Assessment of a multiperiod optimal power flow for power system operation
The optimal power flow is an important tool for power system planning and power system operation. It is used in a 24-hour period to find an economic dispatch of generating units considering network restrictions. The optimal power flow provides valuable information about the operation cost, the trans...
- Autores:
-
Moreno-Chuquen, Ricardo
Cantillo Luna, Sergio Alejandro
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/12917
- Acceso en línea:
- https://hdl.handle.net/10614/12917
- Palabra clave:
- Recursos energéticos renovables
Energía eólica
Renewable energy sources
Wind power
Optimal Power Flow
Power systems
Renewable energy
Flujo de energía óptimo
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
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dc.title.eng.fl_str_mv |
Assessment of a multiperiod optimal power flow for power system operation |
title |
Assessment of a multiperiod optimal power flow for power system operation |
spellingShingle |
Assessment of a multiperiod optimal power flow for power system operation Recursos energéticos renovables Energía eólica Renewable energy sources Wind power Optimal Power Flow Power systems Renewable energy Flujo de energía óptimo |
title_short |
Assessment of a multiperiod optimal power flow for power system operation |
title_full |
Assessment of a multiperiod optimal power flow for power system operation |
title_fullStr |
Assessment of a multiperiod optimal power flow for power system operation |
title_full_unstemmed |
Assessment of a multiperiod optimal power flow for power system operation |
title_sort |
Assessment of a multiperiod optimal power flow for power system operation |
dc.creator.fl_str_mv |
Moreno-Chuquen, Ricardo Cantillo Luna, Sergio Alejandro |
dc.contributor.author.none.fl_str_mv |
Moreno-Chuquen, Ricardo Cantillo Luna, Sergio Alejandro |
dc.subject.armarc.spa.fl_str_mv |
Recursos energéticos renovables Energía eólica |
topic |
Recursos energéticos renovables Energía eólica Renewable energy sources Wind power Optimal Power Flow Power systems Renewable energy Flujo de energía óptimo |
dc.subject.armarc.eng.fl_str_mv |
Renewable energy sources Wind power |
dc.subject.proposal.eng.fl_str_mv |
Optimal Power Flow Power systems Renewable energy |
dc.subject.proposal.spa.fl_str_mv |
Flujo de energía óptimo |
description |
The optimal power flow is an important tool for power system planning and power system operation. It is used in a 24-hour period to find an economic dispatch of generating units considering network restrictions. The optimal power flow provides valuable information about the operation cost, the transmission flows, the generation and the congestion in the system. This information is used by generators, planners, operators and regulators in order to analyze and take decisions about the system at short and long term. The first one corresponds to the information for the operation. The second one corresponds to the information for the planning. This paper proposes a detailed optimal power flow formulation looking for a minimum cost of generation considering wind generation. Five solvers (CBC, CLP, CPLEX, Gurobi and GLPK.) have been used in order to compare differences between them. These solvers are commonly used to solve the multiperiod DC optimal power flow. An IEEE-24 test system is used to compare the solutions provided by the solvers. The findings reveal significant differences between the solvers when they are used to solve the IEEE-24 test system. Additionally, the computing time for each solver is reported. The solvers CPLEX and Gurobi show the lowest computational time to find a solution. |
publishDate |
2020 |
dc.date.issued.none.fl_str_mv |
2020-12 |
