Оптимизация расположения и мощности возобновляемых распределенных источников энергии с использованием модифицированного метода роя частиц
Ключевые слова:
снижение потерь мощности, улучшенная PSO-NTVAC, сетчатые и радиальные сети, оптимальное размещение
Аннотация
Проникновение в энергосистемы возобновляемых распределенных источников, использующих, например, энергию ветра и(или) солнца, обещает множество технических и экологических преимуществ. К ним относятся повышение надежности энергосистемы, обеспечение растущих требований к экологичности, снижение потерь мощности и улучшение профиля напряжения. Однако установка источников распределенной генерации может привести и к негативным последствиям, если их мощность и расположение не определены должным образом. Поэтому необходимо развитие методов поиска оптимальных расположения и мощности энергоустановок распределенной генерации, минимизирующих возможные негативные последствия. Для определения местоположения и мощности источников распределенной генерации в энергосистемах используются как традиционные алгоритмы (линейное программирование, градиентный метод), так и современные эвристические. Метод роя частиц является одним из наиболее эффективных и широко используемых. Предлагается новый вариант алгоритма роя частиц с нелинейными изменяющимися во времени коэффициентами ускорения (PSO-NTVAC) для решения задачи определения оптимального местоположения и мощности нескольких энергоустановок для сетчатых и радиальных сетей. Основная цель рассматриваемой задачи оптимизации состоит в минимизации общих потерь активной мощности системы при удовлетворении всех эксплуатационных ограничений. Предложенная методология апробирована с использованием тестовых схем IEEE, содержащих 14, 30, 57, 33 и 69 шин, при количестве энергоустановок, изменяющемся от 1 до 4. Результат доказывает более высокую в сравнении с аналогами эффективность предложенной модификации PSO-NTVAC для решения задач оптимального размещения нескольких энергоустановок распределенной генерации и выбора их мощности с целью минимизации потерь мощности в энергосистеме.
Литература
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5. Osman M.H., Refaat A., Korovkin N.V. A Novel Method to Extract Single-Diode PV Parameters Based on Datasheet Values. – Электричество, 2021, №. 2, с. 16–21.
6. Refaat A., Elgamal M., Korovkin N.V. A Novel Grid-Connected Photovoltaic Centralized Inverter Topology to Improve the Power Harvest during Partial Shading Condition. – Электричество, 2019, №. 7, с. 59–68, DOI: 10.24160/0013-5380-2019-7-59-68.
7. ChithraDevi S.A., Lakshminarasimman L., Balamurugan R. Stud Krill Herd Algorithm for Multiple DG Placement and Sizing in a Radial Distribution System. – Engineering Science and Technology, an International Journal, 2017, vol. 20, No. 2, pp. 748–759, DOI: 10.1016/j.jestch.2016.11.009.
8. Martín García J.A., Gil-Mena A.J. Optimal Distributed Generation Location and Size Using a Modified Teaching-Learning Based Optimization Algorithm. – International Journal of Electrical Power and Energy Systems, 2013, vol. 50, No. 1, pp. 65–75, DOI: 10.1016/j.ijepes.2013.02.023.
9. Rezaee Jordehi A. Allocation of Distributed Generation Units in Electric Power Systems: A Review. – Renewable and Sustainable Energy Reviews, 2016, vol. 56, pp. 893–905, DOI: 10.1016/j.rser.2015.11.086.
10. Reddy P.D.P., Reddy V.C.V., Manohar T.G. Whale Optimization Algorithm for Optimal Sizing of Renewable Resources for Loss Reduction in Distribution Systems. – Renewables: Wind, Water, and Solar, 2017, vol. 4, No. 1, pp. 1–13, DOI: 10.1186/s40807-017-0040-1.
11. Refaat A., Osman M.H., Korovkin N.V. Optimum Power Extraction from Non-Uniform Aged PV Array Using Current Collector Optimizer Topology. – Электричество, 2019, №. 10, с. 54–60.
12. Wang C., Nehrir M.H. Analytical approaches for optimal placement of distributed generation sources in power systems. – IEEE Transactions on Power Systems, 2004, vol. 19, No. 4, pp. 2068–2076, DOI: 10.1109/TPWRS.2004.836189.
13. Shehata A.A., Ahmed M.K. State estimation accuracy enhancement for optimal power system steady state modes. – IOP Conference Series: Materials Science and Engineering, 2019, vol. 643, No. 1, DOI: 10.1088/1757-899X/643/1/012049.
