Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation

Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch aft...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Energies (Basel) Ročník 13; číslo 13; s. 3310
Hlavní autoři: Leon, Luis M., Bretas, Arturo S., Rivera, Sergio
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.07.2020
Témata:
ISSN:1996-1073, 1996-1073
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective.
AbstractList Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective.
Author Bretas, Arturo S.
Leon, Luis M.
Rivera, Sergio
Author_xml – sequence: 1
  givenname: Luis M.
  orcidid: 0000-0001-9873-2979
  surname: Leon
  fullname: Leon, Luis M.
– sequence: 2
  givenname: Arturo S.
  orcidid: 0000-0003-4006-0764
  surname: Bretas
  fullname: Bretas, Arturo S.
– sequence: 3
  givenname: Sergio
  orcidid: 0000-0002-2995-1147
  surname: Rivera
  fullname: Rivera, Sergio
BookMark eNptUdtqGzEQFSWFXJqXfIGgbwUn0s7e9BhM7RgCcaF9FtrdkbNG1jhaucY_0O-u1g7phehF4uicMzNnLtmZJ4-M3UhxC6DEHXoJEgCk-MAupFLlRIoKzv56n7PrYViLdODIvGC_vu1MF0zsW-PcgU_JDzGY3mPH3374MtAqmM2m9ys-o7DZuQST52RHQUww-vZf8dM29hvj-JL2GPjM0Z7v-_jMl88U6Se5aJLvHD2Go9Un9tEaN-D1633Ffsy-fp8-TB6f5ovp_eOkhVLGSVcXtpAGEDqDRjVZnmOlRAktFhbKsmlQqszWVSdlU9VgbS1BtYVAAWVWNXDFFiffjsxab0PqMRw0mV4fAQorbUIa2aFWeVVC0aTYsiaXCusst4hjhabLy0Imr88nr22glx0OUa9pF3xqX2dJUFQy5Z5YX06sNtAwBLRvVaXQ49r0n7UlsviP3PbxGNCYq3tP8huKuZ3u
CitedBy_id crossref_primary_10_1016_j_ijepes_2022_108636
crossref_primary_10_1016_j_epsr_2020_106877
crossref_primary_10_1109_ACCESS_2025_3532750
crossref_primary_10_3390_app12031129
crossref_primary_10_3390_su17156738
Cites_doi 10.1016/j.ijepes.2017.09.023
10.1109/AEIT.2015.7415271
10.1109/TPWRS.2010.2051168
10.1109/PTC.2017.7981225
10.1109/ISGT.2019.8791673
10.3390/en10081199
10.1109/TPWRS.2016.2551278
10.1109/TPWRS.2008.2002175
10.1109/MPE.2016.2573862
10.1109/TCNS.2014.2309732
10.1109/ICPEICES.2016.7853437
10.1109/TPWRS.2012.2219080
10.1016/j.epsr.2011.04.003
10.3906/elk-1704-209
10.1109/PTC.2019.8810833
10.1109/TPWRS.2015.2396523
10.1016/j.ijepes.2019.105646
10.3390/en13030516
10.1109/ISCAS.2012.6271569
10.1145/2851613.2851899
10.1155/2011/942672
ContentType Journal Article
Copyright 2020. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2020. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
ABUWG
AFKRA
AZQEC
BENPR
CCPQU
DWQXO
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
DOA
DOI 10.3390/en13133310
DatabaseName CrossRef
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest One Community College
ProQuest Central
ProQuest Central Premium
ProQuest One Academic
ProQuest Publicly Available Content
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
DatabaseTitleList
CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: ProQuest Publicly Available Content
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1996-1073
ExternalDocumentID oai_doaj_org_article_947635b1072b419e824feebbe1bd4651
10_3390_en13133310
GroupedDBID 29G
2WC
5GY
5VS
7XC
8FE
8FG
8FH
AADQD
AAHBH
AAYXX
ABDBF
ACUHS
ADBBV
ADMLS
AENEX
AFFHD
AFKRA
AFZYC
ALMA_UNASSIGNED_HOLDINGS
BCNDV
BENPR
CCPQU
CITATION
CS3
DU5
EBS
ESX
FRP
GROUPED_DOAJ
GX1
I-F
IAO
KQ8
L6V
L8X
MODMG
M~E
OK1
OVT
P2P
PHGZM
PHGZT
PIMPY
PROAC
TR2
TUS
ABUWG
AZQEC
DWQXO
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c361t-d85f51a3e3daea9b244e79063ce5f366bbe192f87d11b783ff8139c50e03627b3
IEDL.DBID PIMPY
ISICitedReferencesCount 8
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000552354500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1996-1073
IngestDate Tue Oct 14 19:09:04 EDT 2025
Mon Jun 30 10:59:59 EDT 2025
Sat Nov 29 07:12:49 EST 2025
Tue Nov 18 21:13:38 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 13
