A Modified Rao-2 Algorithm for Optimal Power Flow Incorporating Renewable Energy Sources
In this paper, a modified Rao-2 (MRao-2) algorithm is proposed to solve the problem of optimal power flow (OPF) in a power system incorporating renewable energy sources (RES). Quasi-oppositional and Levy flight methods are used to improve the performance of the Rao algorithm. To demonstrate effectiv...
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| Published in | Mathematics (Basel) Vol. 9; no. 13; p. 1532 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.07.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math9131532 |
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| Abstract | In this paper, a modified Rao-2 (MRao-2) algorithm is proposed to solve the problem of optimal power flow (OPF) in a power system incorporating renewable energy sources (RES). Quasi-oppositional and Levy flight methods are used to improve the performance of the Rao algorithm. To demonstrate effectiveness of the MRao-2 technique, it is tested on two standard test systems: an IEEE 30-bus system and an IEEE 118-bus system. The objective function of the OPF is the minimization of fuel cost in five scenarios. The IEEE 30-bus system reflects fuel cost minimization in three scenarios (without RES, with RES, and with RES under contingency state), while the IEEE 118-bus system reflects fuel cost minimization in two scenarios (without RES and with RES). The achieved results of various scenarios using the suggested MRao-2 technique are compared with those obtained using five recent techniques: Atom Search Optimization (ASO), Turbulent Flow of Water-based Optimization (TFWO), Marine Predators Algorithm (MPA), Rao-1, Rao-3 algorithms, as well as the conventional Rao-2 algorithm. Those comparisons confirm the superiority of the MRao-2 technique over those other algorithms in solving the OPF problem. |
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| AbstractList | In this paper, a modified Rao-2 (MRao-2) algorithm is proposed to solve the problem of optimal power flow (OPF) in a power system incorporating renewable energy sources (RES). Quasi-oppositional and Levy flight methods are used to improve the performance of the Rao algorithm. To demonstrate effectiveness of the MRao-2 technique, it is tested on two standard test systems: an IEEE 30-bus system and an IEEE 118-bus system. The objective function of the OPF is the minimization of fuel cost in five scenarios. The IEEE 30-bus system reflects fuel cost minimization in three scenarios (without RES, with RES, and with RES under contingency state), while the IEEE 118-bus system reflects fuel cost minimization in two scenarios (without RES and with RES). The achieved results of various scenarios using the suggested MRao-2 technique are compared with those obtained using five recent techniques: Atom Search Optimization (ASO), Turbulent Flow of Water-based Optimization (TFWO), Marine Predators Algorithm (MPA), Rao-1, Rao-3 algorithms, as well as the conventional Rao-2 algorithm. Those comparisons confirm the superiority of the MRao-2 technique over those other algorithms in solving the OPF problem. |
| Author | Kamel, Salah Khurshaid, Tahir Selim, Ali Hassan, Mohamed H. Domínguez-García, José Luis |
| Author_xml | – sequence: 1 givenname: Mohamed H. orcidid: 0000-0003-1754-4883 surname: Hassan fullname: Hassan, Mohamed H. – sequence: 2 givenname: Salah orcidid: 0000-0001-9505-5386 surname: Kamel fullname: Kamel, Salah – sequence: 3 givenname: Ali orcidid: 0000-0002-3034-2592 surname: Selim fullname: Selim, Ali – sequence: 4 givenname: Tahir orcidid: 0000-0001-6113-123X surname: Khurshaid fullname: Khurshaid, Tahir – sequence: 5 givenname: José Luis surname: Domínguez-García fullname: Domínguez-García, José Luis |
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| Cites_doi | 10.1016/j.engappai.2020.103666 10.1109/59.761902 10.1007/s00202-019-00762-4 10.1016/j.asoc.2020.106141 10.1016/j.energy.2018.06.137 10.1016/j.knosys.2018.08.030 10.1007/s00366-020-01008-9 10.1109/ACCESS.2021.3056423 10.1016/j.asoc.2020.106252 10.1016/j.ijepes.2014.06.031 10.1109/ACCESS.2021.3059665 10.1016/j.ijepes.2015.07.034 10.1002/2050-7038.12858 10.1049/iet-gtd.2013.0724 10.1007/s12667-012-0056-y 10.3390/en11071692 10.1109/TPWRS.2017.2695963 10.1111/exsy.12674 10.1016/j.epsr.2016.09.025 10.1016/j.ijepes.2013.04.021 10.1016/j.ijepes.2015.05.011 10.1016/j.conengprac.2020.104672 10.3390/en9090678 10.1049/iet-gtd.2015.0892 10.1016/j.enconman.2012.01.017 10.1109/59.744492 10.3390/su12135283 10.1016/j.ijleo.2020.164559 10.1080/15325008.2015.1041625 10.1016/j.engappai.2017.10.019 10.3390/app10186604 10.1016/j.ijleo.2021.166439 10.1016/j.epsr.2019.105989 10.1016/j.ijepes.2015.12.021 10.17512/znb.2019.1.07 10.1049/iet-gtd.2010.0109 10.1002/2050-7038.12270 10.1016/j.ijleo.2019.163846 10.1016/j.renene.2016.08.026 10.1016/j.ijepes.2018.01.024 10.1109/ACCESS.2019.2947626 10.1007/s00500-020-05431-4 10.1002/etep.494 10.1016/j.energy.2019.04.159 10.1007/s00521-020-05455-9 10.1109/ACCESS.2019.2958279 10.1016/j.eswa.2020.113377 10.3390/en13164265 10.1016/j.enconman.2020.113722 10.1049/iet-gtd.2018.0053 10.3390/en11092270 |