dc.date.accessioned.none.fl_str_mv |
2021-03-26T16:24:07Z |
dc.date.available.none.fl_str_mv |
2021-03-26T16:24:07Z |
dc.type.spa.fl_str_mv |
Artículo de revista |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_998f http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
dc.type.content.eng.fl_str_mv |
Text |
dc.type.driver.eng.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ARTCORT |
dc.type.version.eng.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
http://purl.org/coar/resource_type/c_6501 |
status_str |
publishedVersion |
dc.identifier.issn.none.fl_str_mv |
18276660 |
dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/10614/12917 |
identifier_str_mv |
18276660 |
url |
https://hdl.handle.net/10614/12917 |
dc.language.iso.eng.fl_str_mv |
eng |
language |
eng |
dc.relation.citationendpage.spa.fl_str_mv |
492 |
dc.relation.citationissue.spa.fl_str_mv |
Número 6 |
dc.relation.citationstartpage.spa.fl_str_mv |
484 |
dc.relation.citationvolume.spa.fl_str_mv |
Volumen 15 |
dc.relation.cites.spa.fl_str_mv |
Moreno-Chuquen, Ricardo y Cantillo-Luna, Sergio. Assessment of a multiperiod optimal power flow for power system operation. En: International Review of Electrical Engineering (I.R.E.E.), volumen 15, número 6 (Noviembre-Diciembre, 2020), páginas 484-492. ISSN 1827- 6660 |
dc.relation.ispartofjournal.eng.fl_str_mv |
International Review of Electrical Engineering (I.R.E.E.) |
dc.relation.references.spa.fl_str_mv |
[1] Al Hasibi, R., Hadi, S., Sarjiya, S., Multi-Objective Optimization of Integrated Power System Expansion Planning with Renewable Energy-Based Distributed Generation, (2019) International Review of Electrical Engineering (IREE), 14 (1), pp. 19-31. doi: https://doi.org/10.15866/iree.v14i1.16082 [2] Sangwato, S., Oonsivilai, A., Optimal Power Flow with Interline Power Flow Controller Using Hybrid Genetic Algorithm, (2015) International Review of Electrical Engineering (IREE), 10 (6), pp. 727-733. doi: https://doi.org/10.15866/iree.v10i6.7568 [3] Lakdja, F., Abdeslam, D., Gherbi, F., Optimal Location of Thyristor-Controlled Series Compensator for Optimal Power Flows, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 465-472 [4] R.A. Jabr. Adjustable robust OPF with renewable energy sources. IEEE Trans Power Syst, vol. 28 n. 4, 2013, pp 4742–4751. [5] A. Castillo, X. Jiang, D.F. Gayme. Lossy DCOPF for optimizing congested grids with renewable energy and storage. Proceedings of the American Control Conference. Institute of Electrical and Electronics Engineers Inc. June 4-6, 2014, Portland, OR, United States. [6] T. Geetha, V. Jayashankar. Generation dispatch with storage and renewables under availability-based tariff. IEEE Region 10 Annual International Conference TENCON. 2008. [7] Gourma, A., Berdai, A., Reddak, M., Tytiuk, V., Reliability and Optimization Strategy in an Interconnected Network at a Wind Farm, (2018) International Review on Modelling and Simulations (IREMOS), 11 (2), pp. 76-83. doi: https://doi.org/10.15866/iremos.v11i2.13596 [8] Varanasi, J., Tripathi, M., Performance Comparison of Generalized Regression Network, Radial Basis Function Network and Support Vector Regression for Wind Power Forecasting, (2019) International Review on Modelling and Simulations (IREMOS), 12 (1), pp. 16-23. doi: https://doi.org/10.15866/iremos.v12i1.15781 [9] Srivastava, A., Bajpai, R., An Efficient Maximum Power Extraction Algorithm for Wind Energy Conversion System Using Model Predictive Control, (2019) International Journal on Energy Conversion (IRECON), 7 (3), pp. 93-107. doi: https://doi.org/10.15866/irecon.v7i3.17403 [10] A. Castillo, D. F. Gayme. Evaluating the effects of real power losses in optimal power flow-based storage integration. IEEE Transactions on Control of Network