Optimal power load flow considering stochastic wind and solar power
Corresponding Author(s) : Jalal Tavalaei
Future Energy,
Vol. 4 No. 2 (2025): May 2025 Issue
Abstract
Optimal power flow (OPF) is a popular model in the study of power systems that aims to achieve optimization and operational stability while minimizing costs. Multiple research documents depict the various methods and algorithms to further explore system configurations that would achieve OPF or multi-objective OPF. In relation to power systems, many power plants rely on non-renewable sources such as fossil fuels to generate power to be supplied to cities, towns, and rural areas, but these sources are steadily decreasing in their availability and are no longer suitable for sustainability. Renewable sources (solar, wind, and hydro) have been around for decades and have been found to be suitable alternatives for power plants, but due to their stochastic nature, the power needed via this method of generation is inconsistent. The relationship between the types of sources and OPF can be seen via costs, emissions, and power since the costs required for generation and distribution are dependent on their source, be they renewable or non-renewable, including the possibility of a decrease in emissions from these power plants. This research is expected to show that OPF can be achieved using renewable sources within power systems, even with their stochastic behaviors.
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- Rehman, N., Mufti, M.U.D. and Gupta, N., 2024. Power flow analysis in a distribution system penetrated with renewable energy sources: a review. International Journal of Ambient Energy, 45(1), p.2305701.
- Halimatussadiah, A., Kruger, W., Wagner, F., Afifi, F.A.R., Lufti, R.E.G. and Kitzing, L., 2024. The country of perpetual potential: Why is it so difficult to procure renewable energy in Indonesia. Renewable and Sustainable Energy Reviews, 201, p.114627.
- Ghafoor, A., Aldahmashi, J., Apsley, J., Djurović, S., Ma, X. and Benbouzid, M., 2024. Intelligent Integration of Renewable Energy Resources Review: Generation and Grid Level Opportunities and Challenges. Energies, 17(17), p.4399.
- Bilal, M., Bokoro, P.N. and Sharma, G., 2025. Hybrid optimization for sustainable design and sizing of standalone microgrids integrating renewable energy, diesel generators, and battery storage with environmental considerations. Results in Engineering, 25, p.103764.
- J. Carpentier, Contribution a l’etude du dispatching economique. Bulletin de la Société Francaise des électriciens, 3(1), pp.431-447, 1962.
- [13] Zhou, M., Wang, L., Hu, F., Zhu, Z., Zhang, Q., Kong, W., Zhou, G., Wu, C. and Cui, E., 2024. ISSA-LSTM: A new data-driven method of heat load forecasting for building air conditioning. Energy and Buildings, p.114698.
- Lin, J., Tavalaei, J., Yeo, L.Y., Zhou, Y., Afrouzi, H.N. and Ektesabi, M.M., 2024, September. Hybrid CNN-BiLSTM Model for Power Quality Disturbance Classification. In 2024 IEEE International Conference on Advanced Power Engineering and Energy (APEE) (pp. 112-116). IEEE.
- A.K. Khames et al., “Optimal Power Flow with Stochastic Renewable Energy Using Three Mixture Component Distribution Functions”, vol.15, no.13, pp5-19, 2022, doi: 10.3390/su15010334.
- Megaptche, C.A.M., Waita, S., Kim, H., Musau, P.M. and Aduda, B.O., 2024. Multi-dimensional analysis in optimal sizing of hybrid renewable energy systems for green energy growth in Garoua, Cameroon: From techno-economic and social models to policies. Energy Conversion and Management, 315, p.118804.
- Tavalaei, J., Habibuddin, M.H., Naderipour, A. and Mohd Zin, A.A., 2018. Development of nonuniform transmission line protection for accurate distance protection: computational analysis of an adaptive distance relay characteristic. International Transactions on Electrical Energy Systems, 28(4), p.e2514.
- S. Xuewei et al., "Research on Energy Storage Configuration Method Based on Wind and Solar Volatility," 2020 10th International Conference on Power and Energy Systems (ICPES), Chengdu, China, 2020, pp. 464-468, doi: 10.1109/ICPES51309.2020.9349645.