14. Babaei E., Galvani S., Nejabatkhah F. Optimal Placement of DG Units Considering Power Losses Minimization and Voltage Stability Enhancement in Power System. – International Journal of Automation and Control Engineering, 2014, vol. 3, No. 1, DOI: 10.14355/ijace.2014.0301.01.
15. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Distribution System for Power Loss Reduction Using PSO Algorithm. – Procedia Technology, 2016, vol. 25, No. Raerest, pp. 785–792, DOI: 10.1016/j.protcy.2016.08.173.
16. Shehata A.A., et al. Optimal Placement and Sizing of FACTS Devices Based on Autonomous Groups Partical Swarm Optimization Technique. – Archives of Electrical Engineering, 2020, vol. 70, No. 1, DOI: 10.24425/aee.2021.136059.
17. Shukla T.N., et al. Optimal Sizing of Distributed Generation Placed on Radial Distribution System. – Electric Power Components and Systems, 2010, vol. 38, No. 3, pp. 260–274, DOI: 10.1080/15325000903273403.
18. Abu-Mouti F.S., El-Hawary M.E. Optimal Distributed Generation Allocation and Sizing in Distribution Systems Via Artificial Bee Colony Algorithm. – IEEE Transactions on Power Delivery, 2011, vol. 26, No. 4, pp. 2090–2101, DOI: 10.1109/TPWRD.2011.2158246.
19. Elattar E.E., et al. Optimal Location and Sizing of Distributed Generators Based on Renewable Energy Sources Using Modified Moth Flame Optimization Technique. – IEEE Access, 2020, vol. 8, pp. 109625–109638, DOI: 10.1109/ACCESS.2020.3001758.
20. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Radial Distribution System for Multi Objectives Using Whale Optimization Algorithm. – Alexandria Engineering Journal, 2018, vol. 57, No. 4, pp. 2797–2806, DOI: 10.1016/j.aej.2017.11.003.
21. Mohamed I.A., Kowsalya M. Optimal Size and Siting of Multiple Distributed Generators in Distribution System Using Bacterial Foraging Optimization. – Swarm and Evolutionary Computation, 2014, vol. 15, pp. 58–65, DOI: 10.1016/j.swevo.2013.12.001.
22. Wang L., Singh C. Reliability-Constrained Optimum Placement of Reclosers and Distributed Generators in Distribution Networks Using an Ant Colony System Algorithm. – IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, 2008, vol. 38, No. 6, pp. 757–764, DOI: 10.1109/TSMCC.2008.2001573.
23. Arya L.D., Koshti A., Choube S.C. Distributed Generation Planning Using Differential Evolution Accounting Voltage Stability Consideration. – International Journal of Electrical Power and Energy Systems, 2012, vol. 42, No. 1, pp. 196–207, DOI: 10.1016/j.ijepes.2012.04.011.
24. Reddy P.D.P., Reddy V., Manohar T. Ant Lion Optimization Algorithm for Optimal Sizing of Renewable Energy Resources for Loss Reduction in Distribution Systems. – Journal of Electrical Systems and Information Technology, 2018, vol. 5, No. 3, pp. 663–680, DOI: 10.1016/j.jesit.2017.06.001.
25. Sun J., Feng B., Xu W. Particle Swarm Optimization with Particles Having Quantum Behavior. – Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004, 2004, vol. 1, pp. 325–331, DOI: 10.1109/cec.2004.1330875.
26. Alrashidi M.R., El-Hawary M.E. A Survey of Particle Swarm Optimization Applications in Electric Power Systems. – IEEE Transactions on Evolutionary Computation, 2009, vol. 13, No. 4, pp. 913–918, DOI:10.1109/TEVC.2006.880326.
27. Ratnaweera A., Halgamuge S.K., Watson H.C. Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients. – IEEE Transactions on Evolutionary Computation, 2004, vol. 8, No. 3, pp. 240–255, DOI: 10.1109/TEVC.2004.826071.
28. Samakpong T., Ongsakul W., Manjiparambil N.M. Optimal Power Flow Incorporating Renewable Uncertainty Related Opportunity Costs. – Computational Intelligence, 2020, DOI: 10.1111/coin.12316.
