.8999999900913073), "1" => Dict{String, Any}("va" => 3.9551084954116407, "vm" => 0.9178896115768624), "5" => Dict{String, Any}("va" => -0.7695989397156218, "vm" => 0.9413800134626014), "2" => Dict{String, Any}("va" => -0.6574104691939039, "vm" => 0.9421095463638939), "6" => Dict{String, Any}("va" => -0.8254740984679912, "vm" => 0.9409689065116826), "10" => Dict{String, Any}("va" => 5.0185159268929675, "vm" => 0.9048635910623125), "3" => Dict{String, Any}("va" => -0.3270759541200902, "vm" => 0.967421494353016)))), "per_unit" => false)

[ Main | Info ] : Solution Values for Distribution system(s): Dict{String, Any}("nw" => Dict{String, Dict{String, Any}}("4" => Dict("line" => Dict{String, Any}("3bus_unbal_nogen_mn.ohline" => Dict{String, Any}("qf" => [400.5777180879746, 449.1439873945076, 448.7567158126756], "qt" => [-400.3834881406001, -449.61753973455666, -449.40808066075476], "pt" => [-1202.2047813968609, -900.9716820211081, -901.437570378043], "pf" => [1204.092342226798, 901.8028241168121, 902.6707125959695]), "3bus_unbal_nogen_mn_2.quad" => Dict{String, Any}("qf" => [400.3857159633698, 449.61909326817045, 449.40944838966254], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.206724198158, 900.9725348138786, 901.4388339186033]), "3bus_unbal_nogen_mn.quad" => Dict{String, Any}("qf" => [400.3834881406001, 449.61753973455666, 449.40808066075476], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.2047813968609, 900.9716820211081, 901.437570378043]), "3bus_unbal_nogen_mn_2.ohline" => Dict{String, Any}("qf" => [400.5820103770306, 449.147016724407, 448.75940230925625], "qt" => [-400.3857159633698, -449.61909326817045, -449.40944838966254], "pt" => [-1202.206724198158, -900.9725348138786, -901.4388339186033], "pf" => [1204.0959489625075, 901.8044071741432, 902.673061143103])), "settings" => Dict{String, Any}("sbase" => 100000.0), "transformer" => Dict{String, Any}("3bus_unbal_nogen_mn_2.subxf" => Dict{String, Any}("q" => [[400.60383553276677, 449.1607731500957, 448.77317528774904], [-400.5820103770306, -449.147016724407, -448.75940230925625]], "p" => [[1204.0981313859945, 901.8057826939303, 902.6744388456775], [-1204.0959489625075, -901.8044071741432, -902.673061143103]]), "3bus_unbal_nogen_mn.subxf" => Dict{String, Any}("q" => [[400.59952401926625, 449.1577317466543, 448.77047663804154], [-400.5777180879746, -449.1439873945076, -448.7567158126756]], "p" => [[1204.0945224674979, 901.804198545205, 902.672088661453], [-1204.092342226798, -901.8028241168121, -902.6707125959695]])), "load" => Dict{String, Any}("3bus_unbal_nogen_mn_2.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn_2.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn_2.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001])), "bus" => Dict{String, Any}("3bus_unbal_nogen_mn.loadbus" => Dict{String, Any}("va" => [-0.8302295799057324, -120.79137859901346, 119.2504000096645], "vm" => [7.472201725143692, 7.48392238161073, 7.479449806375467]), "3bus_unbal_nogen_mn.sourcebus" => Dict{String, Any}("va" => [-0.7706229194665752, -120.77035368944988, 119.22965458272802], "vm" => [125.00492912857915, 125.0049742054994, 125.00503001738106]), "3bus_unbal_nogen_mn.primary" => Dict{String, Any}("va" => [-0.7991413115394987, -120.78074600616584, 119.23848685007212], "vm" => [7.487284000425346, 7.492696895897028, 7.490619086774545]), "3bus_unbal_nogen_mn_2.primary" => Dict{String, Any}("va" => [-0.855042232531755, -120.83663088144945, 119.18261888118052], "vm" => [7.484002753336548, 7.489418049928727, 7.487339328524334]), "3bus_unbal_nogen_mn.substation" => Dict{String, Any}("va" => [-0.7715260550666929, -120.77101852028557, 119.22898904907676], "vm" => [7.500242832893439, 7.500243675517293, 7.50024705477223]), "3bus_unbal_nogen_mn_2.sourcebus" => Dict{String, Any}("va" => [-0.8264989754781323, -120.82622950863666, 119.173778769923], "vm" => [124.95033736057859, 124.95038246062096, 124.95043829748143]), "3bus_unbal_nogen_mn_2.substation" => Dict{String, Any}("va" => [-0.8274029028977026, -120.8268949215367, 119.17311265297246], "vm" => [7.496967303220576, 7.496968146567504, 7.496971527361585]), "3bus_unbal_nogen_mn_2.loadbus" => Dict{String, Any}("va" => [-0.8861577649359917, -120.84727282112708, 119.19454256329932], "vm" => [7.468913830909152, 7.480639684348965, 7.476165145424161])), "per_unit" => false), "1" => Dict("line" => Dict{String, Any}("3bus_unbal_nogen_mn.ohline" => Dict{String, Any}("qf" => [400.57771808779745, 449.1439873947322, 448.7567158126303], "qt" => [-400.38348814059987, -449.6175397346913, -449.40808066071014], "pt" => [-1202.204781396862, -900.9716820213755, -901.4375703783082], "pf" => [1204.09234222689, 901.8028241171684, 902.6707125964111]), "3bus_unbal_nogen_mn_2.quad" => Dict{String, Any}("qf" => [400.3857159634153, 449.6190932679933, 449.40944838961826], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.2067241982484, 900.9725348139676, 901.4388339183369]), "3bus_unbal_nogen_mn.quad" => Dict{String, Any}("qf" => [400.38348814059987, 449.6175397346913, 449.40808066071014], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.204781396862, 900.9716820213755, 901.4375703783082]), "3bus_unbal_nogen_mn_2.ohline" => Dict{String, Any}("qf" => [400.5820103772543, 449.14701672423075, 