- P. Lezhniuk, S. Kravchuk, V. Netrebskiy, V. Komar and V. Lesko, "Forecasting Hourly Photovoltaic Generation on Day Ahead," 2019 IEEE 6th International Conference on Energy Smart Systems (ESS), Kyiv, Ukraine, 2019, pp. 184-187, doi: 10.1109/ESS.2019.8764245.
- A. Georgiev and S. Sulakov, "Modelling of Hourly Wind Generation using Pan-European Climatic Data Base and Weibull Probability Distribution," 2019 16th International Conference on the European Energy Market (EEM), Ljubljana, Slovenia, 2019, pp. 1-4, doi: 10.1109/EEM.2019.8916461.
- Hassan, M., Biswas, S.P., Chowdhury, S.A.H., Mondal, S., Islam, M.R. and Shah, R., 2024. Fault classification and localization of multi-machine-based ieee benchmark test case power transmission lines using optimizable weighted extreme learning machine. Electric Power Systems Research, 235, p.110857.
- A. Nath, A. K. M. A. Rahman Chowdhury and N. Mohammad, "Optimum Power Flow of Modified IEEE 9 Bus System using ELD Optimization Method," 2019 IEEE International Conference on Power, Electrical, and Electronics and Industrial Applications (PEEIACON), Dhaka, Bangladesh, 2019, pp. 91-94, doi: 10.1109/PEEIACON48840.2019.9071941.
- Z. -Y. Wang and H. -D. Chiang, "A Necessary and Sufficient Condition for Computed OPF Solutions to be Locally Optimal," in IEEE Transactions on Power Systems, vol. 38, no. 6, pp. 5491-5500, Nov. 2023, doi: 10.1109/TPWRS.2022.3230901.
- Mehallou, A., M’hamdi, B., Amari, A., Teguar, M., Rabehi, A., Guermoui, M., Alharbi, A.H., El-Kenawy, E.S.M. and Khafaga, D.S., 2025. Optimal multiobjective design of an autonomous hybrid renewable energy system in the Adrar Region, Algeria. Scientific Reports, 15(1), p.4173.
- Verma, V., Sorathiya, V., Sonowal, G. and Reddy, M.S., 2024. Hybrid optimization for integration of renewable energy systems into smart grids. Measurement: Sensors, 33, p.101170.
- Onawale, S. and Wang, X., 2024, May. AC OPF Studies for Smart Grid with Renewable Energy Integration. In 2024 International Conference on Control, Automation and Diagnosis (ICCAD) (pp. 1-6). IEEE.
- Roy, A., Dutta, S., Bhattacharya, A., Biswas, S. and Roy, P.K., 2025. LFC based OPF with renewable energy, BESS and FOPID controller using QODTBO algorithm. Journal of Energy Storage, 115, p.115782.
References
Rehman, N., Mufti, M.U.D. and Gupta, N., 2024. Power flow analysis in a distribution system penetrated with renewable energy sources: a review. International Journal of Ambient Energy, 45(1), p.2305701.
Halimatussadiah, A., Kruger, W., Wagner, F., Afifi, F.A.R., Lufti, R.E.G. and Kitzing, L., 2024. The country of perpetual potential: Why is it so difficult to procure renewable energy in Indonesia. Renewable and Sustainable Energy Reviews, 201, p.114627.
Ghafoor, A., Aldahmashi, J., Apsley, J., Djurović, S., Ma, X. and Benbouzid, M., 2024. Intelligent Integration of Renewable Energy Resources Review: Generation and Grid Level Opportunities and Challenges. Energies, 17(17), p.4399.
Bilal, M., Bokoro, P.N. and Sharma, G., 2025. Hybrid optimization for sustainable design and sizing of standalone microgrids integrating renewable energy, diesel generators, and battery storage with environmental considerations. Results in Engineering, 25, p.103764.
J. Carpentier, Contribution a l’etude du dispatching economique. Bulletin de la Société Francaise des électriciens, 3(1), pp.431-447, 1962.
[13] Zhou, M., Wang, L., Hu, F., Zhu, Z., Zhang, Q., Kong, W., Zhou, G., Wu, C. and Cui, E., 2024. ISSA-LSTM: A new data-driven method of heat load forecasting for building air conditioning. Energy and Buildings, p.114698.