29. Jithendranath J., Das D. Multi-Objective Optimal Power Flow in Islanded Microgrids with Solar PV Generation by NLTV-MOPSO. – IETE Journal of Research, 2021, DOI: 10.1080/03772063.2021.1886609.
30. Chaturvedi K.T., Pandit M., Srivastava L. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch. – IEEE Transactions on Power Systems, 2008, vol. 23, No. 3, pp. 1079–1087, DOI: 10.1109/TPWRS.2008.926455.
31. Chen K., et al. An Ameliorated Particle Swarm Optimizer for Solving Numerical Optimization Problems. – Applied Soft Computing Journal, 2018, vol. 73, pp. 482–496, DOI: 10.1016/j.asoc.2018.09.007.
32. Mamdouh K.A., Shehata A.A., Korovkin N.V. Multi-Objective Voltage Control and Reactive Power Optimization Based on Multi-Objective Particle Swarm Algorithm. – IOP Conference Series: Materials Science and Engineering, 2019, vol. 643, No. 1, DOI: 10.1088/1757-899X/643/1/012089.
#
1. Ahmed M.K., Osman M.H., Korovkin N.V. Optimal reactive power dispatch in power system comprising renewable energy sources by means of a multi-objective particle swarm algorithm. – Materials Science. Power Engineering, 2021, vol. 27, No. 1, pp. 5–20, DOI: 10.18721/JEST.27101.
2. Hung D.Q., Nadarajah М, Bansal R. Analytical Expressions for DG Allocation in Primary Distribution Networks. – IEEE Transactions on Energy Conversion, 2010, vol. 25, No. 3, pp. 814–820, DOI: 10.1109/TEC.2010.2044414.
3. Prabha D.R., et al. Optimal Location and Sizing of Distributed Generation Unit Using Intelligent Water Drop Algorithm. – Sustainable Energy Technologies and Assessments, 2015, vol. 11, pp. 106–113, DOI: 10.1016/j.seta.2015.07.003.
4. Vadhera S., Mahajan S. Optimal Allocation of Dispersed Generation Unit in a Network System. – International Conference on Microelectronics, Computing and Communication (MicroCom), 2016, pp. 0–4, 2016, DOI: 10.1109/MicroCom.2016.7522519.
5. Osman M.H., Refaat A., Korovkin N.V. A Novel Method to Extract Single-Diode PV Parameters Based on Datasheet Values. – Elektrichestvo, 2021, No. 2, pp. 16–21.
6. Refaat A., Elgamal M., Korovkin N.V. A Novel Grid-Connected Photovoltaic Centralized Inverter Topology to Improve the Power Harvest during Partial Shading Condition. – Elektrichestvo, 2019, No. 7, pp. 59–68, DOI: 10.24160/0013-5380-2019-7-59-68.
7. ChithraDevi S.A., Lakshminarasimman L., Balamurugan R. Stud Krill Herd Algorithm for Multiple DG Placement and Sizing in a Radial Distribution System. – Engineering Science and Technology, an International Journal, 2017, vol. 20, No. 2, pp. 748–759, DOI: 10.1016/j.jestch.2016.11.009.
8. Martín García J.A., Gil-Mena A.J. Optimal Distributed Generation Location and Size Using a Modified Teaching-Learning Based Optimization Algorithm. – International Journal of Electrical Power and Energy Systems, 2013, vol. 50, No. 1, pp. 65–75, DOI: 10.1016/j.ijepes.2013.02.023.
9. Rezaee Jordehi A. Allocation of Distributed Generation Units in Electric Power Systems: A Review. – Renewable and Sustainable Energy Reviews, 2016, vol. 56, pp. 893–905, DOI: 10.1016/j.rser.2015.11.086.
10. Reddy P.D.P., Reddy V.C.V., Manohar T.G. Whale Optimization Algorithm for Optimal Sizing of Renewable Resources for Loss Reduction in Distribution Systems. – Renewables: Wind, Water, and Solar, 2017, vol. 4, No. 1, pp. 1–13, DOI: 10.1186/s40807-017-0040-1.
11. Refaat A., Osman M.H., Korovkin N.V. Optimum Power Extraction from Non-Uniform Aged PV Array Using Current Collector Optimizer Topology. – Elektrichestvo, 2019, No. 10, pp. 54–60.