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c361t-d85f51a3e3daea9b244e79063ce5f366bbe192f87d11b783ff8139c50e03627b3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-9873-2979
0000-0003-4006-0764
0000-0002-2995-1147
OpenAccessLink https://www.proquest.com/publiccontent/docview/2419571199?pq-origsite=%requestingapplication%
PQID 2419571199
PQPubID 2032402
ParticipantIDs doaj_primary_oai_doaj_org_article_947635b1072b419e824feebbe1bd4651
proquest_journals_2419571199
crossref_primary_10_3390_en13133310
crossref_citationtrail_10_3390_en13133310
PublicationCentury 2000
PublicationDate 2020-07-01
PublicationDateYYYYMMDD 2020-07-01
PublicationDate_xml – month: 07
  year: 2020
  text: 2020-07-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Energies (Basel)
PublicationYear 2020
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Capitanescu (ref_9) 2008; 23
ref_14
ref_13
ref_12
ref_11
ref_10
Tang (ref_2) 2016; 32
Vargas (ref_27) 2011; 14
Ngoc (ref_3) 2017; 25
ref_18
Capitanescu (ref_1) 2019; 81
ref_16
Nasr (ref_17) 2020; 117
ref_15
Cao (ref_8) 2015; 31
Wang (ref_19) 2012; 28
Zimmerman (ref_21) 2011; 26
ref_24
ref_22
ref_20
Karbalaei (ref_7) 2018; 96
Low (ref_25) 2014; 1
ref_26
Bernal (ref_23) 2019; 18
ref_5
ref_4
ref_6
References_xml – volume: 96
  start-page: 23
  year: 2018
  ident: ref_7
  article-title: A new method for solving preventive security-constrained optimal power flow based on linear network compression
  publication-title: Int. J. Electr. Power Energy Syst.
  doi: 10.1016/j.ijepes.2017.09.023
– ident: ref_5
– ident: ref_10
  doi: 10.1109/AEIT.2015.7415271
– ident: ref_26
– volume: 26
  start-page: 12
  year: 2011
  ident: ref_21
  article-title: MATPOWER: Steady-State Operations, Planning and Analysis Tools for Power Systems Research and Education
  publication-title: IEEE Trans. Power Syst.
  doi: 10.1109/TPWRS.2010.2051168
– ident: ref_11
  doi: 10.1109/PTC.2017.7981225
– ident: ref_15
  doi: 10.1109/ISGT.2019.8791673
– ident: ref_13
  doi: 10.3390/en10081199
– ident: ref_16
– volume: 32
  start-page: 590
  year: 2016
  ident: ref_2
  article-title: An automated transient stability constrained optimal power flow based on trajectory sensitivity analysis
  publication-title: IEEE Trans. Power Syst.
  doi: 10.1109/TPWRS.2016.2551278
– volume: 23
  start-page: 1533
  year: 2008
  ident: ref_9
  article-title: A new iterative approach to the corrective security-constrained optimal power flow problem
  publication-title: IEEE Trans. Power Syst.
  doi: 10.1109/TPWRS.2008.2002175
– volume: 18
  start-page: 137
  year: 2019
  ident: ref_23
  article-title: Mathematical Uncertainty Cost Functions for Controllable Photo-Voltaic Generators considering Uniform Distributions
  publication-title: WSEAS Trans. Math.
– volume: 14
  start-page: 38
  year: 2011
  ident: ref_27
  article-title: Latin American Energy Markets: Investment Opportunities in Nonconventional Renewables
  publication-title: IEEE Power Energy Mag.
  doi: 10.1109/MPE.2016.2573862
– volume: 1
  start-page: 15
  year: 2014
  ident: ref_25
  article-title: Convex relaxation of optimal power flow—Part I: Formulations and equivalence
  publication-title: IEEE Trans. Control Netw. Syst.
  doi: 10.1109/TCNS.2014.2309732
– ident: ref_12
  doi: 10.1109/ICPEICES.2016.7853437
– volume: 28
  start-page: 1666
  year: 2012
  ident: ref_19
  article-title: A computational strategy to solve preventive risk-based security-constrained OPF
  publication-title: IEEE Trans. Power Syst.
  doi: 10.1109/TPWRS.2012.2219080
– volume: 81
  start-page: 1731
  year: 2019
  ident: ref_1
  article-title: State of the art, challenges, and future trends in security constrained optimal power flow
  publication-title: Electr. Power Syst. Res.