Lin, J., Tavalaei, J., Yeo, L.Y., Zhou, Y., Afrouzi, H.N. and Ektesabi, M.M., 2024, September. Hybrid CNN-BiLSTM Model for Power Quality Disturbance Classification. In 2024 IEEE International Conference on Advanced Power Engineering and Energy (APEE) (pp. 112-116). IEEE.
A.K. Khames et al., “Optimal Power Flow with Stochastic Renewable Energy Using Three Mixture Component Distribution Functions”, vol.15, no.13, pp5-19, 2022, doi: 10.3390/su15010334.
Megaptche, C.A.M., Waita, S., Kim, H., Musau, P.M. and Aduda, B.O., 2024. Multi-dimensional analysis in optimal sizing of hybrid renewable energy systems for green energy growth in Garoua, Cameroon: From techno-economic and social models to policies. Energy Conversion and Management, 315, p.118804.
Tavalaei, J., Habibuddin, M.H., Naderipour, A. and Mohd Zin, A.A., 2018. Development of nonuniform transmission line protection for accurate distance protection: computational analysis of an adaptive distance relay characteristic. International Transactions on Electrical Energy Systems, 28(4), p.e2514.
S. Xuewei et al., "Research on Energy Storage Configuration Method Based on Wind and Solar Volatility," 2020 10th International Conference on Power and Energy Systems (ICPES), Chengdu, China, 2020, pp. 464-468, doi: 10.1109/ICPES51309.2020.9349645.
P. Lezhniuk, S. Kravchuk, V. Netrebskiy, V. Komar and V. Lesko, "Forecasting Hourly Photovoltaic Generation on Day Ahead," 2019 IEEE 6th International Conference on Energy Smart Systems (ESS), Kyiv, Ukraine, 2019, pp. 184-187, doi: 10.1109/ESS.2019.8764245.
A. Georgiev and S. Sulakov, "Modelling of Hourly Wind Generation using Pan-European Climatic Data Base and Weibull Probability Distribution," 2019 16th International Conference on the European Energy Market (EEM), Ljubljana, Slovenia, 2019, pp. 1-4, doi: 10.1109/EEM.2019.8916461.
Hassan, M., Biswas, S.P., Chowdhury, S.A.H., Mondal, S., Islam, M.R. and Shah, R., 2024. Fault classification and localization of multi-machine-based ieee benchmark test case power transmission lines using optimizable weighted extreme learning machine. Electric Power Systems Research, 235, p.110857.
A. Nath, A. K. M. A. Rahman Chowdhury and N. Mohammad, "Optimum Power Flow of Modified IEEE 9 Bus System using ELD Optimization Method," 2019 IEEE International Conference on Power, Electrical, and Electronics and Industrial Applications (PEEIACON), Dhaka, Bangladesh, 2019, pp. 91-94, doi: 10.1109/PEEIACON48840.2019.9071941.
Z. -Y. Wang and H. -D. Chiang, "A Necessary and Sufficient Condition for Computed OPF Solutions to be Locally Optimal," in IEEE Transactions on Power Systems, vol. 38, no. 6, pp. 5491-5500, Nov. 2023, doi: 10.1109/TPWRS.2022.3230901.
Mehallou, A., M’hamdi, B., Amari, A., Teguar, M., Rabehi, A., Guermoui, M., Alharbi, A.H., El-Kenawy, E.S.M. and Khafaga, D.S., 2025. Optimal multiobjective design of an autonomous hybrid renewable energy system in the Adrar Region, Algeria. Scientific Reports, 15(1), p.4173.
Verma, V., Sorathiya, V., Sonowal, G. and Reddy, M.S., 2024. Hybrid optimization for integration of renewable energy systems into smart grids. Measurement: Sensors, 33, p.101170.
Onawale, S. and Wang, X., 2024, May. AC OPF Studies for Smart Grid with Renewable Energy Integration. In 2024 International Conference on Control, Automation and Diagnosis (ICCAD) (pp. 1-6). IEEE.
Roy, A., Dutta, S., Bhattacharya, A., Biswas, S. and Roy, P.K., 2025. LFC based OPF with renewable energy, BESS and FOPID controller using QODTBO algorithm. Journal of Energy Storage, 115, p.115782.