Systems, vol 5, n. 3. Sep 2018, pp 1132–1145. [11] Sharifzadeh H, Amjady N, Zareipour H. Multi-period stochastic security-constrained OPF considering the uncertainty sources of wind power, load demand and equipment unavailability. Electric Power Systems Research, vol. 146, n. 5. May 2017, pp. 33–42. [12] Boonchuay, K. Tomsovic, F. Li, W. Ongsakul. Robust optimization-based DC optimal power flow for managing wind generation uncertainty. AIP Conference Procedings, vol 1499, n. 1. May 2014, pp 31–35. [13] Rahmat Azami MSJ and GH. Economic load Dispatch and DCOptimal Power Flow Problem-PSO versus LR. International Journal of Multidisciplinary Sciences and Engineering, vol. 2, n. 9. Dec 2011, pp 8–13. [14] A. Soroudi. Power System Optimization Modeling in GAMS. (Springer International Publishing, 2017). [15] R. A. Jabr, S. Karaki, J. A. Korbane. Robust Multi-Period OPF with Storage and Renewables. IEEE Transactions on Power Systems, vol. 30 n. 5. Sep 2015, pp. 2790–2799. [16] B. Eldridge, R. O’Neill, A. Castillo. An Improved Method for the DCOPF with Losses. IEEE Transactions on Power Systems vol. 33, n. 4. July 2018, pp. 3779–3788. [17] P. Maghouli, A. Soroudi, A. Keane. Robust computational framework for mid-term techno-economical assessment of energy storage. IET Generation, Transmission & Distribution, vol. 10 n. 3. Feb 2016, pp. 822–831. [18] Hafez, A., AlSadi, S., Nassar, Y., Chaotic Optimization Versus Genetic Algorithm for Optimal Tuning of Static Synchronous Series Compensator Stabilizing Controller, (2019) International Review of Electrical Engineering (IREE), 14 (3), pp. 159-172 doi: https://doi.org/10.15866/iree.v14i3.16163 [19] Mmary, E., Marungsri, B., Multiobjective Optimization of Renewable Distributed Generations in Radial Distribution Networks with Optimal Power Factor, (2018) International Review of Electrical Engineering (IREE), 13 (4), pp. 297-304. doi: https://doi.org/10.15866/iree.v13i4.15069 [20] Adam, K., Miyauchi, H., Optimization of a Photovoltaic Hybrid Energy Storage System Using Energy Storage Peak Shaving, (2019) International Review of Electrical Engineering (IREE), 14 (1), pp. 8-18. doi: https://doi.org/10.15866/iree.v14i1.16162 [21] Oloulade, A., Moukengue, A., Vianou, A., Multi-Criteria Optimization of the Functionning of a Distribution Network in Normal Operating Regime, (2018) International Review of Electrical Engineering (IREE), 13 (4), pp. 290-296. doi: https://doi.org/10.15866/iree.v13i4.14401 [22] Hassoune, A., Khafallah, M., Mesbahi, A., Benaaouinate, L., ouragba, T., Control Strategies of a Smart Topology of EVs Charging Station Based Grid Tied RES-Battery, (2018) International Review of Electrical Engineering (IREE), 13 (5), pp. 385-396. doi: https://doi.org/10.15866/iree.v13i5.15520 [23] Moreno, R. Identification of Topological Vulnerabilities for Power Systems Networks. In 2018 IEEE Power & Energy Society General Meeting (PESGM), pp. 1-5. doi: https://doi.org/10.1109/PESGM.2018.8586143 [24] Moreno-Chuquen, R., Obando-Ceron, J., Network Topological Notions for Power Systems Security Assessment, (2018) International Review of Electrical Engineering (IREE), 13 (3), pp. 237-245. doi: https://doi.org/10.15866/iree.v13i3.14210 [25] Khemmook, P., Khomfoi, S., Transient Stability Improvement Using Coordinated Control of Solar PVs and Solid State Transformers, (2018) International Review of Electrical Engineering (IREE), 13 (6), pp. 486-494. doi: https://doi.org/10.15866/iree.v13i6.15869 [26] Omar, A., Ali, Z., Abdel Aleem, S., Abou-El-Zahab, E., Sharaf, A., A Dynamic Switched Compensation Scheme for GridConnected Wind Energy Systems Using Cuckoo Search Algorithm, (2019) International Journal on Energy Conversion (IRECON), 7 (2), pp. 64-74. doi: https://doi.org/10.15866/irecon.v7i2.16895 [27] Mauledoux, M., Valencia, A., Avilés, O., Genetic Algorithm Optimization for DC Micro Grid Design, a Case of Study, (2017) International Review of Electrical Engineering (IREE), 12 (4), pp. 318-323. doi: https://doi.org/10.15866/iree.v12i4.11544 [28] Jabri, M., Aloui, H., Genetic Lagrangian Relaxation Selection Method for the Solution of Unit Commitment Problem, (2019) International Journal on Engineering Applications (IREA), 7 (2), pp. 59-64. doi: https://doi.org/10.15866/irea.v7i2.17022 [29] Prodromidis, G., Tsiaras, E., Coutelieris, F., Autonomous Buildings with Electricity by Renewables, (2018) International Journal on Energy Conversion (IRECON), 6 (5), pp. 153-159. doi: https://doi.org/10.15866/irecon.v6i5.15919 [30] Rizk-Allah, R., Abdel Mageed, H., El-Sehiemy, R., Abdel Aleem, S., El Shahat, A., A New Sine Cosine Optimization Algorithm for Solving Combined Non-Convex Economic and Emission Power Dispatch Problems, (2017) International Journal on Energy Conversion (IRECON), 5 (6), pp. 180-192. doi: https://doi.org/10.15866/irecon.v5i6.14291 [31] Syahputra, R., Robandi, I., Ashari, M., Performance Improvement of Radial Distribution Network with Distributed Generation Integration Using Extended Particle Swarm Optimization Algorithm, (2015) International Review of Electrical Engineering (IREE), 10 (2), pp. 293-304. doi: https://doi.org/10.15866/iree.v10i2.5410 [32] Muthukumar, K., Jayalalitha, S., Ramaswamy, M., PSO Embedded Artificial Bee Colony Algorithm for Optimal Shunt Capacitor Allocation and Sizing in Radial Distribution Networks with Voltage Dependent Load Models, (2015) International Review of Electrical Engineering (IREE), 10 (2), pp. 305-320. doi: https://doi.org/10.15866/iree.v10i2.5481 [33] Moreno, R., Obando, J., Gonzalez, G., An integrated OPF dispatching model with wind power and demand response for day-ahead markets, (2019) International Journal of Electrical and Computer Engineering (IJECE), 4 (4), pp. 2794-2802. doi: http://doi.org/10.11591/ijece.v9i4.pp2794-2802 [34] Wongdet, P., Leeton, U., Marungsri, B., Line Loss Reduction by Optimal Location of Battery Energy Storage System for the Daily Operation in Microgrid with Distributed Generations, (2018) International Journal on Energy Conversion (IRECON), 6 (3), pp. 83-89. doi: https://doi.org/10.15866/irecon.v6i3.15095 [35] Obando, J., Gonzalez, G., Moreno, R., Quantification of operating reserves with high penetration of wind power considering extreme values, (2020) International Journal of Electrical and Computer Engineering (IJECE), 10 (2), pp. 1693-1700. doi: http://doi.org/10.11591/ijece.v10i2.pp1693-1700 [36] J. Yi-Xiong, C. Hao-Zhong, Y. Jian-yong, Z. Li, New discrete method for particle swarm optimization and its application in transmission network expansion planning, Electric Power Systems Research, vol. 77 n. 3-4, 2007, pp. 227-233. doi. http://dx.doi.org/10.1016/j.epsr.2006.02.016 [37] COIN-OR Branch and Cut Interface Julia package. Accessed on Aug. 4, 2019. [Online]. Available: https://github.com/JuliaOpt/Cbc.jl [38] COIN-OR Linear Programming Interface Julia package. Accessed on Aug. 5, 2019. [Online]. Available: https://github.com/JuliaOpt/Clp.jl [39] IBM ILOG CPLEX Optimization Studio V12.9.0 documentation. Accessed on Aug. 4, 2019. [Online]. Available: https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/i log.odms.studio.help/Optimization_Studio/topics/COS_home.html [40] The GUROBI Manual. Accessed on August 5, 2019. [Online]. Available: https://www.gurobi.com/documentation/8.1/refman/index.html [41] Julia GNU Linear Programming Kit (GLPK) package. Accessed on August 5, 2019. [Online]. Available: https://github.com/JuliaOpt/GLPK.jl [42] Julia for Mathematical Optimization (JuMP) package. Accessed on Aug. 4, 2019. [Online]. Available: |