12. Wang C., Nehrir M.H. Analytical approaches for optimal placement of distributed generation sources in power systems. – IEEE Transactions on Power Systems, 2004, vol. 19, No. 4, pp. 2068–2076, DOI: 10.1109/TPWRS.2004.836189.
13. Shehata A.A., Ahmed M.K. State estimation accuracy enhancement for optimal power system steady state modes. – IOP Conference Series: Materials Science and Engineering, 2019, vol. 643, No. 1, DOI: 10.1088/1757-899X/643/1/012049.
14. Babaei E., Galvani S., Nejabatkhah F. Optimal Placement of DG Units Considering Power Losses Minimization and Voltage Stability Enhancement in Power System. – International Journal of Automation and Control Engineering, 2014, vol. 3, No. 1, DOI: 10.14355/ijace.2014.0301.01.
15. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Distribution System for Power Loss Reduction Using PSO Algorithm. – Procedia Technology, 2016, vol. 25, No. Raerest, pp. 785–792, DOI: 10.1016/j.protcy.2016.08.173.
16. Shehata A.A., et al. Optimal Placement and Sizing of FACTS Devices Based on Autonomous Groups Partical Swarm Optimization Technique. – Archives of Electrical Engineering, 2020, vol. 70, No. 1, DOI: 10.24425/aee.2021.136059.
17. Shukla T.N., et al. Optimal Sizing of Distributed Generation Placed on Radial Distribution System. – Electric Power Components and Systems, 2010, vol. 38, No. 3, pp. 260–274, DOI: 10.1080/15325000903273403.
18. Abu-Mouti F.S., El-Hawary M.E. Optimal Distributed Generation Allocation and Sizing in Distribution Systems Via Artificial Bee Colony Algorithm. – IEEE Transactions on Power Delivery, 2011, vol. 26, No. 4, pp. 2090–2101, DOI: 10.1109/TPWRD.2011.2158246.
19. Elattar E.E., et al. Optimal Location and Sizing of Distributed Generators Based on Renewable Energy Sources Using Modified Moth Flame Optimization Technique. – IEEE Access, 2020, vol. 8, pp. 109625–109638, DOI: 10.1109/ACCESS.2020.3001758.
20. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Radial Distribution System for Multi Objectives Using Whale Optimization Algorithm. – Alexandria Engineering Journal, 2018, vol. 57, No. 4, pp. 2797–2806, DOI: 10.1016/j.aej.2017.11.003.
21. Mohamed I.A., Kowsalya M. Optimal Size and Siting of Multiple Distributed Generators in Distribution System Using Bacterial Foraging Optimization. – Swarm and Evolutionary Computation, 2014, vol. 15, pp. 58–65, DOI: 10.1016/j.swevo.2013.12.001.
22. Wang L., Singh C. Reliability-Constrained Optimum Placement of Reclosers and Distributed Generators in Distribution Networks Using an Ant Colony System Algorithm. – IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, 2008, vol. 38, No. 6, pp. 757–764, DOI: 10.1109/TSMCC.2008.2001573.
23. Arya L.D., Koshti A., Choube S.C. Distributed Generation Planning Using Differential Evolution Accounting Voltage Stability Consideration. – International Journal of Electrical Power and Energy Systems, 2012, vol. 42, No. 1, pp. 196–207, DOI: 10.1016/j.ijepes.2012.04.011.
24. Reddy P.D.P., Reddy V., Manohar T. Ant Lion Optimization Algorithm for Optimal Sizing of Renewable Energy Resources for Loss Reduction in Distribution Systems. – Journal of Electrical Systems and Information Technology, 2018, vol. 5, No. 3, pp. 663–680, DOI: 10.1016/j.jesit.2017.06.001.
25. Sun J., Feng B., Xu W. Particle Swarm Optimization with Particles Having Quantum Behavior. – Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004, 2004, vol. 1, pp. 325–331, DOI: 10.1109/cec.2004.1330875.
26. Alrashidi M.R., El-Hawary M.E. A Survey of Particle Swarm Optimization Applications in Electric Power Systems. – IEEE Transactions on Evolutionary Computation, 2009, vol. 13, No. 4, pp. 913–918, DOI:10.1109/TEVC.2006.880326.
27. Ratnaweera A., Halgamuge S.K., Watson H.C. Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients. – IEEE Transactions on Evolutionary Computation, 2004, vol. 8, No. 3, pp. 240–255, DOI: 10.1109/TEVC.2004.826071.
