Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface

The Optimal Reactive Power Dispatch (ORPD) problem consists of finding the optimal settings of reactive power resources within a network, usually with the aim of minimizing active power losses. The ORPD is a nonlinear and nonconvex optimization problem that involves both discrete and continuous vari...

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Autores:
Sánchez-Mora, Martin M.
Bernal-Romero, David Lionel
Montoya, Oscar Danilo
Villa Acevedo, Walter M.
López Lezama, Jesús M.
Tipo de recurso:
Fecha de publicación:
2022
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/11128
Acceso en línea:
https://hdl.handle.net/20.500.12585/11128
https://doi.org/10.3390/computation10080128
Palabra clave:
Combinatorial optimization
DIgSILENT software
Genetic algorithm
Mean variance mapping optimization
Optimal reactive power dispatch
Power losses minimization
Python programming language
LEMB
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.title.spa.fl_str_mv Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
title Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
spellingShingle Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
Combinatorial optimization
DIgSILENT software
Genetic algorithm
Mean variance mapping optimization
Optimal reactive power dispatch
Power losses minimization
Python programming language
LEMB
title_short Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
title_full Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
title_fullStr Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
title_full_unstemmed Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
title_sort Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface
dc.creator.fl_str_mv Sánchez-Mora, Martin M.
Bernal-Romero, David Lionel
Montoya, Oscar Danilo
Villa Acevedo, Walter M.
López Lezama, Jesús M.
dc.contributor.author.none.fl_str_mv Sánchez-Mora, Martin M.
Bernal-Romero, David Lionel
Montoya, Oscar Danilo
Villa Acevedo, Walter M.
López Lezama, Jesús M.
dc.subject.keywords.spa.fl_str_mv Combinatorial optimization
DIgSILENT software
Genetic algorithm
Mean variance mapping optimization
Optimal reactive power dispatch
Power losses minimization
Python programming language
topic Combinatorial optimization
DIgSILENT software
Genetic algorithm
Mean variance mapping optimization
Optimal reactive power dispatch
Power losses minimization
Python programming language
LEMB
dc.subject.armarc.none.fl_str_mv LEMB
description The Optimal Reactive Power Dispatch (ORPD) problem consists of finding the optimal settings of reactive power resources within a network, usually with the aim of minimizing active power losses. The ORPD is a nonlinear and nonconvex optimization problem that involves both discrete and continuous variables; the former include transformer tap positions and settings of reactor banks, while the latter include voltage magnitude settings in generation buses. In this paper, the ORPD problem is modeled as a mixed integer nonlinear programming problem and solved through two different metaheuristic techniques, namely the Mean Variance Mapping Optimization and the genetic algorithm. As a novelty, the solution of the ORPD problem is implemented through a PythonDIgSILENT interface that combines the strengths of both software. Several tests were performed on the IEEE 6-, 14-, and 39-bus test systems evidencing the applicability of the proposed approach. The results were contrasted with those previously reported in the specialized literature, matching, and in some cases improving, the reported solutions with lower computational times.