448.75940230921145], "qt" => [-400.3857159634153, -449.6190932679933, -449.40944838961826], "pt" => [-1202.2067241982484, -900.9725348139676, -901.4388339183369], "pf" => [1204.095948962688, 901.8044071742323, 902.6730611427464])), "settings" => Dict{String, Any}("sbase" => 100000.0), "transformer" => Dict{String, Any}("3bus_unbal_nogen_mn_2.subxf" => Dict{String, Any}("q" => [[400.60383553298436, 449.16077317266615, 448.77317528770436], [-400.5820103772543, -449.14701672423075, -448.75940230921145]], "p" => [[1204.0981315680738, 901.8057830578177, 902.6744392091184], [-1204.095948962688, -901.8044071742323, -902.6730611427464]]), "3bus_unbal_nogen_mn.subxf" => Dict{String, Any}("q" => [[400.59952401908913, 449.15773174687035, 448.7704766493643], [-400.57771808779745, -449.1439873947322, -448.7567158126303]], "p" => [[1204.0945221037925, 901.8041985455613, 902.6720886618943], [-1204.09234222689, -901.8028241171684, -902.6707125964111]])), "load" => Dict{String, Any}("3bus_unbal_nogen_mn_2.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn_2.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn_2.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001])), "bus" => Dict{String, Any}("3bus_unbal_nogen_mn.loadbus" => Dict{String, Any}("va" => [-0.830229579920092, -120.79137859902801, 119.25040000964974], "vm" => [7.4722017251430914, 7.483922381610104, 7.479449806374842]), "3bus_unbal_nogen_mn.sourcebus" => Dict{String, Any}("va" => [-0.7706229194809523, -120.77035368946459, 119.22965458271331], "vm" => [125.0049291285691, 125.00497420548916, 125.00503001737073]), "3bus_unbal_nogen_mn.primary" => Dict{String, Any}("va" => [-0.7991413115538781, -120.78074600618037, 119.23848685005738], "vm" => [7.4872840004247445, 7.4926968958964055, 7.490619086773919]), "3bus_unbal_nogen_mn_2.primary" => Dict{String, Any}("va" => [-0.8550422325640687, -120.83663088148208, 119.18261888114806], "vm" => [7.484002753335518, 7.489418049927689, 7.487339328523306]), "3bus_unbal_nogen_mn.substation" => Dict{String, Any}("va" => [-0.7715260550810701, -120.77101852030012, 119.22898904906208], "vm" => [7.5002428328928366, 7.500243675516679, 7.5002470547716085]), "3bus_unbal_nogen_mn_2.sourcebus" => Dict{String, Any}("va" => [-0.8264989755103133, -120.826229508669, 119.17377876989066], "vm" => [124.95033736056153, 124.95038246060375, 124.95043829746425]), "3bus_unbal_nogen_mn_2.substation" => Dict{String, Any}("va" => [-0.827402902930025, -120.82689492156933, 119.17311265293998], "vm" => [7.4969673032195505, 7.496968146566467, 7.496971527360553]), "3bus_unbal_nogen_mn_2.loadbus" => Dict{String, Any}("va" => [-0.8861577649683284, -120.84727282115972, 119.19454256326688], "vm" => [7.468913830908116, 7.4806396843479295, 7.476165145423132])), "per_unit" => false), "2" => Dict("line" => Dict{String, Any}("3bus_unbal_nogen_mn.ohline" => Dict{String, Any}("qf" => [400.5777180878409, 449.1439873945529, 448.75671581271985], "qt" => [-400.3834881405547, -449.6175397345132, -449.40808066079904], "pt" => [-1202.2047813968604, -900.9716820211088, -901.4375703779534], "pf" => [1204.0923422269757, 901.8028241166346, 902.6707125959689]), "3bus_unbal_nogen_mn_2.quad" => Dict{String, Any}("qf" => [400.3857159633255, 449.6190932685255, 449.40944838966266], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.2067241982472, 900.9725348141451, 901.4388339188698]), "3bus_unbal_nogen_mn.quad" => Dict{String, Any}("qf" => [400.3834881405547, 449.6175397345132, 449.40808066079904], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.2047813968604, 900.9716820211088, 901.4375703779534]), "3bus_unbal_nogen_mn_2.ohline" => Dict{String, Any}("qf" => [400.58201037707516, 449.1470167248505, 448.75940230925687], "qt" => [-400.3857159633255, -449.6190932685255, -449.40944838966266], "pt" => [-1202.2067241982472, -900.9725348141451, -901.4388339188698], "pf" => [1204.095948962507, 901.8044071744985, 902.6730611437251])), "settings" => Dict{String, Any}("sbase" => 100000.0), "transformer" => Dict{String, Any}("3bus_unbal_nogen_mn_2.subxf" => Dict{String, Any}("q" => [[400.6038355441561, 449.16077316190854, 448.7731752991101], [-400.58201037707516, -449.1470167248505, -448.75940230925687]], "p" => [[1204.098131204093, 901.8057832399824, 902.6744390281976], [-1204.095948962507, -901.8044071744985, -902.6730611437251]]), "3bus_unbal_nogen_mn.subxf" => Dict{String, Any}("q" => [[400.5995240305012, 449.157731758069, 448.77047663808975], [-400.5777180878409, -449.1439873945529, -448.75671581271985]], "p" => [[1204.0945224676755, 901.8041985450279, 902.6720886614527], [-1204.0923422269757, -901.8028241166346, -902.6707125959689]])), "load" => Dict{String, Any}("3bus_unbal_nogen_mn_2.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn_2.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn_2.