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Fitness Distance Balance Based Triangulation Topology Aggregation Optimizer for Optimal Power Flow Including Renewable Energy Sources

Year 2024, Volume: 28 Issue: 2, 221 - 234, 23.08.2024
https://doi.org/10.19113/sdufenbed.1518219

Abstract

With the substantial increase in the amount of energy demanded and consumed today, there is also an increase in energy generation from renewable energy sources. Including renewable energy sources in an electrical grid and using them introduces the problem of planning the network in the most economical and efficient way. This thesis addresses the optimal power flow problem, which is one of the power system problems integrated with wind and solar power, both renewable energy sources. The optimal power flow problem is an optimization problem with a nonlinear structure and various constraints, where the best values of control parameters are determined. Additionally, combining the nature of solar and wind energy increases the complexity of the problem. Heuristic search algorithms, which are a type of artificial intelligence technique, are preferred in solving such problems. In this thesis, the Triangulation Topology Aggregation Optimizer (TTAO) algorithm was first developed based on distance adequacy balance for the solution of the optimal power flow problem. The developed algorithm was applied to the optimal power flow problem including wind and solar energy sources and compared with the results of different algorithms in the literature. The obtained results clearly show that the proposed algorithm is effective in this power system problem.

References

  • [1] Duman, S., Güvenç, U., Sönmez, Y., & Yörükeren, N. (2012). Optimal power flow using gravitational search algorithm. Energy conversion and management, 59, 86-95.
  • [2] Y. Hınıslıoğlu, “Kaotik güve sürüsü algoritması kullanarak rüzgar gücü entegreli optimal güç akışı,” Yüksek lisans tezi, Elektrik Elektronik Mühendisliği, Fen Bilimleri Enstitüsü, Düzce Üniversitesi, Düzce, Türkiye, 2018. [3] Kaymaz, E., Duman, S., & Guvenc, U. (2021). Optimal power flow solution with stochastic wind power using the Lévy coyote optimization algorithm. Neural Computing and Applications, 33(12), 6775-6804.
  • [4] Yan, X., & Quintana, V. H. (1999). Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Transactions on Power Systems, 14(2), 709-717.
  • [5] Habibollahzadeh, H., Luo, G. X., & Semlyen, A. (1989). Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology. IEEE Transactions on Power Systems, 4(2), 530-537.
  • [6] Burchett, R. C., Happ, H. H., & Vierath, D. R. (1984). Quadratically convergent optimal power flow. IEEE Transactions on Power Apparatus and Systems, (11), 3267-3275.
  • [7] Devaraj, D., & Yegnanarayana, B. (2005). Genetic-algorithm-based optimal power flow for security enhancement. IEE Proceedings-Generation, Transmission and Distribution, 152(6), 899-905.
  • [8] Lai, L. L., Ma, J. T., Yokoyama, R., & Zhao, M. (1997). Improved genetic algorithms for optimal power flow under both normal and contingent operation states. International Journal of Electrical Power & Energy Systems, 19(5), 287-292.
  • [9] Abido, M. A. (2002). Optimal power flow using tabu search algorithm. Electric power components and systems, 30(5), 469-483.
  • [10] Abido, M. A. (2002). Optimal power flow using particle swarm optimization. International Journal of Electrical Power & Energy Systems, 24(7), 563-571.
  • [11] Varadarajan, M., & Swarup, K. S. (2008). Solving multi-objective optimal power flow using differential evolution. IET Generation, Transmission & Distribution, 2(5), 720-730.
  • [12] Ozkaya, B. (2024). Enhanced growth optimizer algorithm with dynamic fitness-distance balance method for solution of security-constrained optimal power flow problem in the presence of stochastic wind and solar energy. Applied Energy, 368, 123499.
  • [13] Sallam, K. M., Hossain, M. A., Elsayed, S., Chakrabortty, R. K., Ryan, M. J., & Abido, M. A. (2024). Optimal power flow considering intermittent solar and wind generation using multi-operator differential evolution algorithm. Electric Power Systems Research, 232, 110377.
  • [14] Trojovský, P., Trojovská, E., & Akbari, E. (2024). Economical-environmental-technical optimal power flow solutions using a novel self-adaptive wild geese algorithm with stochastic wind and solar power. Scientific Reports, 14(1), 4135.
  • [15] Adhikari, A., Jurado, F., Naetiladdanon, S., Sangswang, A., Kamel, S., & Ebeed, M. (2023). Stochastic optimal power flow analysis of power system with renewable energy sources using Adaptive Lightning Attachment Procedure Optimizer. International Journal of Electrical Power & Energy Systems, 153, 109314.
  • [16] Huy, T. H. B., Doan, H. T., Vo, D. N., Lee, K. H., & Kim, D. (2023). Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution. Applied Soft Computing, 149, 110977.
  • [17] Hassan, M. H., Elsayed, S. K., Kamel, S., Rahmann, C., & Taha, I. B. (2022). Developing chaotic Bonobo optimizer for optimal power flow analysis considering stochastic renewable energy resources. International Journal of Energy Research, 46(8), 11291-11325.
  • [18] Alghamdi, A. S. (2022). A hybrid firefly–JAYA algorithm for the optimal power flow problem considering wind and solar power generations. Applied Sciences, 12(14), 7193.
  • [19] Li, S., Gong, W., Wang, L., & Gu, Q. (2022). Multi-objective optimal power flow with stochastic wind and solar power. Applied Soft Computing, 114, 108045.