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Moreno-Chuquen, Ricardo3529d64b6cb8f4b63523eb51d5054f92Cantillo Luna, Sergio Alejandro 2021-03-26T16:24:07Z2021-03-26T16:24:07Z2020-1218276660https://hdl.handle.net/10614/12917The optimal power flow is an important tool for power system planning and power system operation. It is used in a 24-hour period to find an economic dispatch of generating units considering network restrictions. The optimal power flow provides valuable information about the operation cost, the transmission flows, the generation and the congestion in the system. This information is used by generators, planners, operators and regulators in order to analyze and take decisions about the system at short and long term. The first one corresponds to the information for the operation. The second one corresponds to the information for the planning. This paper proposes a detailed optimal power flow formulation looking for a minimum cost of generation considering wind generation. Five solvers (CBC, CLP, CPLEX, Gurobi and GLPK.) have been used in order to compare differences between them. These solvers are commonly used to solve the multiperiod DC optimal power flow. An IEEE-24 test system is used to compare the solutions provided by the solvers. The findings reveal significant differences between the solvers when they are used to solve the IEEE-24 test system. Additionally, the computing time for each solver is reported. The solvers CPLEX and Gurobi show the lowest computational time to find a solution.9 páginasapplication/pdfengAssessment of a multiperiod optimal power flow for power system operationArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_998fhttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTCORTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Recursos energéticos renovablesEnergía eólicaRenewable energy sourcesWind powerOptimal Power FlowPower systemsRenewable energyFlujo de energía óptimoNápoles, Italia492Número 6484Volumen 15Moreno-Chuquen, Ricardo y Cantillo-Luna, Sergio. Assessment of a multiperiod optimal power flow for power system operation. En: International Review of Electrical Engineering (I.R.E.E.), volumen 15, número 6 (Noviembre-Diciembre, 2020), páginas 484-492. ISSN 1827- 6660International Review of Electrical Engineering (I.R.E.E.)[1] Al Hasibi, R., Hadi, S., Sarjiya, S., Multi-Objective Optimization of Integrated Power System Expansion Planning with Renewable Energy-Based Distributed Generation, (2019) International Review of Electrical Engineering (IREE), 14 (1), pp. 19-31. doi: https://doi.org/10.15866/iree.v14i1.16082[2] Sangwato, S., Oonsivilai, A., Optimal Power Flow with Interline Power Flow Controller Using Hybrid Genetic Algorithm, (2015) International Review of Electrical Engineering (IREE), 10 (6), pp. 727-733. doi: https://doi.org/10.15866/iree.v10i6.7568[3] Lakdja, F., Abdeslam, D., Gherbi, F., Optimal Location of Thyristor-Controlled Series Compensator for Optimal Power Flows, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 465-472[4] R.A. Jabr. Adjustable robust OPF with renewable energy sources. IEEE Trans Power Syst, vol. 28 n. 4, 2013, pp 4742–4751.[5] A. Castillo, X. Jiang, D.F. Gayme. Lossy DCOPF for optimizing congested grids with renewable energy and storage. Proceedings of the American Control Conference. Institute of Electrical and Electronics Engineers Inc. June 4-6, 2014, Portland, OR, United States.[6] T. Geetha, V. Jayashankar. Generation dispatch with storage and renewables under availability-based tariff. IEEE Region 10 Annual International Conference TENCON. 2008.