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| References | Elattar (ref_4) 2019; 178 Taha (ref_43) 2018; 12 Duman (ref_45) 2020; 30 Rao (ref_23) 2020; 89 Hasanien (ref_56) 2015; 43 Zhao (ref_49) 2019; 163 ref_10 Frank (ref_6) 2012; 3 Momoh (ref_7) 1999; 14 Rao (ref_27) 2020; 7 Premalatha (ref_53) 2015; 73 Lekouaghet (ref_22) 2021; 229 Yan (ref_8) 1999; 14 Kaymaz (ref_18) 2021; 33 ref_15 Shaheen (ref_5) 2021; 9 Yu (ref_42) 2019; 7 Attia (ref_14) 2018; 99 Zabaiou (ref_30) 2014; 8 Farhat (ref_35) 2010; 4 ref_25 ref_24 Ghasemi (ref_50) 2020; 92 Karami (ref_52) 2013; 53 Faramarzi (ref_51) 2020; 152 Dede (ref_26) 2020; 175 Sultana (ref_40) 2014; 63 Niknam (ref_55) 2012; 58 Biswas (ref_32) 2018; 68 Chambers (ref_3) 2019; 177 Birogul (ref_33) 2019; 7 Kamel (ref_16) 2021; 25 Elattar (ref_31) 2018; 159 Abaci (ref_2) 2016; 79 Pena (ref_48) 2018; 33 ref_34 Hassan (ref_28) 2021; 9 Sharma (ref_29) 2021; 38 Shaheen (ref_12) 2016; 10 ref_38 Taher (ref_11) 2019; 101 Rao (ref_37) 2020; 11 Sharma (ref_39) 2016; 74 Wang (ref_20) 2020; 210 Warid (ref_13) 2020; 91 Premkumar (ref_19) 2020; 208 ref_47 Jian (ref_21) 2021; 231 ref_44 ref_41 ref_9 Sulaiman (ref_17) 2021; 106 Sulaiman (ref_1) 2021; 31 Hazra (ref_46) 2011; 21 Nwulu (ref_36) 2017; 101 Mohamed (ref_54) 2017; 142 |
| References_xml | – volume: 92 start-page: 103666 year: 2020 ident: ref_50 article-title: A novel and effective optimization algorithm for global optimization and its engineering applications: Turbulent Flow of Water-based Optimization (TFWO) publication-title: Eng. Appl. Artif. Intell. doi: 10.1016/j.engappai.2020.103666 – volume: 14 start-page: 709 year: 1999 ident: ref_8 article-title: Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances publication-title: IEEE Trans. Power Syst. doi: 10.1109/59.761902 – volume: 101 start-page: 121 year: 2019 ident: ref_11 article-title: Modified grasshopper optimization framework for optimal power flow solution publication-title: Electr. Eng. doi: 10.1007/s00202-019-00762-4 – volume: 89 start-page: 106141 year: 2020 ident: ref_23 article-title: Constrained design optimization of selected mechanical system components using Rao algorithms publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2020.106141 – volume: 159 start-page: 496 year: 2018 ident: ref_31 article-title: Modified harmony search algorithm for combined economic emission dispatch of microgrid incorporating renewable sources publication-title: Energy doi: 10.1016/j.energy.2018.06.137 – volume: 163 start-page: 283 year: 2019 ident: ref_49 article-title: Atom search optimization and its application to solve a hydrogeologic parameter estimation problem publication-title: Knowl.-Based Syst. doi: 10.1016/j.knosys.2018.08.030 – volume: 7 start-page: 830 year: 2020 ident: ref_27 article-title: Quasi-oppositional-based Rao algorithms for multi-objective design optimization of selected heat sinks publication-title: J. Comput. Des. Eng. – ident: ref_24 doi: 10.1007/s00366-020-01008-9 – volume: 9 start-page: 23264 year: 2021 ident: ref_28 article-title: Optimal Reactive Power Dispatch With Time-Varying Demand and Renewable Energy Uncertainty Using Rao-3 Algorithm publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3056423 – volume: 91 start-page: 106252 year: 2020 ident: ref_13 article-title: Optimal power flow using the AMTPG-Jaya algorithm publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2020.106252 – volume: 63 start-page: 534 year: 2014 ident: ref_40 article-title: Multi-objective quasi-oppositional teaching learning based optimization for optimal location of distributed generator in radial distribution systems publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2014.06.031 – volume: 9 start-page: 35846 year: 2021 ident: ref_5 article-title: Solving of Optimal Power Flow Problem Including Renewable Energy Resources Using HEAP Optimization Algorithm publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3059665 – volume: 74 start-page: 348 year: 2016 ident: ref_39 article-title: Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2015.07.034 – volume: 31 start-page: e12858 year: 2021 ident: ref_1 article-title: Optimal power flow with stochastic solar power using barnacles mating optimizer publication-title: Int. Trans. Electr. Energy Syst. doi: 10.1002/2050-7038.12858 – volume: 8 start-page: 924 year: 2014 ident: ref_30 article-title: Preventive control approach for voltage stability improvement using voltage stability constrained optimal power flow based on static line voltage stability indices publication-title: IET Gener. Transm. Distrib. doi: 10.1049/iet-gtd.2013.0724 – volume: 3 start-page: 221 year: 2012 ident: ref_6 article-title: Optimal power flow: A bibliographic survey I publication-title: Energy Syst. doi: 10.1007/s12667-012-0056-y – ident: ref_15 doi: 10.3390/en11071692 – volume: 33 start-page: 281 year: 2018 ident: ref_48 article-title: An Extended IEEE 118-Bus Test System With High Renewable Penetration publication-title: IEEE Trans. Power Syst. doi: 10.1109/TPWRS.2017.2695963 – volume: 38 start-page: e12674 year: 2021 ident: ref_29 article-title: Classification of Parkinson disease using binary Rao optimization algorithms publication-title: Expert Syst. doi: 10.1111/exsy.12674 – volume: 142 start-page: 190 year: 2017 ident: ref_54 article-title: Optimal power flow using moth swarm algorithm publication-title: Electr. Power Syst. Res. doi: 10.1016/j.epsr.2016.09.025 – volume: 53 start-page: 219 year: 2013 ident: ref_52 article-title: Artificial bee colony algorithm for solving multi-objective optimal power flow problem publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2013.04.021 – ident: ref_38 – volume: 73 start-page: 393 year: 2015 ident: ref_53 article-title: Optimal power flow for a deregulated power system using adaptive real coded biogeography-based optimization publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2015.05.011 – volume: 106 start-page: 104672 year: 2021 ident: ref_17 article-title: Solving optimal power flow problem with stochastic wind–solar–small hydro power using barnacles mating optimizer publication-title: Control Eng. Pract. doi: 10.1016/j.conengprac.2020.104672 – ident: ref_47 doi: 10.3390/en9090678 – volume: 10 start-page: 1634 year: 2016 ident: ref_12 article-title: Solving multi-objective optimal power flow problem via forced initialised differential evolution algorithm publication-title: IET Gener. Transm. Distrib. doi: 10.1049/iet-gtd.2015.0892 – volume: 58 start-page: 197 year: 2012 ident: ref_55 article-title: A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect publication-title: Energy Convers. Manag. doi: 10.1016/j.enconman.2012.01.017 – volume: 11 start-page: 107 year: 2020 ident: ref_37 article-title: Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems publication-title: Int. J. Ind. Eng. Comput. – volume: 14 start-page: 96 year: 1999 ident: ref_7 article-title: A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches publication-title: IEEE Trans. Power Syst. doi: 10.1109/59.744492 – ident: ref_34 doi: 10.3390/su12135283 – volume: 208 start-page: 164559 year: 2020 ident: ref_19 article-title: A new metaphor-less algorithms for the photovoltaic cell parameter estimation publication-title: Optik doi: 10.1016/j.ijleo.2020.164559 – volume: 43 start-page: 1548 year: 2015 ident: ref_56 article-title: Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms publication-title: Electr. Power Compon. Syst. doi: 10.1080/15325008.2015.1041625 – volume: 68 start-page: 81 year: 2018 ident: ref_32 article-title: Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques publication-title: Eng. Appl. Artif. Intell. doi: 10.1016/j.engappai.2017.10.019 – ident: ref_41 doi: 10.3390/app10186604 – volume: 231 start-page: 166439 year: 2021 ident: ref_21 article-title: Parameters identification of photovoltaic models using modified Rao-1 optimization algorithm publication-title: Optik (Stuttgart) doi: 10.1016/j.ijleo.2021.166439 – volume: 177 start-page: 105989 year: 2019 ident: ref_3 article-title: Solving constrained optimal power flow with renewables using hybrid modified imperialist competitive algorithm and sequential quadratic programming publication-title: Electr. Power Syst. Res. doi: 10.1016/j.epsr.2019.105989 – volume: 79 start-page: 1 year: 2016 ident: ref_2 article-title: Differential search algorithm for solving multi-objective optimal power flow problem publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2015.12.021 – volume: 175 start-page: 50 year: 2020 ident: ref_26 article-title: New Optimization Algorithms and their Application for 2d Truss Structures publication-title: Zesz. Nauk. Politech. Częstochowskiej. Bud. doi: 10.17512/znb.2019.1.07 – ident: ref_44 – volume: 4 start-page: 989 year: 2010 ident: ref_35 article-title: Dynamic adaptive bacterial foraging algorithm for optimum economic dispatch with valve-point effects and wind power publication-title: IET Gener. Transm. Distrib. doi: 10.1049/iet-gtd.2010.0109 – volume: 30 start-page: 1 year: 2020 ident: ref_45 article-title: Optimal power flow of power systems with controllable wind-photovoltaic energy systems via differential evolutionary particle swarm optimization publication-title: Int. Trans. Electr. Energy Syst. doi: 10.1002/2050-7038.12270 – volume: 210 start-page: 163846 year: 2020 ident: ref_20 article-title: Parameter estimation of photovoltaic cell model with Rao-1 algorithm publication-title: Optik (Stuttgart) doi: 10.1016/j.ijleo.2019.163846 – volume: 101 start-page: 16 year: 2017 ident: ref_36 article-title: Optimal dispatch for a microgrid incorporating renewables and demand response publication-title: Renew. Energy doi: 10.1016/j.renene.2016.08.026 – volume: 99 start-page: 331 year: 2018 ident: ref_14 article-title: Optimal power flow solution in power systems using a novel Sine-Cosine algorithm publication-title: Int. J. Electr. Power Energy Syst. doi: 10.1016/j.ijepes.2018.01.024 – volume: 7 start-page: 150729 year: 2019 ident: ref_42 article-title: Oppositional Jaya Algorithm With Distance-Adaptive Coefficient in Solving Directional Over Current Relays Coordination Problem publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2947626 – ident: ref_25 – volume: 25 start-page: 4027 year: 2021 ident: ref_16 article-title: An improved version of salp swarm algorithm for solving optimal power flow problem publication-title: Soft Comput. doi: 10.1007/s00500-020-05431-4 – volume: 21 start-page: 1028 year: 2011 ident: ref_46 article-title: A multi-objective optimal power flow using particle swarm optimization publication-title: Eur. Trans. Electr. Power doi: 10.1002/etep.494 – volume: 178 start-page: 598 year: 2019 ident: ref_4 article-title: Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement publication-title: Energy doi: 10.1016/j.energy.2019.04.159 – volume: 33 start-page: 6775 year: 2021 ident: ref_18 article-title: Optimal power flow solution with stochastic wind power using the Lévy coyote optimization algorithm publication-title: Neural Comput. Appl. doi: 10.1007/s00521-020-05455-9 – volume: 7 start-page: 184468 year: 2019 ident: ref_33 article-title: Hybrid Harris Hawk Optimization Based on Differential Evolution (HHODE) Algorithm for Optimal Power Flow Problem publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2958279 – volume: 152 start-page: 113377 year: 2020 ident: ref_51 article-title: Marine Predators Algorithm: A nature-inspired metaheuristic publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2020.113377 – ident: ref_10 doi: 10.3390/en13164265 – volume: 229 start-page: 113722 year: 2021 ident: ref_22 article-title: Estimation of the photovoltaic cells/modules parameters using an improved Rao-based chaotic optimization technique publication-title: Energy Convers. Manag. doi: 10.1016/j.enconman.2020.113722 – volume: 12 start-page: 3421 year: 2018 ident: ref_43 article-title: Optimal reactive power resources sizing for power system operations enhancement based on improved grey wolf optimiser publication-title: IET Gener. Transm. Distrib. doi: 10.1049/iet-gtd.2018.0053 – ident: ref_9 doi: 10.3390/en11092270 |
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| Snippet | In this paper, a modified Rao-2 (MRao-2) algorithm is proposed to solve the problem of optimal power flow (OPF) in a power system incorporating renewable... |
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| SubjectTerms | Algorithms Alternative energy sources Buses Climate change Contingency Design optimization Electricity distribution Energy resources Fluid dynamics Food science fuel cost minimization Fuels Industrial plant emissions modified Rao algorithm optimal power flow Optimization Optimization algorithms Optimization techniques Parameter estimation Power flow Power plants Renewable energy sources Renewable resources |
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| Title | A Modified Rao-2 Algorithm for Optimal Power Flow Incorporating Renewable Energy Sources |
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