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001])), "bus" => Dict{String, Any}("3bus_unbal_nogen_mn.loadbus" => Dict{String, Any}("va" => [-0.8302295799209277, -120.79137859902852, 119.25040000964935], "vm" => [7.472201725143105, 7.483922381610151, 7.479449806374883]), "3bus_unbal_nogen_mn.sourcebus" => Dict{String, Any}("va" => [-0.7706229194816114, -120.77035368946491, 119.22965458271298], "vm" => [125.00492912856943, 125.00497420548972, 125.00503001737137]), "3bus_unbal_nogen_mn.primary" => Dict{String, Any}("va" => [-0.79914131155471, -120.78074600618085, 119.23848685005699], "vm" => [7.48728400042476, 7.492696895896448, 7.4906190867739575]), "3bus_unbal_nogen_mn_2.primary" => Dict{String, Any}("va" => [-0.85504223255677, -120.83663088147543, 119.18261888115482], "vm" => [7.4840027533357, 7.489418049927836, 7.487339328523451]), "3bus_unbal_nogen_mn.substation" => Dict{String, Any}("va" => [-0.77152605508187, -120.77101852030057, 119.2289890490616], "vm" => [7.500242832892855, 7.5002436755167095, 7.500247054771646]), "3bus_unbal_nogen_mn_2.sourcebus" => Dict{String, Any}("va" => [-0.826498975503429, -120.82622950866259, 119.1737787698974], "vm" => [124.95033736056432, 124.95038246060629, 124.95043829746685]), "3bus_unbal_nogen_mn_2.substation" => Dict{String, Any}("va" => [-0.8274029029227165, -120.82689492156277, 119.17311265294684], "vm" => [7.496967303219722, 7.496968146566622, 7.49697152736071]), "3bus_unbal_nogen_mn_2.loadbus" => Dict{String, Any}("va" => [-0.8861577649610355, -120.84727282115303, 119.19454256327364], "vm" => [7.468913830908303, 7.480639684348074, 7.476165145423272])), "per_unit" => false), "3" => Dict("line" => Dict{String, Any}("3bus_unbal_nogen_mn.ohline" => Dict{String, Any}("qf" => [400.5777180877519, 449.1439873945082, 448.75671581263083], "qt" => [-400.38348814055513, -449.6175397345571, -449.4080806607989], "pt" => [-1202.20478139695, -900.9716820211972, -901.4375703778643], "pf" => [1204.092342226887, 901.8028241168124, 902.6707125957021]), "3bus_unbal_nogen_mn_2.quad" => Dict{String, Any}("qf" => [400.38571596332577, 449.6190932680813, 449.40944838961764], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.2067241981586, 900.9725348138778, 901.4388339183367]), "3bus_unbal_nogen_mn.quad" => Dict{String, Any}("qf" => [400.38348814055513, 449.6175397345571, 449.4080806607989], "qt" => [-399.999, -450.00000000000006, -450.00000000000006], "pt" => [-1200.0, -900.0000000000001, -900.0000000000001], "pf" => [1202.20478139695, 900.9716820211972, 901.4375703778643]), "3bus_unbal_nogen_mn_2.ohline" => Dict{String, Any}("qf" => [400.5820103769862, 449.14701672440617, 448.759402309122], "qt" => [-400.38571596332577, -449.6190932680813, -449.40944838961764], "pt" => [-1202.2067241981586, -900.9725348138778, -901.4388339183367], "pf" => [1204.0959489624188, 901.8044071739638, 902.6730611429242])), "settings" => Dict{String, Any}("sbase" => 100000.0), "transformer" => Dict{String, Any}("3bus_unbal_nogen_mn_2.subxf" => Dict{String, Any}("q" => [[400.6038355327163, 449.16077315009466, 448.773175287606], [-400.5820103769862, -449.14701672440617, -448.759402309122]], "p" => [[1204.0981315678043, 901.8057826937508, 902.6744388454978], [-1204.0959489624188, -901.8044071739638, -902.6730611429242]]), "3bus_unbal_nogen_mn.subxf" => Dict{String, Any}("q" => [[400.5995240190437, 449.1577317239183, 448.7704766379962], [-400.5777180877519, -449.1439873945082, -448.75671581263083]], "p" => [[1204.0945224675868, 901.8041985452063, 902.6720886611851], [-1204.092342226887, -901.8028241168124, -902.6707125957021]])), "load" => Dict{String, Any}("3bus_unbal_nogen_mn_2.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn.l1" => Dict{String, Any}("qd_bus" => [399.999], "pd_bus" => [1200.0], "qd" => [399.999], "pd" => [1200.0]), "3bus_unbal_nogen_mn_2.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn_2.l2" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001]), "3bus_unbal_nogen_mn.l3" => Dict{String, Any}("qd_bus" => [450.00000000000006], "pd_bus" => [900.0000000000001], "qd" => [450.00000000000006], "pd" => [900.0000000000001])), "bus" => Dict{String, Any}("3bus_unbal_nogen_mn.loadbus" => Dict{String, Any}("va" => [-0.8302295799131064, -120.79137859902089, 119.25040000965717], "vm" => [7.4722017251435435, 7.483922381610589, 7.479449806375325]), "3bus_unbal_nogen_mn.sourcebus" => Dict{String, Any}("va" => [-0.7706229194739376, -120.77035368945725, 119.22965458272064], "vm" => [125.00492912857676, 125.00497420549705, 125.00503001737864]), "3bus_unbal_nogen_mn.primary" => Dict{String, Any}("va" => [-0.7991413115468873, -120.78074600617322, 119.23848685006479], "vm" => [7.487284000425199, 7.492696895896888, 7.490619086774399]), "3bus_unbal_nogen_mn_2.primary" => Dict{String, Any}("va" => [-0.85504223254311, -120.8366308814605, 119.18261888116959], "vm" => [7.484002753336263, 7.489418049928443, 7.487339328524058]), "3bus_unbal_nogen_mn.substation" => Dict{String, Any}("va" => [-0.7715260550740553, -120.77101852029291, 119.2289890490694], "vm" => [7.500242832893295, 7.500243675517153, 7.500247054772084]), "3bus_unbal_nogen_mn_2.sourcebus" => Dict{String, Any}("va" => [-0.8264989754893535, -120.82622950864773, 119.17377876991193], "vm" => [124.95033736057383, 124.95038246061625, 124.95043829747675]), "3bus_unbal_nogen_mn_2.substation" => Dict{String, Any}("va" => [-0.8274029029090649, -120.82689492154778, 119.17311265296155], "vm" => [7.496967303220288, 7.496968146567221, 7.496971527361306]), "3bus_unbal_nogen_mn_2.loadbus" => Dict{String, Any}("va" => [-0.8861577649473606, -120.84727282113812, 119.19454256328841], "vm" => [7.468913830908865, 7.480639684348685, 7.4761651454238836])), "per_unit" => false)))