  • [20] Guvenc, U., Duman, S., Kahraman, H. T., Aras, S., & Katı, M. (2021). Fitness–Distance Balance based adaptive guided differential evolution algorithm for security-constrained optimal power flow problem incorporating renewable energy sources. Applied Soft Computing, 108, 107421.
  • [21] Rambabu, M., VenkataNagesh Kumar, G., Venkateswara Rao, B., & Sravan Kumar, B. (2021). Optimal power flow solution of an integrated power system using elephant herd optimization algorithm incorporating stochastic wind and solar power. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 1-21.
  • [22] Riaz, M., Hanif, A., Hussain, S. J., Memon, M. I., Ali, M. U., & Zafar, A. (2021). An optimization-based strategy for solving optimal power flow problems in a power system integrated with stochastic solar and wind power energy. Applied Sciences, 11(15), 6883.
  • [23] Farhat, M., Kamel, S., Atallah, A. M., & Khan, B. (2021). Optimal power flow solution based on jellyfish search optimization considering uncertainty of renewable energy sources. IEEE Access, 9, 100911-100933.
  • [24] Khamees, A. K., Abdelaziz, A. Y., Eskaros, M. R., El-Shahat, A., & Attia, M. A. (2021). Optimal power flow solution of wind-integrated power system using novel metaheuristic method. Energies, 14(19), 6117.
  • [25] Khan, I. U., Javaid, N., Gamage, K. A., Taylor, C. J., Baig, S., & Ma, X. (2020). Heuristic algorithm based optimal power flow model incorporating stochastic renewable energy sources. IEEE Access, 8, 148622-148643.
  • [26] Duman, S., Rivera, S., Li, J., & Wu, L. (2020). Optimal power flow of power systems with controllable wind‐photovoltaic energy systems via differential evolutionary particle swarm optimization. International Transactions on Electrical Energy Systems, 30(4), e12270.
  • [27] Elattar, E. E. (2019). Optimal power flow of a power system incorporating stochastic wind power based on modified moth swarm algorithm. IEEE Access, 7, 89581-89593.
  • [28] Salkuti, S. R. (2019). Optimal power flow using multi-objective glowworm swarm optimization algorithm in a wind energy integrated power system. International Journal of Green Energy, 16(15), 1547-1561.
  • [29] Mishra, C., Singh, S. P., & Rokadia, J. (2015). Optimal power flow in the presence of wind power using modified cuckoo search. IET Generation, Transmission & Distribution, 9(7), 615-626.
  • [30] Panda, A., & Tripathy, M. (2015). Security constrained optimal power flow solution of wind-thermal generation system using modified bacteria foraging algorithm. Energy, 93, 816-827.
  • [31] Biswas, P. P., Suganthan, P. N., & Amaratunga, G. A. (2017). Optimal power flow solutions incorporating stochastic wind and solar power. Energy conversion and management, 148, 1194-1207.
  • [32] Zhao, S., Zhang, T., Cai, L., & Yang, R. (2024). Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications. Expert Systems with Applications, 238, 121744.
  • [33] Kahraman, H. T., Aras, S., & Gedikli, E. (2020). Fitness-distance balance (FDB): a new selection method for meta-heuristic search algorithms. Knowledge-Based Systems, 190, 105169.
  • [34] M. J. Morshed and A. Asgharpour, “Hybrid imperialist competitive-sequential quadratic programming (HIC-SQP) algorithm for solving economic load dispatch with incorporating stochastic wind power: A comparative study on heuristic optimization techniques,” Energy Conversion Management, vol. 84, pp. 30–40, 2014.
  • [35] U. Güvenç, S. Duman, and E. Kaymaz, “Economic Dispatch of Power System Including Wind Power using Salp Swarm Algorithm,” presented at 7th International Conference on Advanced Technologies (ICAT'18), Antalya, Turkey, 2018.
  • [36] Jones, M. W., & Satherley, R. A. (2001, May). Shape representation using space filled sub-voxel distance fields. In Proceedings international conference on shape modeling and applications (pp. 316-325). IEEE.
  • [37] Reddy, P. V. N., Padmini, G. R., Govindaraj, P., & Sudhakar, M. S. (2022). Robust feature descriptor employing square triangle tessellation for shape retrieval. Wireless Personal Communications, 1-14.
  • [38] Laczkovich, M. (2021). Irregular tilings of regular polygons with similar triangles. Discrete & Computational Geometry, 66(4), 1239-1261.
  • [39] Soifer, A., & Soifer, A. (2009). How Does One Cut a Triangle? I (pp. 15-23). Springer New York.
  • [40] Jiang, M., Wang, Z., Hong, H., & Yen, G. G. (2020). Knee point-based imbalanced transfer learning for dynamic multiobjective optimization. IEEE Transactions on Evolutionary Computation, 25(1), 117-129.
  • [41] Forrest, S. (1996). Genetic algorithms. ACM computing surveys (CSUR), 28(1), 77-80.
  • [42] S. Aras, E. Gedikli ve H. T. Kahraman, “A novel stochastic fractal search algorithm with fitness-distance balance for global numerical optimization”, Swarm and Evolutionary Computation, c. 61, ss. 100821, 2021.
  • [43] S. Duman, H. T. Kahraman, Y. Sonmez, U. Guvenc, M. Kati ve S. Aras, “A powerful meta-heuristic search algorithm for solving global optimization and realworld solar photovoltaic parameter estimation problems”, Engineering, Applications of Artificial Intelligence, c. 111, ss. 104763, 2022.
  • [44] S. Duman, H. T. Kahraman, U. Guvenc, ve S. Aras, “Development of a Lévy flight and FDB-based coyote optimization algorithm for global optimization and realworld ACOPF problems”, Soft Computing, c. 25, sayı 8, ss. 6577-6617, 2021.

Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi

Year 2024, Volume: 28 Issue: 2, 221 - 234, 23.08.2024
https://doi.org/10.19113/sdufenbed.1518219

Abstract

Günümüzde talep edilen ve tüketilen enerji miktarında çok yoğun artışların olması ile birlikte, yenilenebilir enerji kaynaklarından enerji üretiminde artışlar olmaktadır. Bir elektrik şebekesinde yenilenebilir enerji kaynaklarının dahil edilerek kullanılması ile birlikte ağın ekonomik ve verimli çalışabilmesi için en uygun şeklide planlanması problemini de ortaya çıkarmaktadır. Bu tez çalışmasında, yenilenebilir enerji kaynaklarından olan rüzgâr ve gücü entegreli güç sistemleri problemlerinden olan optimal güç akışı problemi ele alınmıştır. Optimal güç akışı problemi doğrusal olmayan yapıya ve çeşitli kısıtlamalara sahip olan, kontrol parametrelerin en uygun değerlerinin belirlendiği bir optimizasyon problemidir. Ayrıca, güneş ve rüzgar enerjisinin doğasını birleştirmek problemin karmaşıklığını artırmaktadır. Bu tür problemlerin çözümünde yapay zeka tekniklerinden olan sezgisel arama algoritmaları tercih edilmektedir. Bu tez çalışmasında optimal güç akışı probleminin çözümü için Üçgenleme topolojisi toplama iyileştiricisi (ÜTTİ) algoritmasının öncelikle mesafe uygunluk dengesi tabanlı geliştirilmesi gerçekleştirilmiştir. Geliştirilen algoritma rüzgar ve güneş enerji kaynaklarının dahil edildiği optimal güç akışı probleminde uygulanmış olup, literatürdeki farklı algoritmaların sonuçları ile karşılaştırılmıştır. Elde edile sonuçlar, önerilen algoritmanın bu güç sistemi probleminde etkili olduğunu açık bir şekilde göstermektedir.