publishDate 2022
dc.date.accessioned.none.fl_str_mv 2022-10-05T12:26:27Z
dc.date.available.none.fl_str_mv 2022-10-05T12:26:27Z
dc.date.issued.none.fl_str_mv 2022-07-25
dc.date.submitted.none.fl_str_mv 2022-09-30
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
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dc.type.spa.spa.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.identifier.citation.spa.fl_str_mv Sánchez-Mora, M.M.; Bernal-Romero, D.L.; Montoya, O.D.; Villa Acevedo, W.M.; López-Lezama, J.M. Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface. Computation 2022, 10, 128. https://doi.org/10.3390/computation10080128
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/11128
dc.identifier.doi.none.fl_str_mv https://doi.org/10.3390/computation10080128
dc.identifier.instname.spa.fl_str_mv Universidad Tecnológica de Bolívar
dc.identifier.reponame.spa.fl_str_mv Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv Sánchez-Mora, M.M.; Bernal-Romero, D.L.; Montoya, O.D.; Villa Acevedo, W.M.; López-Lezama, J.M. Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface. Computation 2022, 10, 128. https://doi.org/10.3390/computation10080128
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/11128
https://doi.org/10.3390/computation10080128
dc.language.iso.spa.fl_str_mv eng
language eng
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dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 24 Páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.source.spa.fl_str_mv Computation Vol.10 N° 8 (2022)
institution Universidad Tecnológica de Bolívar
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spelling Sánchez-Mora, Martin M.47f83a24-df85-4a58-8009-c0ece6312ce4Bernal-Romero, David Lionel92b4db2c-95be-4502-bb3c-74213711c838Montoya, Oscar Danilo9fa8a75a-58fa-436d-a6e2-d80f718a4ea8Villa Acevedo, Walter M.b3ac5a1a-9e8e-483f-99b8-f8f02774668cLópez Lezama, Jesús M.26e59177-5d26-454f-96f0-88275a529dc22022-10-05T12:26:27Z2022-10-05T12:26:27Z2022-07-252022-09-30Sánchez-Mora, M.M.; Bernal-Romero, D.L.; Montoya, O.D.; Villa Acevedo, W.M.; López-Lezama, J.M. Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interface. Computation 2022, 10, 128. https://doi.org/10.3390/computation10080128https://hdl.handle.net/20.500.12585/11128https://doi.org/10.3390/computation10080128Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThe Optimal Reactive Power Dispatch (ORPD) problem consists of finding the optimal settings of reactive power resources within a network, usually with the aim of minimizing active power losses. The ORPD is a nonlinear and nonconvex optimization problem that involves both discrete and continuous variables; the former include transformer tap positions and settings of reactor banks, while the latter include voltage magnitude settings in generation buses. In this paper, the ORPD problem is modeled as a mixed integer nonlinear programming problem and solved through two different metaheuristic techniques, namely the Mean Variance Mapping Optimization and the genetic algorithm. As a novelty, the solution of the ORPD problem is implemented through a PythonDIgSILENT interface that combines the strengths of both software. Several tests were performed on the IEEE 6-, 14-, and 39-bus test systems evidencing the applicability of the proposed approach. The results were contrasted with those previously reported in the specialized literature, matching, and in some cases improving, the reported solutions with lower computational times.24 Páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Computation Vol.10 N° 8 (2022)Solving the Optimal Reactive Power Dispatch Problem through a Python-DIgSILENT Interfaceinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Combinatorial optimizationDIgSILENT softwareGenetic algorithmMean variance