[ Main | Info ] : Solution Values for Boundary(ies): Dict{String, Any}("multinetwork" => true, "nw" => Dict{String, Any}("4" => Dict{String, Any}("boundary" => Dict{String, Any}("(100002, voltage_source.3bus_unbal_nogen_mn_2.source, 6)" => Dict{String, Any}("pbound_to" => [-1204.1049622880614, -901.8100181254906, -902.6783506307055], "qbound_to" => [-400.630030776433, -449.177722118188, -448.78980036204024]), "(100002, 6, voltage_source.3bus_unbal_nogen_mn_2.source)" => Dict{String, Any}("pbound_fr" => [3008.593331044258], "qbound_fr" => [1298.597553256661]), "(100001, 5, voltage_source.3bus_unbal_nogen_mn.source)" => Dict{String, Any}("pbound_fr" => [3008.5857746079846], "qbound_fr" => [1298.5874491212335]), "(100001, voltage_source.3bus_unbal_nogen_mn.source, 5)" => Dict{String, Any}("pbound_to" => [-1204.101347358377, -901.8084302478388, -902.6759970017687], "qbound_to" => [-400.6256962072555, -449.17466583314587, -448.7870870808322]))), "1" => Dict{String, Any}("boundary" => Dict{String, Any}("(100002, voltage_source.3bus_unbal_nogen_mn_2.source, 6)" => Dict{String, Any}("pbound_to" => [-1204.1049624672987, -901.8100184922217, -902.6783509913059], "qbound_to" => [-400.6300307993883, -449.17772215213427, -448.78980037337016]), "(100002, 6, voltage_source.3bus_unbal_nogen_mn_2.source)" => Dict{String, Any}("pbound_fr" => [3008.5933319508263], "qbound_fr" => [1298.5975533248927]), "(100001, 5, voltage_source.3bus_unbal_nogen_mn.source)" => Dict{String, Any}("pbound_fr" => [3008.5857742450717], "qbound_fr" => [1298.5874491439454]), "(100001, voltage_source.3bus_unbal_nogen_mn.source, 5)" => Dict{String, Any}("pbound_to" => [-1204.1013469861416, -901.8084302538781, -902.6759970050523], "qbound_to" => [-400.6256961956958, -449.17466584472527, -448.78708710352413]))), "2" => Dict{String, Any}("boundary" => Dict{String, Any}("(100002, voltage_source.3bus_unbal_nogen_mn_2.source, 6)" => Dict{String, Any}("pbound_to" => [-1204.1049621118384, -901.8100186687032, -902.6783508103842], "qbound_to" => [-400.63003079917036, -449.17772213001075, -448.7898003847704]), "(100002, 6, voltage_source.3bus_unbal_nogen_mn_2.source)" => Dict{String, Any}("pbound_fr" => [3008.593331590926], "qbound_fr" => [1298.5975533139513]), "(100001, 5, voltage_source.3bus_unbal_nogen_mn.source)" => Dict{String, Any}("pbound_fr" => [3008.585774607983], "qbound_fr" => [1298.5874491439235]), "(100001, voltage_source.3bus_unbal_nogen_mn.source, 5)" => Dict{String, Any}("pbound_to" => [-1204.1013473528665, -901.8084302476616, -902.6759970074544], "qbound_to" => [-400.6256962184772, -449.1746658331913, -448.7870870922549]))), "3" => Dict{String, Any}("boundary" => Dict{String, Any}("(100002, voltage_source.3bus_unbal_nogen_mn_2.source, 6)" => Dict{String, Any}("pbound_to" => [-1204.1049624727136, -901.8100181281534, -902.6783506390512], "qbound_to" => [-400.6300307763823, -449.1777221295564, -448.7898003846302]), "(100002, 6, voltage_source.3bus_unbal_nogen_mn_2.source)" => Dict{String, Any}("pbound_fr" => [3008.5933312399184], "qbound_fr" => [1298.5975532905688]), "(100001, 5, voltage_source.3bus_unbal_nogen_mn.source)" => Dict{String, Any}("pbound_fr" => [3008.58577461065], "qbound_fr" => [1298.587449086865]), "(100001, voltage_source.3bus_unbal_nogen_mn.source, 5)" => Dict{String, Any}("pbound_to" => [-1204.1013473527794, -901.8084302506836, -902.6759970071865], "qbound_to" => [-400.62569618428887, -449.1746658104148, -448.7870870921613])))))