References

  • [1] Duman, S., Güvenç, U., Sönmez, Y., & Yörükeren, N. (2012). Optimal power flow using gravitational search algorithm. Energy conversion and management, 59, 86-95.
  • [2] Y. Hınıslıoğlu, “Kaotik güve sürüsü algoritması kullanarak rüzgar gücü entegreli optimal güç akışı,” Yüksek lisans tezi, Elektrik Elektronik Mühendisliği, Fen Bilimleri Enstitüsü, Düzce Üniversitesi, Düzce, Türkiye, 2018. [3] Kaymaz, E., Duman, S., & Guvenc, U. (2021). Optimal power flow solution with stochastic wind power using the Lévy coyote optimization algorithm. Neural Computing and Applications, 33(12), 6775-6804.
  • [4] Yan, X., & Quintana, V. H. (1999). Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Transactions on Power Systems, 14(2), 709-717.
  • [5] Habibollahzadeh, H., Luo, G. X., & Semlyen, A. (1989). Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology. IEEE Transactions on Power Systems, 4(2), 530-537.
  • [6] Burchett, R. C., Happ, H. H., & Vierath, D. R. (1984). Quadratically convergent optimal power flow. IEEE Transactions on Power Apparatus and Systems, (11), 3267-3275.
  • [7] Devaraj, D., & Yegnanarayana, B. (2005). Genetic-algorithm-based optimal power flow for security enhancement. IEE Proceedings-Generation, Transmission and Distribution, 152(6), 899-905.
  • [8] Lai, L. L., Ma, J. T., Yokoyama, R., & Zhao, M. (1997). Improved genetic algorithms for optimal power flow under both normal and contingent operation states. International Journal of Electrical Power & Energy Systems, 19(5), 287-292.
  • [9] Abido, M. A. (2002). Optimal power flow using tabu search algorithm. Electric power components and systems, 30(5), 469-483.
  • [10] Abido, M. A. (2002). Optimal power flow using particle swarm optimization. International Journal of Electrical Power & Energy Systems, 24(7), 563-571.
  • [11] Varadarajan, M., & Swarup, K. S. (2008). Solving multi-objective optimal power flow using differential evolution. IET Generation, Transmission & Distribution, 2(5), 720-730.
  • [12] Ozkaya, B. (2024). Enhanced growth optimizer algorithm with dynamic fitness-distance balance method for solution of security-constrained optimal power flow problem in the presence of stochastic wind and solar energy. Applied Energy, 368, 123499.
  • [13] Sallam, K. M., Hossain, M. A., Elsayed, S., Chakrabortty, R. K., Ryan, M. J., & Abido, M. A. (2024). Optimal power flow considering intermittent solar and wind generation using multi-operator differential evolution algorithm. Electric Power Systems Research, 232, 110377.
  • [14] Trojovský, P., Trojovská, E., & Akbari, E. (2024). Economical-environmental-technical optimal power flow solutions using a novel self-adaptive wild geese algorithm with stochastic wind and solar power. Scientific Reports, 14(1), 4135.
  • [15] Adhikari, A., Jurado, F., Naetiladdanon, S., Sangswang, A., Kamel, S., & Ebeed, M. (2023). Stochastic optimal power flow analysis of power system with renewable energy sources using Adaptive Lightning Attachment Procedure Optimizer. International Journal of Electrical Power & Energy Systems, 153, 109314.
  • [16] Huy, T. H. B., Doan, H. T., Vo, D. N., Lee, K. H., & Kim, D. (2023). Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution. Applied Soft Computing, 149, 110977.
  • [17] Hassan, M. H., Elsayed, S. K., Kamel, S., Rahmann, C., & Taha, I. B. (2022). Developing chaotic Bonobo optimizer for optimal power flow analysis considering stochastic renewable energy resources. International Journal of Energy Research, 46(8), 11291-11325.
  • [18] Alghamdi, A. S. (2022). A hybrid firefly–JAYA algorithm for the optimal power flow problem considering wind and solar power generations. Applied Sciences, 12(14), 7193.
  • [19] Li, S., Gong, W., Wang, L., & Gu, Q. (2022). Multi-objective optimal power flow with stochastic wind and solar power. Applied Soft Computing, 114, 108045.
  • [20] Guvenc, U., Duman, S., Kahraman, H. T., Aras, S., & Katı, M. (2021). Fitness–Distance Balance based adaptive guided differential evolution algorithm for security-constrained optimal power flow problem incorporating renewable energy sources. Applied Soft Computing, 108, 107421.
  • [21] Rambabu, M., VenkataNagesh Kumar, G., Venkateswara Rao, B., & Sravan Kumar, B. (2021). Optimal power flow solution of an integrated power system using elephant herd optimization algorithm incorporating stochastic wind and solar power. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 1-21.
  • [22] Riaz, M., Hanif, A., Hussain, S. J., Memon, M. I., Ali, M. U., & Zafar, A. (2021). An optimization-based strategy for solving optimal power flow problems in a power system integrated with stochastic solar and wind power energy. Applied Sciences, 11(15), 6883.