28. Samakpong T., Ongsakul W., Manjiparambil N.M. Optimal Power Flow Incorporating Renewable Uncertainty Related Opportunity Costs. – Computational Intelligence, 2020, DOI: 10.1111/coin.12316.
29. Jithendranath J., Das D. Multi-Objective Optimal Power Flow in Islanded Microgrids with Solar PV Generation by NLTV-MOPSO. – IETE Journal of Research, 2021, DOI: 10.1080/03772063.2021.1886609.
30. Chaturvedi K.T., Pandit M., Srivastava L. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch. – IEEE Transactions on Power Systems, 2008, vol. 23, No. 3, pp. 1079–1087, DOI: 10.1109/TPWRS.2008.926455.
31. Chen K., et al. An Ameliorated Particle Swarm Optimizer for Solving Numerical Optimization Problems. – Applied Soft Computing Journal, 2018, vol. 73, pp. 482–496, DOI: 10.1016/j.asoc.2018.09.007.
32. Mamdouh K.A., Shehata A.A., Korovkin N.V. Multi-Objective Voltage Control and Reactive Power Optimization Based on Multi-Objective Particle Swarm Algorithm. – IOP Conference Series: Materials Science and Engineering, 2019, vol. 643, No. 1, DOI: 10.1088/1757-899X/643/1/012089.
2. Hung D.Q., Nadarajah М, Bansal R. Analytical Expressions for DG Allocation in Primary Distribution Networks. – IEEE Transactions on Energy Conversion, 2010, vol. 25, No. 3, pp. 814–820, DOI: 10.1109/TEC.2010.2044414.
3. Prabha D.R., et al. Optimal Location and Sizing of Distributed Generation Unit Using Intelligent Water Drop Algorithm. – Sustainable Energy Technologies and Assessments, 2015, vol. 11, pp. 106–113, DOI: 10.1016/j.seta.2015.07.003.
4. Vadhera S., Mahajan S. Optimal Allocation of Dispersed Generation Unit in a Network System. – International Conference on Microelectronics, Computing and Communication (MicroCom), 2016, pp. 0–4, 2016, DOI: 10.1109/MicroCom.2016.7522519.
5. Osman M.H., Refaat A., Korovkin N.V. A Novel Method to Extract Single-Diode PV Parameters Based on Datasheet Values. – Электричество, 2021, №. 2, с. 16–21.
6. Refaat A., Elgamal M., Korovkin N.V. A Novel Grid-Connected Photovoltaic Centralized Inverter Topology to Improve the Power Harvest during Partial Shading Condition. – Электричество, 2019, №. 7, с. 59–68, DOI: 10.24160/0013-5380-2019-7-59-68.
7. ChithraDevi S.A., Lakshminarasimman L., Balamurugan R. Stud Krill Herd Algorithm for Multiple DG Placement and Sizing in a Radial Distribution System. – Engineering Science and Technology, an International Journal, 2017, vol. 20, No. 2, pp. 748–759, DOI: 10.1016/j.jestch.2016.11.009.
8. Martín García J.A., Gil-Mena A.J. Optimal Distributed Generation Location and Size Using a Modified Teaching-Learning Based Optimization Algorithm. – International Journal of Electrical Power and Energy Systems, 2013, vol. 50, No. 1, pp. 65–75, DOI: 10.1016/j.ijepes.2013.02.023.
9. Rezaee Jordehi A. Allocation of Distributed Generation Units in Electric Power Systems: A Review. – Renewable and Sustainable Energy Reviews, 2016, vol. 56, pp. 893–905, DOI: 10.1016/j.rser.2015.11.086.
10. Reddy P.D.P., Reddy V.C.V., Manohar T.G. Whale Optimization Algorithm for Optimal Sizing of Renewable Resources for Loss Reduction in Distribution Systems. – Renewables: Wind, Water, and Solar, 2017, vol. 4, No. 1, pp. 1–13, DOI: 10.1186/s40807-017-0040-1.
11. Refaat A., Osman M.H., Korovkin N.V. Optimum Power Extraction from Non-Uniform Aged PV Array Using Current Collector Optimizer Topology. – Электричество, 2019, №. 10, с. 54–60.
12. Wang C., Nehrir M.H. Analytical approaches for optimal placement of distributed generation sources in power systems. – IEEE Transactions on Power Systems, 2004, vol. 19, No. 4, pp. 2068–2076, DOI: 10.1109/TPWRS.2004.836189.