[7] Gourma, A., Berdai, A., Reddak, M., Tytiuk, V., Reliability and Optimization Strategy in an Interconnected Network at a Wind Farm, (2018) International Review on Modelling and Simulations (IREMOS), 11 (2), pp. 76-83. doi: https://doi.org/10.15866/iremos.v11i2.13596[8] Varanasi, J., Tripathi, M., Performance Comparison of Generalized Regression Network, Radial Basis Function Network and Support Vector Regression for Wind Power Forecasting, (2019) International Review on Modelling and Simulations (IREMOS), 12 (1), pp. 16-23. doi: https://doi.org/10.15866/iremos.v12i1.15781[9] Srivastava, A., Bajpai, R., An Efficient Maximum Power Extraction Algorithm for Wind Energy Conversion System Using Model Predictive Control, (2019) International Journal on Energy Conversion (IRECON), 7 (3), pp. 93-107. doi: https://doi.org/10.15866/irecon.v7i3.17403[10] A. Castillo, D. F. Gayme. Evaluating the effects of real power losses in optimal power flow-based storage integration. IEEE Transactions on Control of Network Systems, vol 5, n. 3. Sep 2018, pp 1132–1145.[11] Sharifzadeh H, Amjady N, Zareipour H. Multi-period stochastic security-constrained OPF considering the uncertainty sources of wind power, load demand and equipment unavailability. Electric Power Systems Research, vol. 146, n. 5. May 2017, pp. 33–42.[12] Boonchuay, K. Tomsovic, F. Li, W. Ongsakul. Robust optimization-based DC optimal power flow for managing wind generation uncertainty. AIP Conference Procedings, vol 1499, n. 1. May 2014, pp 31–35.[13] Rahmat Azami MSJ and GH. Economic load Dispatch and DCOptimal Power Flow Problem-PSO versus LR. International Journal of Multidisciplinary Sciences and Engineering, vol. 2, n. 9. Dec 2011, pp 8–13.[14] A. Soroudi. Power System Optimization Modeling in GAMS. (Springer International Publishing, 2017).[15] R. A. Jabr, S. Karaki, J. A. Korbane. Robust Multi-Period OPF with Storage and Renewables. IEEE Transactions on Power Systems, vol. 30 n. 5. Sep 2015, pp. 2790–2799.[16] B. Eldridge, R. O’Neill, A. Castillo. An Improved Method for the DCOPF with Losses. IEEE Transactions on Power Systems vol. 33, n. 4. July 2018, pp. 3779–3788.[17] P. Maghouli, A. Soroudi, A. Keane. Robust computational framework for mid-term techno-economical assessment of energy storage. IET Generation, Transmission & Distribution, vol. 10 n. 3. Feb 2016, pp. 822–831.[18] Hafez, A., AlSadi, S., Nassar, Y., Chaotic Optimization Versus Genetic Algorithm for Optimal Tuning of Static Synchronous Series Compensator Stabilizing Controller, (2019) International Review of Electrical Engineering (IREE), 14 (3), pp. 159-172 doi: https://doi.org/10.15866/iree.v14i3.16163[19] Mmary, E., Marungsri, B., Multiobjective Optimization of Renewable Distributed Generations in Radial Distribution Networks with Optimal Power Factor, (2018) International Review of Electrical Engineering (IREE), 13 (4), pp. 297-304. doi: https://doi.org/10.15866/iree.v13i4.15069[20] Adam, K., Miyauchi, H., Optimization of a Photovoltaic Hybrid Energy Storage System Using Energy Storage Peak Shaving, (2019) International Review of Electrical Engineering (IREE), 14 (1), pp. 8-18. doi: https://doi.org/10.15866/iree.v14i1.16162[21] Oloulade, A., Moukengue, A., Vianou, A., Multi-Criteria Optimization of the Functionning of a Distribution Network in Normal Operating Regime, (2018) International Review of Electrical Engineering (IREE), 13 (4), pp. 290-296. doi: https://doi.org/10.15866/iree.v13i4.14401[22] Hassoune, A., Khafallah, M., Mesbahi, A., Benaaouinate, L., ouragba, T., Control Strategies of a Smart Topology of EVs Charging Station Based Grid Tied RES-Battery, (2018) International Review of Electrical Engineering (IREE), 13 (5), pp. 385-396. doi: https://doi.org/10.15866/iree.v13i5.15520[23] Moreno, R. Identification of Topological Vulnerabilities for Power Systems Networks. 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