mapping optimizationOptimal reactive power dispatchPower losses minimizationPython programming languageLEMBCartagena de IndiasVilla-Acevedo, W.M.; López-Lezama, J.M.; Valencia-Velásquez, J.A. A Novel Constraint Handling Approach for the Optimal Reactive Power Dispatch Problem. Energies 2018, 11, 2352Marín-Cano, C.C.; Sierra-Aguilar, J.E.; López-Lezama, J.M.; Jaramillo-Duque, Á.; Villegas, J.G. A Novel Strategy to Reduce Computational Burden of the Stochastic Security Constrained Unit Commitment Problem. Energies 2020, 13, 3777Sierra-Aguilar, J.E.; Marín-Cano, C.C.; López-Lezama, J.M.; Jaramillo-Duque, Á.; Villegas, J.G. A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty. Appl. Sci. 2021, 11, 3987Mota-Palomino, R.; Quintana, V.H. Sparse Reactive Power Scheduling by a Penalty Function - Linear Programming Technique. IEEE Trans. Power Syst. 1986, 1, 31–39.Quintana, V.; Santos-Nieto, M. Reactive-power dispatch by successive quadratic programming. IEEE D 1989, 4, 425–435Granville, S. Optimal reactive dispatch through interior point methods. IEEE Trans. Power Syst. 1994, 9, 136–146López-Lezama, J.M.; Cortina-Gómez, J.; Muñoz-Galeano, N. Assessment of the Electric Grid Interdiction Problem using a nonlinear modeling approach. Electr. Power Syst. Res. 2017, 144, 243–254Gracia-Velásquez, D.G.; Morales-Rodríguez, A.S.; Montoya, O.D. Application of the Crow Search Algorithm to the Problem of the Parametric Estimation in Transformers Considering Voltage and Current Measures. Computers 2022, 11, 9.Arenas-Acuña, C.A.; Rodriguez-Contreras, J.A.; Montoya, O.D.; Rivas-Trujillo, E. Black-Hole Optimization Applied to the Parametric Estimation in Distribution Transformers Considering Voltage and Current Measures. Computers 2021, 10, 124.Saldarriaga-Zuluaga, S.D.; López-Lezama, J.M.; Muñoz-Galeano, N. Optimal coordination of over-current relays in microgrids considering multiple characteristic curves. Alex. Eng. J. 2021, 60, 2093–2113.Pareja, L.A.G.; Lezama, J.M.L.; Carmona, O.G. Optimal Placement of Capacitors, Voltage Regulators, and Distributed Generators in Electric Power Distribution Systems. Ingeniería 2020, 25, 334–354Montoya, O.D. Notes on the Dimension of the Solution Space in Typical Electrical Engineering Optimization Problems. Ingeniería 2022, 27, e19310Duman, S.; Sonmez, Y.; Guvencc, U.; Yorukeren. Optimal reactive power dispatch using a gravitational search algorithm. IET Gener. Transm. Distrib. 2012, 6, 563.Shaw, B.; Mukherjee, V.; Ghoshal, S. Solution of reactive power dispatch of power systems by an opposition-based gravitational search algorithm. Int. J. Electr. Power Energy Syst. 2014, 55, 29–40Khazali, A.; Kalantar, M. Optimal reactive power dispatch based on harmony search algorithm. Int. J. Electr. Power Energy Syst. 2011, 33, 684–692.Yoshida, H.; Kawata, K.; Fukuyama, Y.; Takayama, S.; Nakanishi, Y. A particle swarm optimization for reactive power and voltage control considering voltage security assessment. IEEE Trans. Power Syst. 2000, 15, 1232–1239.Cai, G.; Ren, Z.; Yu, T. Optimal Reactive Power Dispatch Based on Modified Particle Swarm Optimization Considering Voltage Stability. In Proceedings of the 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, USA, 24–28 June 2007; pp. 1–5.Vlachogiannis, J.; Lee, K. A Comparative Study on Particle Swarm Optimization for Optimal Steady-State Performance of Power Systems. IEEE Trans. Power Syst. 2006, 21, 1718–1728Gutiérrez, D.; Villa, W.M.; López-Lezama, J.M. Flujo Óptimo Reactivo mediante Optimización por Enjambre de Partículas. Inform. Tecnol. 2017, 28, 215–224Naderi, E.; Narimani, H.; Fathi, M.; Narimani, M.R. A novel fuzzy adaptive configuration of particle swarm optimization to solve large-scale optimal reactive power dispatch. Appl. Soft Comput. 