  doi: 10.1016/j.epsr.2011.04.003
– volume: 25
  start-page: 4696
  year: 2017
  ident: ref_3
  article-title: A novel approach to solve transient stability constrained optimal power flow problems
  publication-title: Turkish J. Electr. Eng. Comput. Sci.
  doi: 10.3906/elk-1704-209
– ident: ref_14
  doi: 10.1109/PTC.2019.8810833
– volume: 31
  start-page: 485
  year: 2015
  ident: ref_8
  article-title: An improved corrective security constrained OPF for meshed AC/DC grids with multi-terminal VSC-HVDC
  publication-title: IEEE Trans. Power Syst.
  doi: 10.1109/TPWRS.2015.2396523
– volume: 117
  start-page: 105646
  year: 2020
  ident: ref_17
  article-title: A multi-objective voltage stability constrained energy management system for isolated microgrids
  publication-title: Int. J. Electr. Power Energy Syst.
  doi: 10.1016/j.ijepes.2019.105646
– ident: ref_4
  doi: 10.3390/en13030516
– ident: ref_22
– ident: ref_20
– ident: ref_18
  doi: 10.1109/ISCAS.2012.6271569
– ident: ref_6
  doi: 10.1145/2851613.2851899
– ident: ref_24
  doi: 10.1155/2011/942672
SSID ssj0000331333
Score 2.3139133
Snippet Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with...
SourceID doaj
proquest
crossref
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
StartPage 3310
SubjectTerms Branch banking
contingency constrained optimal power flow
Inequality
optimal power flow
quadratically constrained quadratic programming
Short term
Systems stability
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA6yeNCD-MT1RUAvHopN0zbJUcXFg-gKKt5K0iQo7G5ltyr-AX-3M2ldVxS8eOkhzaOdmc6jJN9HyIFU1modm8hkcEm1yCIJUTrKE8FsnHteBv6UuwtxeSnv71V_huoL94Q18MCN4I5UipBpBqqUxKRMOZmk3jljHDMWebzR-8ZCzRRTwQdzDsUXb_BIOdT1R27EQhMelZ2JQAGo_4cfDsGlt0yW2qyQHjdPs0Lm3GiVLM5gBa6R9-tnbVFdINTBG0WizUDv4Cyd3qH9ZrfVEEbQHmSjLTcXrTwOqMNBqvL74CvwGUNYu490abQ3qF4p_pul_YeqrsB31RrmbcCpcap1cts7uzk9j1oShajkOasjKzOfMc0dt9ppZSCcO6EgMSld5nmeoyRV4qWwjBkhufcSksIyix3GNmH4BumMqpHbJFRpI7yBWV2cpoZpmUurSxE7kymdiLxLDj8FW5Qtwji-zKCASgOVUHwpoUv2p32fGlyNX3udoH6mPRALOzSAhRSthRR_WUiX7Hxqt2g_0EkBiYvKBGNKbf3HGttkIcFCPOzj3SGdevzsdsl8-VI_TsZ7wTY_AGLD63c
  priority: 102
  providerName: Directory of Open Access Journals
Title Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation
URI https://www.proquest.com/docview/2419571199
https://doaj.org/article/947635b1072b419e824feebbe1bd4651
Volume 13
WOSCitedRecordID wos000552354500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1996-1073
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331333
  issn: 1996-1073
  databaseCode: DOA
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 1996-1073
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331333
  issn: 1996-1073
  databaseCode: M~E
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1996-1073
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331333
  issn: 1996-1073
  databaseCode: BENPR
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Publicly Available Content
  customDbUrl:
  eissn: 1996-1073