As you can see on the output, the dictionary results have extra keys such as nw, which indicate that this is a multinetwork (multi-timestep) optimization problem. Below the nw, you can find the solutions of the respective multinetwork (i.e., timestep) as "#" (e.g., ["nw"]["3"] represents the results for the 3th timestep).

Example Case #3: Solving OPFITD with voltage bounds (support for PowerModelsDistribution (PMD) Transformations)

Test Case #3

The formulation used to solve this optimization problem is the ACP-ACPU formulation.

Additionally, we are specifying a PMD transformation for the distribution system data. This transformation applies voltage bounds to all the nodes in the distribution system(s). The function is called apply_voltage_bounds!(...).

Julia Code for Test Case #3

using PowerModelsITD
using Ipopt

silence!()  # Silences the console, so warning messages or information are not displayed

files_path = joinpath(dirname(pathof(PowerModelsITD)), "..")                    # file path for test cases files
pm_file = joinpath(files_path, "test/data/transmission/case5_withload.m")       # transmission system file
pmd_file = joinpath(files_path, "test/data/distribution/case3_unbalanced.dss")  # distribution system file
boundary_file = joinpath(files_path, "test/data/json/case5_case3_unbal.json")   # boundary file with info. about boundary buses
formulation = NLPowerModelITD{ACPPowerModel, ACPUPowerModel}                    # type of formulation to be used
data = parse_files(pm_file, pmd_file, boundary_file)                        # parse files into dictionary
# apply transformations
apply_voltage_bounds!(data; vm_lb=0.99, vm_ub=1.01)
# solve the optimization problem
result = solve_opfitd(data, formulation, Ipopt.Optimizer; make_si=false)                   # solve the opfitd

# Check the result
@info "Objective: $(result["objective"]) [\$/hr]"
@info "Termination Status of Solver: $(result["termination_status"])"
@info "Solve Time: $(result["solve_time"]) [seconds]"
@info "Solution Values for Distribution system(s): $(result["solution"]["it"]["pmd"]["bus"])"

Console Output for Test Case #3

After running the corresponding code, the user should get the following output displayed on the console.