13. Shehata A.A., Ahmed M.K. State estimation accuracy enhancement for optimal power system steady state modes. – IOP Conference Series: Materials Science and Engineering, 2019, vol. 643, No. 1, DOI: 10.1088/1757-899X/643/1/012049.
14. Babaei E., Galvani S., Nejabatkhah F. Optimal Placement of DG Units Considering Power Losses Minimization and Voltage Stability Enhancement in Power System. – International Journal of Automation and Control Engineering, 2014, vol. 3, No. 1, DOI: 10.14355/ijace.2014.0301.01.
15. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Distribution System for Power Loss Reduction Using PSO Algorithm. – Procedia Technology, 2016, vol. 25, No. Raerest, pp. 785–792, DOI: 10.1016/j.protcy.2016.08.173.
16. Shehata A.A., et al. Optimal Placement and Sizing of FACTS Devices Based on Autonomous Groups Partical Swarm Optimization Technique. – Archives of Electrical Engineering, 2020, vol. 70, No. 1, DOI: 10.24425/aee.2021.136059.
17. Shukla T.N., et al. Optimal Sizing of Distributed Generation Placed on Radial Distribution System. – Electric Power Components and Systems, 2010, vol. 38, No. 3, pp. 260–274, DOI: 10.1080/15325000903273403.
18. Abu-Mouti F.S., El-Hawary M.E. Optimal Distributed Generation Allocation and Sizing in Distribution Systems Via Artificial Bee Colony Algorithm. – IEEE Transactions on Power Delivery, 2011, vol. 26, No. 4, pp. 2090–2101, DOI: 10.1109/TPWRD.2011.2158246.
19. Elattar E.E., et al. Optimal Location and Sizing of Distributed Generators Based on Renewable Energy Sources Using Modified Moth Flame Optimization Technique. – IEEE Access, 2020, vol. 8, pp. 109625–109638, DOI: 10.1109/ACCESS.2020.3001758.
20. Prakash D.B., Lakshminarayana C. Multiple DG Placements in Radial Distribution System for Multi Objectives Using Whale Optimization Algorithm. – Alexandria Engineering Journal, 2018, vol. 57, No. 4, pp. 2797–2806, DOI: 10.1016/j.aej.2017.11.003.
21. Mohamed I.A., Kowsalya M. Optimal Size and Siting of Multiple Distributed Generators in Distribution System Using Bacterial Foraging Optimization. – Swarm and Evolutionary Computation, 2014, vol. 15, pp. 58–65, DOI: 10.1016/j.swevo.2013.12.001.
22. Wang L., Singh C. Reliability-Constrained Optimum Placement of Reclosers and Distributed Generators in Distribution Networks Using an Ant Colony System Algorithm. – IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, 2008, vol. 38, No. 6, pp. 757–764, DOI: 10.1109/TSMCC.2008.2001573.
23. Arya L.D., Koshti A., Choube S.C. Distributed Generation Planning Using Differential Evolution Accounting Voltage Stability Consideration. – International Journal of Electrical Power and Energy Systems, 2012, vol. 42, No. 1, pp. 196–207, DOI: 10.1016/j.ijepes.2012.04.011.
24. Reddy P.D.P., Reddy V., Manohar T. Ant Lion Optimization Algorithm for Optimal Sizing of Renewable Energy Resources for Loss Reduction in Distribution Systems. – Journal of Electrical Systems and Information Technology, 2018, vol. 5, No. 3, pp. 663–680, DOI: 10.1016/j.jesit.2017.06.001.
25. Sun J., Feng B., Xu W. Particle Swarm Optimization with Particles Having Quantum Behavior. – Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004, 2004, vol. 1, pp. 325–331, DOI: 10.1109/cec.2004.1330875.
26. Alrashidi M.R., El-Hawary M.E. A Survey of Particle Swarm Optimization Applications in Electric Power Systems. – IEEE Transactions on Evolutionary Computation, 2009, vol. 13, No. 4, pp. 913–918, DOI:10.1109/TEVC.2006.880326.
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28. Samakpong T., Ongsakul W., Manjiparambil N.M. Optimal Power Flow Incorporating Renewable Uncertainty Related Opportunity Costs. – Computational Intelligence, 2020, DOI: 10.1111/coin.12316.
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