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331333
  issn: 1996-1073
  databaseCode: PIMPY
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3Lb9MwGLeg5cAOvNEKo7IEFw5RkziJ7dPEUCuQWAkI0DhFfrJJXTPajIkLR_5uvs9xuyEQJy4--JVYn_O9Yv9-hDwT0lqlUp3oEopC8TIRYKWTKueZTSvPTOBP-fSGz-fi6EjW8Xr0Oh6r3OjEoKh7tGc8tw1KeGJbgxnzCdgdWfIsk3L_7GuCHFL4rzUSalwnQwTeSgdkWL8-rD9vcy4pYxCSsR6llEG0P3HLLFThBdordinA9_-hnYPJmd3-vy97h9yKrid90e-Vu-SaW94jO1cACe-Tn-_OlcU9AZJbfKfI5hk4JJyl2xZa90e6TmEEnYHLGwnAaOtxQBdua5nfB78FxXQKz66Rk43OFu0FxQQwrY_brgUF2SmYt0fAxqkekI-z6YeXr5LI1JAYVmVdYkXpy0wxx6xySmrwGRyX4P0YV3pWVVo78CS94DbLNBfMewGepylThwaUa_aQDJbt0u0SKpXmXsOsLi0KnSlRCasMT50upcp5NSLPN3JqTIQxx8UsGghnUKbNpUxH5Om271kP3vHXXgco7m0PBNwOFe3qSxO_30YWiNynIVjONYjTibzwzuG6tEU6-RHZ2-yEJmqBdXMp-Ef_bn5MbuYYx4djwHtk0K3O3RNyw3zrTtarMRkeTOf1-3HIF0B5-GM6jlv7F8CYCp4
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VLRJw4I1YKGAJOHCIGsdJbB8Q4rXqqtslSAW1p2DHDiBtN2U3peof4OfwG5nJY1sE4tYDlxwceyI7X-YVez6AJ0o7Z0xoA5vgJTYyCRRa6SCNJHdhWoqi4U_5OJHTqdrb09ka_OzPwtC2yl4nNoraVQXlyDfR0uhEcq71i8NvAbFG0d_VnkKjhcW2PznGkG35fPwG3-_TKBq93X29FXSsAkEhUl4HTiVlwo3wwhlvtEX75qVGS134pBRpaq1Hr6dU0nFupRJlqdBLKpLQk7KXVqDcC7AeI9jDAaxn451sf5XVCYXAoE-0dVCF0OGmn_OmiY7onrF8DUHAH_q_MWqja__bclyHq537zF62eL8Ba35-E66cKap4C368PzKOcI3om50wYiRteDC8Y6s7LGu3pR3gCDZCt70jMWNVSQPq5sRZ8fvgd6hcD_DZGfHKsdGsOmaUxGbZl6quUMnXBuW2VbxJ1G34cC4LcQcG82ru7wLTxsrSolQfxrHlRqXKmUKG3ibaRDIdwrMeCXnRlWKnycxyDMkINfkpaobweNX3sC1A8tderwhQqx5UNLxpqBaf804H5Tqm6oMWA_7IIny8iuLSe5qXdXGa8CFs9FjLO022zE-Bdu_ftx_Bpa3dnUk-GU-378PliPISzbbmDRjUiyP_AC4W3-uvy8XD7qNh8Om8gfkLLsFYIQ
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VLUJw4I1YKGAJOHCINo6T2D4gRGkjqlZLQIB6C34C0nZTdlOq_gF-FL-OcR7bIhC3Hrjk4MdEdj7PjCf2fABPhLRWqVhHOsNHqngWCbTSUZ5wauPcM9Pyp3zc49Op2N-X5Rr8HO7ChGOVg05sFbWtTYiRT9DSyIxTKuXE98ciyq3ixeG3KDBIhT-tA51GB5Fdd3KM27fl850t_NZPk6TYfv_qddQzDESG5bSJrMh8RhVzzCqnpEZb57hEq21c5lmea-3QA_KCW0o1F8x7gR6TyWIXFD_XDOVegHXOcNMzgvXN7Wn5bhXhiRnDDSDrcqIyJuOJm9O2KFzXPWMFW7KAP2xBa-CKa__z1FyHq71bTV526-AGrLn5TbhyJtniLfjx9kjZgHdE5eyEBKbSlh_DWbKqIWV3XO0Ae5AC3fme3IzUPnRo2pto5vfOb1DpHuC7y8A3R4pZfUxCcJuUX-qmRuXfKJTbZfcOom7Dh3OZiDswmtdzdxeIVJp7jVJdnKaaKpELqwyPnc6kSng-hmcDKirTp2gPg5lVuFULCKpOETSGx6u2h11ikr-22gzgWrUIycTbgnrxuep1UyXTkJVQ05gnGqHkRJJ658K4tE3zjI5hY8Bd1Wu4ZXUKunv_rn4ElxCN1d7OdPc-XE5CuKI97bwBo2Zx5B7ARfO9-bpcPOzXD4FP543LXzINYLs
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Quadratically+Constrained+Quadratic+Programming+Formulation+of+Contingency+Constrained+Optimal+Power+Flow+with+Photovoltaic+Generation&rft.jtitle=Energies+%28Basel%29&rft.au=Leon%2C+Luis+M&rft.au=Bretas%2C+Arturo+S&rft.au=Rivera%2C+Sergio&rft.date=2020-07-01&rft.pub=MDPI+AG&rft.eissn=1996-1073&rft.volume=13&rft.issue=13&rft.spage=3310&rft_id=info:doi/10.3390%2Fen13133310&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1996-1073&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1996-1073&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1996-1073&client=summon