[ Main | Info ] : Objective: 18022.355809587236 [$/hr]
[ Main | Info ] : Termination Status of Solver: LOCALLY_SOLVED
[ Main | Info ] : Solve Time: 0.06421494483947754 [seconds]

[ Main | Info ] : Solution Values for Distribution system(s): Dict{String, Any}("3bus_unbal.loadbus" => Dict{String, Any}("va" => [-0.8977463887653532, -120.78309685941274, 119.34177620647625], "vm" => [0.9899999900302301, 0.9946671975187621, 0.9928991397184561]), "3bus_unbal.substation" => Dict{String, Any}("va" => [-0.7693363623113275, -120.76782278704773, 119.23219208890347], "vm" => [0.999742728740167, 0.999743306402737, 0.9997446568367797]), "3bus_unbal.primary" => Dict{String, Any}("va" => [-0.8297020935620707, -120.77556386286943, 119.28178890967312], "vm" => [0.9952384467648019, 0.9973943491437465, 0.9965725113327532]), "3bus_unbal.sourcebus" => Dict{String, Any}("va" => [-0.7671158858601453, -120.76631338622572, 119.23370678684667], "vm" => [0.9997629892456953, 0.9997641961144075, 0.9997655262819723]))

You can see in these results that the voltage magnitude values of the distribution system nodes is between the 0.99 and 1.01 bounds.

Example Case #4: Solving OPFITD with Solution Processors (apply solution processor to convert voltage values solutions from `rectangular` to `polar` coordinates)

Test Case #4

Additionally, we are specificying a PMD transformation for the distribution system data. This transformation applies voltage bounds to all the nodes in the distribution system(s). The function is called apply_voltage_bounds!(...).

Finally, we also want to solve this problem using the ACR-ACRU formulation (i.e., AC OPF in rectangular coordinates) instead of the ACP-ACPU formulation used previously. We also want to show that by applying the solution processor to the solve_opfitd(...) function, we can convert the solution from rectangular to polar coordinates (after the problem has been solved in rectangular coordinates).

Julia Code for Test Case #4

using PowerModelsITD
using Ipopt

silence!()  # Silences the console, so warning messages or information are not displayed

files_path = joinpath(dirname(pathof(PowerModelsITD)), "..")                    # file path for test cases files
pm_file = joinpath(files_path, "test/data/transmission/case5_withload.m")       # transmission system file
pmd_file = joinpath(files_path, "test/data/distribution/case3_unbalanced.dss")  # distribution system file
boundary_file = joinpath(files_path, "test/data/json/case5_case3_unbal.json")   # boundary file with info. about boundary buses
formulation = NLPowerModelITD{ACRPowerModel, ACRUPowerModel}                    # type of formulation to be used

data_rect = parse_files(pm_file, pmd_file, boundary_file)                       # parse files into dictionary - rectangular
data_polar = deepcopy(data_rect)                                                # parse files into dictionary - polar

# apply voltage bounds to both datasets
apply_voltage_bounds!(data_rect; vm_lb=0.99, vm_ub=1.01)
apply_voltage_bounds!(data_polar; vm_lb=0.99, vm_ub=1.01)

# solve the optimization problem
result_rect = solve_opfitd(data_rect, formulation, Ipopt.Optimizer; make_si=false)                                          # solve the opfitd, present result in rectangular
result_polar = solve_opfitd(data_polar, formulation, Ipopt.Optimizer; make_si=false, solution_processors=[sol_data_model!]) # solve the opfitd, present the result in polar

# Check the result
@info "Distribution system(s) voltages in rectangular coordinates: $(result_rect["solution"]["it"]["pmd"]["bus"])"
@info "Distribution system(s) voltages in polar coordinates: $(result_polar["solution"]["it"]["pmd"]["bus"])"

Console Output for Test Case #4

After running the corresponding code, the user should get the following output displayed on the console.

[ Main | Info ] : Distribution system(s) voltages in rectangular coordinates: Dict{String, Any}("3bus_unbal.loadbus" => Dict{String, Any}("vi" => [-0.015511309363640641, -0.8545294554234174, 0.8655223138026301], "vr" => [0.9898784720063777, -0.5090601668099762, -0.4865386272048753]), "3bus_unbal.substation" => Dict{String, Any}("vi" => [-0.013423594907906103, -0.8590267647200966, 0.872425011363218], "vr" => [0.9996526099437699, -0.5114290820733716, -0.48822534573738224]), "3bus_unbal.primary" => Dict{String, Any}("vi" => [-0.014411577636549404, -0.8569394862376708, 0.8692352392326611], "vr" => [0.9951341025954522, -0.5103432319817417, -0.4874288450833038]), "3bus_unbal.sourcebus" => Dict{String, Any}("vi" => [-0.01338512498983875, -0.8590581872270858, 0.8724303155121654], "vr" => [0.9996733881089848, -0.5114171375591623, -0.4882586014767347]))