2017, 53, 441–456. [Duong, T.L.; Duong, M.Q.; Phan, V.D.; Nguyen, T.T. Optimal Reactive Power Flow for Large-Scale Power Systems Using an Effective Metaheuristic Algorithm. J. Electr. Comput. Eng. 2020, 2020, 1–11Londoño, D.C.; Villa-Acevedo, W.M.; López-Lezama, J.M. Assessment of Metaheuristic Techniques Applied to the Optimal Reactive Power Dispatch. In Communications in Computer and Information Science; Springer International Publishing: Cham, Switzerland, 2019; pp. 250–262Saddique, M.S.; Bhatti, A.R.; Haroon, S.S.; Sattar, M.K.; Amin, S.; Sajjad, I.A.; ul Haq, S.S.; Awan, A.B.; Rasheed, N. Solution to optimal reactive power dispatch in transmission system using meta-heuristic techniques—Status and technological review. Electr. Power Syst. Res. 2020, 178, 106031.Zhao, J.; Zhang, Z.; Yao, J.; Yang, S.; Wang, K. A distributed optimal reactive power flow for global transmission and distribution network. Int. J. Electr. Power Energy Syst. 2019, 104, 524–536Khan, N.H.; Wang, Y.; Tian, D.; Raja, M.A.Z.; Jamal, R.; Muhammad, Y. Design of Fractional Particle Swarm Optimization Gravitational Search Algorithm for Optimal Reactive Power Dispatch Problems. IEEE Access 2020, 8, 146785–146806.Jamal, R.; Men, B.; Khan, N.H.; Raja, M.A.Z.; Muhammad, Y. Application of Shannon Entropy Implementation Into a Novel Fractional Particle Swarm Optimization Gravitational Search Algorithm (FPSOGSA) for Optimal Reactive Power Dispatch Problem. IEEE Access 2021, 9, 2715–2733.Vlachogiannis, J.G.; Lee, K.Y. Quantum-Inspired Evolutionary Algorithm for Real and Reactive Power Dispatch. IEEE Trans. Power Syst. 2008, 23, 1627–1636.Ela, A.A.E.; Abido, M.; Spea, S. Differential evolution algorithm for optimal reactive power dispatch. Electr. Power Syst. Res. 2011, 81, 458–464.Bakirtzis, A.; Biskas, P.; Zoumas, C.; Petridis, V. Optimal power flow by enhanced genetic algorithm. IEEE Trans. Power Syst. 2002, 17, 229–236.Ara, A.L.; Kazemi, A.; Gahramani, S.; Behshad, M. Optimal reactive power flow using multi-objective mathematical programming. Sci. Iran. 2012, 19, 1829–1836. [Bernal-Romero, D.L.; Montoya, O.D.; Arias-Londoño, A. Solution of the Optimal Reactive Power Flow Problem Using a Discrete-Continuous CBGA Implemented in the DigSILENT Programming Language. Computers 2021, 10, 151.Ganesh, S.; Perilla, A.; Torres, J.R.; Palensky, P.; van der Meijden, M. Validation of EMT Digital Twin Models for Dynamic Voltage Performance Assessment of 66 kV Offshore Transmission Network. Appl. Sci. 2020, 11, 244Mei, R.N.S.; Sulaiman, M.H.; Mustaffa, Z.; Daniyal, H. Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique. Appl. Soft Comput. 2017, 59, 210–222. doi: 10.1016/j.asoc.2017.05.057Bhongade, S.; Tomar, A.; Goigowal, S.R. Minimization of Optimal Reactive Power Dispatch Problem using BAT Algorithm. In Proceedings of the 2020 IEEE First International Conference on Smart Technologies for Power, Energy and Control (STPEC), Nagpur, India, 25–26 September 2020; IEEE: Piscataway, NJ, USA, 2020Abido, M.A. Optimal Power Flow Using Tabu Search Algorithm. Electr. Power Compon. Syst. 2002, 30, 469–483.Lenin, K. Reduction of active power loss by improved tabu search algorithm. Int. J. Res. GRANTHAALAYAH 2018, 6, 1–9ElSayed, S.K.; Elattar, E.E. Slime Mold Algorithm for Optimal Reactive Power Dispatch Combining with Renewable Energy Sources. Sustainability 2021, 13, 5831Rojas, D.G.; Lezama, J.L.; Villa, W. Metaheuristic Techniques Applied to the Optimal Reactive Power Dispatch: a Review. IEEE Lat. Am. Trans. 