  • [23] Farhat, M., Kamel, S., Atallah, A. M., & Khan, B. (2021). Optimal power flow solution based on jellyfish search optimization considering uncertainty of renewable energy sources. IEEE Access, 9, 100911-100933.
  • [24] Khamees, A. K., Abdelaziz, A. Y., Eskaros, M. R., El-Shahat, A., & Attia, M. A. (2021). Optimal power flow solution of wind-integrated power system using novel metaheuristic method. Energies, 14(19), 6117.
  • [25] Khan, I. U., Javaid, N., Gamage, K. A., Taylor, C. J., Baig, S., & Ma, X. (2020). Heuristic algorithm based optimal power flow model incorporating stochastic renewable energy sources. IEEE Access, 8, 148622-148643.
  • [26] Duman, S., Rivera, S., Li, J., & Wu, L. (2020). Optimal power flow of power systems with controllable wind‐photovoltaic energy systems via differential evolutionary particle swarm optimization. International Transactions on Electrical Energy Systems, 30(4), e12270.
  • [27] Elattar, E. E. (2019). Optimal power flow of a power system incorporating stochastic wind power based on modified moth swarm algorithm. IEEE Access, 7, 89581-89593.
  • [28] Salkuti, S. R. (2019). Optimal power flow using multi-objective glowworm swarm optimization algorithm in a wind energy integrated power system. International Journal of Green Energy, 16(15), 1547-1561.
  • [29] Mishra, C., Singh, S. P., & Rokadia, J. (2015). Optimal power flow in the presence of wind power using modified cuckoo search. IET Generation, Transmission & Distribution, 9(7), 615-626.
  • [30] Panda, A., & Tripathy, M. (2015). Security constrained optimal power flow solution of wind-thermal generation system using modified bacteria foraging algorithm. Energy, 93, 816-827.
  • [31] Biswas, P. P., Suganthan, P. N., & Amaratunga, G. A. (2017). Optimal power flow solutions incorporating stochastic wind and solar power. Energy conversion and management, 148, 1194-1207.
  • [32] Zhao, S., Zhang, T., Cai, L., & Yang, R. (2024). Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications. Expert Systems with Applications, 238, 121744.
  • [33] Kahraman, H. T., Aras, S., & Gedikli, E. (2020). Fitness-distance balance (FDB): a new selection method for meta-heuristic search algorithms. Knowledge-Based Systems, 190, 105169.
  • [34] M. J. Morshed and A. Asgharpour, “Hybrid imperialist competitive-sequential quadratic programming (HIC-SQP) algorithm for solving economic load dispatch with incorporating stochastic wind power: A comparative study on heuristic optimization techniques,” Energy Conversion Management, vol. 84, pp. 30–40, 2014.
  • [35] U. Güvenç, S. Duman, and E. Kaymaz, “Economic Dispatch of Power System Including Wind Power using Salp Swarm Algorithm,” presented at 7th International Conference on Advanced Technologies (ICAT'18), Antalya, Turkey, 2018.
  • [36] Jones, M. W., & Satherley, R. A. (2001, May). Shape representation using space filled sub-voxel distance fields. In Proceedings international conference on shape modeling and applications (pp. 316-325). IEEE.
  • [37] Reddy, P. V. N., Padmini, G. R., Govindaraj, P., & Sudhakar, M. S. (2022). Robust feature descriptor employing square triangle tessellation for shape retrieval. Wireless Personal Communications, 1-14.
  • [38] Laczkovich, M. (2021). Irregular tilings of regular polygons with similar triangles. Discrete & Computational Geometry, 66(4), 1239-1261.
  • [39] Soifer, A., & Soifer, A. (2009). How Does One Cut a Triangle? I (pp. 15-23). Springer New York.
  • [40] Jiang, M., Wang, Z., Hong, H., & Yen, G. G. (2020). Knee point-based imbalanced transfer learning for dynamic multiobjective optimization. IEEE Transactions on Evolutionary Computation, 25(1), 117-129.
  • [41] Forrest, S. (1996). Genetic algorithms. ACM computing surveys (CSUR), 28(1), 77-80.
  • [42] S. Aras, E. Gedikli ve H. T. Kahraman, “A novel stochastic fractal search algorithm with fitness-distance balance for global numerical optimization”, Swarm and Evolutionary Computation, c. 61, ss. 100821, 2021.
  • [43] S. Duman, H. T. Kahraman, Y. Sonmez, U. Guvenc, M. Kati ve S. Aras, “A powerful meta-heuristic search algorithm for solving global optimization and realworld solar photovoltaic parameter estimation problems”, Engineering, Applications of Artificial Intelligence, c. 111, ss. 104763, 2022.
  • [44] S. Duman, H. T. Kahraman, U. Guvenc, ve S. Aras, “Development of a Lévy flight and FDB-based coyote optimization algorithm for global optimization and realworld ACOPF problems”, Soft Computing, c. 25, sayı 8, ss. 6577-6617, 2021.
There are 43 citations in total.