[ Main | Info ] : Distribution system(s) voltages in polar coordinates: Dict{String, Any}("3bus_unbal.loadbus" => Dict{String, Any}("va" => [-0.8977463956228972, -120.78309686739179, 119.34177619725007], "vm" => [0.989999994979725, 0.9946672024445378, 0.9928991446530021]), "3bus_unbal.substation" => Dict{String, Any}("va" => [-0.7693363704348831, -120.76782279518537, 119.23219208076581], "vm" => [0.9997427336408314, 0.9997433113034004, 0.9997446617374346]), "3bus_unbal.primary" => Dict{String, Any}("va" => [-0.8297021010938084, -120.77556387092758, 119.28178890104428], "vm" => [0.9952384516880516, 0.9973943540560338, 0.9965725162491212]), "3bus_unbal.sourcebus" => Dict{String, Any}("va" => [-0.767115894005601, -120.7663133943784, 119.23370677869384], "vm" => [0.9997629941462579, 0.9997642010149662, 0.9997655311825235]))

Example Case #5: Solving OPFITD with Results in `MATH` Model (instead of default `ENG`)

Test Case #5

The formulation used to solve this optimization problem is the ACP-ACPU formulation.

However, different from all the examples presented above, in this case, the result of the distribution systems will be obtained in the MATH model instead of the default ENG model. See here for a more detailed explanation regarding the different models supported by PMD/PMITD.

Julia Code for Test Case #5

using PowerModelsITD
using Ipopt

silence!()  # Silences the console, so warning messages or information are not displayed

files_path = joinpath(dirname(pathof(PowerModelsITD)), "..")                    # file path for test cases files
pm_file = joinpath(files_path, "test/data/transmission/case5_withload.m")       # transmission system file
pmd_file = joinpath(files_path, "test/data/distribution/case3_unbalanced.dss")  # distribution system file
boundary_file = joinpath(files_path, "test/data/json/case5_case3_unbal.json")   # boundary file with info. about boundary buses
formulation = NLPowerModelITD{ACPPowerModel, ACPUPowerModel}                    # type of formulation to be used
data = parse_files(pm_file, pmd_file, boundary_file)                            # parse files into dictionary
result = solve_opfitd(data, formulation, Ipopt.Optimizer; solution_model="MATH") # solve the opfitd, present result in MATH model instead of default ENG

# Check the result
@info "Objective: $(result["objective"]) [\$/hr]"
@info "Termination Status of Solver: $(result["termination_status"])"
@info "Solve Time: $(result["solve_time"]) [seconds]"
@info "Solution Values (MATH model) for Distribution system(s): $(result["solution"]["it"]["pmd"])"
@info "Solution Values (MATH model) for Boundary(ies): $(result["solution"]["it"]["pmitd"])"

Console Output for Test Case #5

After running the corresponding code, the user should get the following output displayed on the console.

[ Main | Info ] : Objective: 17953.746512039743 [$/hr]
[ Main | Info ] : Termination Status of Solver: LOCALLY_SOLVED
[ Main | Info ] : Solve Time: 0.07705187797546387 [seconds]