2016, 14, 2253–2263Aghbolaghi, A.J.; Tabatabaei, N.M.; Boushehri, N.S.; Parast, F.H. Reactive Power Optimization in AC Power Systems. In Power Systems; Springer International Publishing: Cham, Switzerland, 2017; pp. 345–409.Barboza, L.V.; Ziirn, H.H.; Salgado, R. Load Tap Change Transformers: A Modeling Reminder. IEEE Power Eng. Rev. 2001, 21, 51–52Londoño-Tamayo, D.; Villa-Acevedo, J.L.L..W. Mean-Variance Mapping Optimization Algorithm Applied to the Optimal Reactive Power Dispatch. INGECUC 2021, 17, 239–255.Sharif, S.; Taylor, J. MINLP formulation of optimal reactive power flow. In Proceedings of the IEEE 1997 American Control Conference (Cat. No.97CH36041), Albuquerque, NM, USA, 8–10 May 1997Morán-Burgos, J.A.; Sierra-Aguilar, J.E.; Villa-Acevedo, W.M.; López-Lezama, J.M. A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals. Appl. Sci. 2021, 11, 8535Acosta, M.N.; Adiyabazar, C.; Gonzalez-Longatt, F.; Andrade, M.A.; Torres, J.R.; Vazquez, E.; Santos, J.M.R. Optimal UnderFrequency Load Shedding Setting at Altai-Uliastai Regional Power System, Mongolia. Energies 2020, 13, 5390.Gonzalez-Longatt, F.M.; Rueda, J.L. (Eds.) PowerFactory Applications for Power System Analysis; Springer International Publishing: Cham, Switzerland, 2014.Bifaretti, S.; Bonaiuto, V.; Pipolo, S.; Terlizzi, C.; Zanchetta, P.; Gallinelli, F.; Alessandroni, S. Power Flow Management by Active Nodes: A Case Study in Real Operating Conditions. Energies 2021, 14, 4519Dierbach, C. Python as a First Programming Language. J. Comput. Sci. Coll. 2014, 29, 73Thurner, L.; Scheidler, A.; Schäfer, F.; Menke, J.H.; Dollichon, J.; Meier, F.; Meinecke, S.; Braun, M. Pandapower—An Open-Source Python Tool for Convenient Modeling, Analysis, and Optimization of Electric Power Systems. IEEE Trans. Power Syst. 2018, 33, 6510–6521Milano, F. A python-based software tool for power system analysis. In Proceedings of the 2013 IEEE Power Energy Society General Meeting, Vancouver, BC, Canada, 21–25 July 2013; pp. 1–5Condren, J.; An, S. Automation of transmission planning analysis process using Python and GTK+. In Proceedings of the 2006 IEEE Power Engineering Society General Meeting, London, UK, 18–22 June 2006; p. 8Yusuff, A.; Mosetlhe, T.; Ayodele, T. Statistical method for identification of weak nodes in power system based on voltage magnitude deviation. Electr. Power Syst. Res. 2021, 200, 107464.Latif, A.; Ahmad, I.; Palensky, P.; Gawlik, W. Multi-objective reactive power dispatch in distribution networks using modified bat algorithm. In Proceedings of the 2016 IEEE Green Energy and Systems Conference (IGSEC), Long Beach, CA, USA, 6–7 June 2016; pp. 1–7Mean Variance Mapping Optimization Algorithm. Available online: https://pypi.org/project/MVMO/ (accessed on 30 April 2022)Pymoo: Multi-Objective Optimization in Python. Available online: https://pymoo.org/index.html (accessed on 30 April 2022)Blank, J.; Deb, K. Pymoo: Multi-Objective Optimization in Python. IEEE Access 2020, 8, 89497–89509Implemtación de MVMO y GA en DigSilent Power Factory con Python. Available online: https://github.com/Msanchez1002/ MVMO_GA (accessed on 30 April 2022)Agudelo, L.; López-Lezama, J.M.; Muñoz-Galeano, N. Vulnerability assessment of power systems to intentional attacks using a specialized genetic algorithm. Dyna 2015, 82, 78–84GA: Genetic Algorithm. Available online: https://pymoo.org/algorithms/soo/ga.html (accessed on 30 April 2022).MVMo: Mean Variance Mapping Optimization Algorithm. Available online: https://github.com/dgusain1/MVMO (accessed on 30 April 2022).Erlich, I.; Venayagamoorthy, G.K.; Worawat, N. A Mean-Variance Optimization algorithm. In Proceedings of the IEEE Congress on Evolutionary Computation, Barcelona, Spain, 18–23 July 2010; pp. 1–6Rueda, J.L.; Erlich, I. Optimal dispatch of reactive power sources by using MVMO optimization. In Proceedings of the 2013 IEEE Computational Intelligence Applications in Smart Grid (CIASG), Singapore, 16–19 April 2013; pp. 29–36. Rueda, J.L.; Erlich, I. Evaluation of the mean-variance mapping optimization for solving multimodal problems. 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