Details

Primary Language Turkish
Subjects Electrical Energy Transmission, Networks and Systems, Photovoltaic Power Systems, Wind Energy Systems
Journal Section Articles
Authors

Ali Yazıcı 0009-0008-7714-8077

Uğur Güvenç 0000-0002-5193-7990

Publication Date August 23, 2024
Submission Date July 18, 2024
Acceptance Date July 23, 2024
Published in Issue Year 2024 Volume: 28 Issue: 2

Cite

APA Yazıcı, A., & Güvenç, U. (2024). Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(2), 221-234. https://doi.org/10.19113/sdufenbed.1518219
AMA Yazıcı A, Güvenç U. Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi. J. Nat. Appl. Sci. August 2024;28(2):221-234. doi:10.19113/sdufenbed.1518219
Chicago Yazıcı, Ali, and Uğur Güvenç. “Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28, no. 2 (August 2024): 221-34. https://doi.org/10.19113/sdufenbed.1518219.
EndNote Yazıcı A, Güvenç U (August 1, 2024) Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 2 221–234.
IEEE A. Yazıcı and U. Güvenç, “Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi”, J. Nat. Appl. Sci., vol. 28, no. 2, pp. 221–234, 2024, doi: 10.19113/sdufenbed.1518219.
ISNAD Yazıcı, Ali - Güvenç, Uğur. “Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28/2 (August 2024), 221-234. https://doi.org/10.19113/sdufenbed.1518219.
JAMA Yazıcı A, Güvenç U. Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi. J. Nat. Appl. Sci. 2024;28:221–234.
MLA Yazıcı, Ali and Uğur Güvenç. “Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 28, no. 2, 2024, pp. 221-34, doi:10.19113/sdufenbed.1518219.
Vancouver Yazıcı A, Güvenç U. Yenilenebilir Enerji Kaynaklarını İçeren Optimal Güç Akışı İçin Uygunluk Mesafe Dengesi Tabanlı Üçgenleme Topolojisi Toplama İyileştiricisi. J. Nat. Appl. Sci. 2024;28(2):221-34.

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