[ Main | Info ] : Solution Values (MATH model) for Distribution system(s): Dict{String, Any}("branch" => Dict{String, Any}("4" => Dict{String, Any}("qf" => [1354.795202241865, 1507.3400640138161, 1504.5761375753734], "qt" => [-1354.6163225169614, -1507.2344513630767, -1504.4700979169072], "pt" => [-3367.119671256992, -2346.3650144634003, -2354.829891017304], "pf" => [3367.119671256992, 2346.3650144634003, 2354.8298910173044]), "1" => Dict{String, Any}("qf" => [1344.7785535214057, 1503.9392726830868, 1502.43791779139], "qt" => [-1333.3300000000002, -1500.0000000000002, -1500.0000000000002], "pt" => [-3333.3323371531164, -2333.3323371935803, -2333.3323371900296], "pf" => [3351.5305232165006, 2340.3516279866967, 2344.8964126191295]), "5" => Dict{String, Any}("qf" => [1354.7952022418647, 1507.3400640138161, 1504.5761375753734], "qt" => [-1354.795202241865, -1507.3400640138161, -1504.5761375753734], "pt" => [-3367.119671256992, -2346.3650144634003, -2354.8298910173044], "pf" => [3367.1286152278885, 2346.3702946258413, 2354.835193007617]), "2" => Dict{String, Any}("qf" => [1354.6163225169614, 1507.2344513630765, 1504.4700979169072], "qt" => [-1344.7785535214057, -1503.9392726830868, -1502.43791779139], "pt" => [-3351.5305232165006, -2340.3516279866967, -2344.8964126191295], "pf" => [3367.110727286094, 2346.3597337552624, 2354.8245890269895]), "6" => Dict{String, Any}("qf" => [1355.0096276913357, 1507.4706735124998, 1504.7037665348369], "qt" => [-1354.7952022418647, -1507.3400640138161, -1504.5761375753734], "pt" => [-3367.1286152278885, -2346.3702946258413, -2354.835193007617], "pf" => [3367.1850486607445, 2346.4026604158908, 2354.8649645151804]), "3" => Dict{String, Any}("qf" => [-1354.6163225169614, -1507.2344513630765, -1504.4700979169072], "qt" => [1354.6163225169614, 1507.2344513630767, 1504.4700979169072], "pt" => [3367.119671256992, 2346.3650144634003, 2354.829891017304], "pf" => [-3367.110727286094, -2346.3597337552624, -2354.8245890269895])), "gen" => Dict{String, Any}("1" => Dict{String, Any}("qg_bus" => [-0.0, -0.0, -0.0], "qg" => [-0.0, -0.0, -0.0], "pg" => [666.6676628468832, 666.6676628064197, 666.6676628099706], "pg_bus" => [666.6676628468832, 666.6676628064197, 666.6676628099706])), "transformer" => Dict{String, Any}("1" => Dict{String, Any}("qf" => [1354.7952022418647, 1507.3400640138161, 1504.5761375753734], "qt" => [-1354.7952022418647, -1507.3400640138161, -1504.5761375753734], "pt" => [-3367.1286152278885, -2346.3702946258413, -2354.835193007617], "pf" => [3367.1286152278885, 2346.3702946258413, 2354.835193007617]), "2" => Dict{String, Any}("qf" => [-1354.6163225169614, -1507.2344513630765, -1504.4700979169072], "qt" => [1354.6163225169614, 1507.2344513630765, 1504.4700979169072], "pt" => [3367.110727286094, 2346.3597337552624, 2354.8245890269895], "pf" => [-3367.110727286094, -2346.3597337552624, -2354.8245890269895])), "settings" => Dict{String, Any}("sbase_default" => 100000.0, "vbases_default" => Dict{String, Real}("4" => 132.79056191361394), "voltage_scale_factor" => 1000.0, "sbase" => 100000.0, "power_scale_factor" => 1000.0, "base_frequency" => 60.0), "multinetwork" => false, "load" => Dict{String, Any}("1" => Dict{String, Any}("qd_bus" => [1500.0000000000002], "pd_bus" => [3000.0000000000005], "qd" => [1500.0000000000002], "pd" => [3000.0000000000005]), "2" => Dict{String, Any}("qd_bus" => [1500.0000000000002], "pd_bus" => [3000.0000000000005], "qd" => [1500.0000000000002], "pd" => [3000.0000000000005]), "3" => Dict{String, Any}("qd_bus" => [1333.3300000000002], "pd_bus" => [4000.0], "qd" => [1333.3300000000002], "pd" => [4000.0])), "bus" => Dict{String, Any}("8" => Dict{String, Any}("va" => [-0.8064197613818459, -120.80551025323088, 119.19451148306055], "vm" => [0.5427404621782935, 0.5427412225103798, 0.5427420415368795]), "4" => Dict{String, Any}("va" => [-0.8064197613818459, -120.80551025323088, 119.19451148306055], "vm" => [124.83030630100751, 124.83048117738736, 124.8306695534823]), "1" => Dict{String, Any}("va" => [-0.9542852429015141, -120.82463162589393, 119.31695673367102], "vm" => [7.406969380817659, 7.446613395025093, 7.431619824571949]), "5" => Dict{String, Any}("va" => [-0.8089868491003656, -120.80727720360223, 119.19273784447546], "vm" => [0.5427292370876581, 0.542729249043147, 0.5427300853404582]), "2" => Dict{String, Any}("va" => [-0.8089341499650244, -120.8072185671511, 119.19279637320398], "vm" => [7.489646348633082, 7.489651704574486, 7.489663202448464]), "6" => Dict{String, Any}("va" => [-0.8089341499650244, -120.8072185671511, 119.19279637320398], "vm" => [0.5427279962777596, 0.5427283843894555, 0.5427292175687293]), "7" => Dict{String, Any}("va" => [-0.8063670574676239, -120.8054516152584, 119.19457001333551], "vm" => [0.5427392213907619, 0.5427403578738178, 0.5427411737823131]), "9" => Dict{String, Any}("va" => [-0.8036120919989638, -120.80361209199894, 119.19638790800104], "vm" => [124.83485996888251, 124.83485996888251, 124.83485996888251]), "3" => Dict{String, Any}("va" => [-0.8772138344778904, -120.81603057758366, 119.24896754768255], "vm" => [7.4514218741879255, 7.4697354940559455, 7.462765580863505])), "per_unit" => false)

[ Main | Info ] : Solution Values (MATH model) for Boundary(ies): Dict{String, Any}("multinetwork" => false, "boundary" => Dict{String, Any}("(100001, 9, 5)" => Dict{String, Any}("pbound_to" => [-3367.1850486607445, -2346.4026604158908, -2354.8649645151804], "qbound_to" => [-1355.0096276913357, -1507.4706735124998, -1504.7037665348369]), "(100001, 5, 9)" => Dict{String, Any}("pbound_fr" => [8068.452673591816], "qbound_fr" => [4367.184067738673])))

As seen in the console output, the nodes/buses are now referenced by their MATH names (i.e., numbers) and not their actual ENG name.