|
Presenting an optimization method for inertia pricing in power systems based on renewable energy sources, with the aim of improving efficiency and reducing operational costs
|
Fardin Zaremansouri1   , Masoud Rashidinejad *1 , Amir Abdollahi1 , Sobhan Dorahaki2 , Ebrahim Pirmoradi1 |
1- Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran,
2- Department of Electrical Engineering, Qatar University, Doha, Qatar |
|
|
Abstract: (1120 Views) |
This paper investigates the critical challenge of simultaneously managing electrical energy supply and inertia services in modern power systems. With the increasing share of renewable energy sources and the reduction of mechanical inertia resulting from the replacement of traditional generators, the frequency stability of the grid is compromised. Acknowledging the necessity of new mechanisms, this research offers a comprehensive framework to address this issue.The main problem studied is the modeling of power system operation under the influence of renewable energy sources, considering the concurrent needs for energy and inertia. This model is formulated as a constrained optimization problem, aiming to determine the optimal operational schedule of controllable resources to maximize economic performance and grid stability, while adhering to technical constraints.The primary method employed is the use of mathematical programming and optimization analysis to derive pricing mechanisms. The power system operation problem is modeled, considering the constraint of providing minimum inertia, and Karush-Kuhn-Tucker (KKT) optimality conditions are used for sensitivity analysis and extraction of economic prices. By analyzing the dual variables corresponding to the power balance constraint and the minimum inertia provision constraint, analytical formulas for energy price and the comprehensive price of network inertia services are derived.The extracted prices not only reflect the costs of energy production but also the economic value of inertia services.These results indicate that creating a market for inertia services can provide the necessary incentives for investment in inertia-providing technologies (such as ES) and significantly contribute to enhancing grid stability. The validity of the results is confirmed through simulations on a representative network with a significant share of renewable energy sources and comparison with data. This research provides practical solutions for improving the performance of power systems with a high penetration of renewable energy sources and increasing the stability of the electricity grid. |
|
| Keywords: Virtual inertia, renewable energy resources, ancillary services pricing, frequency stability, electricity price |
|
|
Full-Text [PDF 1635 kb]
(2972 Downloads)
|
Type of Study: Research |
Received: 2025/04/19 | Accepted: 2025/11/23 | Published: 2025/12/27
|
|
|
|
|
|
|
| References |
1. Agarwal, D., Singh, P., & El Sayed, M. A. (2023). The Karush-Kuhn-Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems. Mathematics and Computers in Simulation, 205, 861-877. [ DOI:10.1016/j.matcom.2022.10.024] 2. Badesa, L., Matamala, C., Zhou, Y., & Strbac, G. (2023). Assigning Shadow Prices to Synthetic Inertia and Frequency Response Reserves from Renewable Energy Sources. IEEE Transactions on Sustainable Energy, 14(1), 12-26. [ DOI:10.1109/TSTE.2022.3198324] 3. Bao, F., Guo, J., Wang, W., & Wang, B. (2021). Cooperative Control Strategy of Multiple VSGs in Microgrid Based on Adjacent Information. IEEE Access, 9, 125603-125615. [ DOI:10.1109/ACCESS.2021.3110848] 4. Daniel S. Kirschen, & Goran Strbac. (2018). Fundamentals of Power System Economics (2nd ed.). John Wiley & Sons Ltd. 5. Erfaghi, Y., Doroudi, A., & Professor, A. (2023). Inertia constant and damping coefficient estimation in multi-area interconnected power systems. Quality & Productivity Iranian Electric Industry Journal Quality &, 12(4), 2024. 6. Fadheel, B. A., Izzri Abdul Wahab, N., Mahdi, A. J., Amran Bin Mohd Radzi, M., & Che Soh, A. B. (2021). Review of the Virtual Inertia Strategies from Intermittent Renewable Energy Resources on the Power System. 2021 12th International Renewable Energy Congress, IREC 2021. [ DOI:10.1109/IREC52758.2021.9624801] 7. Fernández-Guillamón, A., Gómez-Lázaro, E., Muljadi, E., & Molina-García, Á. (2019). Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time. In Renewable and Sustainable Energy Reviews (Vol. 115). Elsevier Ltd. [ DOI:10.1016/j.rser.2019.109369] 8. Fernández-Guillamón, A., Gómez-Lázaro, E., Muljadi, E., & Molina-Garcia, Á. (2021). A Review of Virtual Inertia Techniques for Renewable Energy-Based Generators. In Renewable Energy - Technologies and Applications. IntechOpen. [ DOI:10.5772/intechopen.92651] 9. Guvenc, U., Altun, B. E., Duman, S., & Emre Altun, B. (2012). Optimal power flow using genetic algorithm based on similarity. In Energy Education Science and Technology Part A: Energy Science and Research (Vol. 29, Number 1). https://www.researchgate.net/publication/286136216 10. Hosny, M., Marei, M. I., & Mohamad, A. M. I. (2025). Adaptive hybrid virtual inertia controller for PMSG-based wind turbine based on fuzzy logic control. Scientific Reports, 15(1). [ DOI:10.1038/s41598-025-87986-6] 11. Jafari, M., Gharehpetian, G. B., & Anvari-Moghaddam, A. (2024). On the Role of Virtual Inertia Units in Modern Power Systems: A Review of Control Strategies, Applications and Recent Developments. In International Journal of Electrical Power and Energy Systems (Vol. 159). Elsevier Ltd. [ DOI:10.1016/j.ijepes.2024.110067] 12. Karlilar Pata, S., & Balcilar, M. (2024). Decarbonizing energy: Evaluating fossil fuel displacement by renewables in OECD countries. Environmental Science and Pollution Research, 31(21), 31304-31313. [ DOI:10.1007/s11356-024-33324-8] 13. Kuang, X., Lamadrid, A. J., & Zuluaga, L. F. (2019). Pricing in non-convex markets with quadratic deliverability costs. Energy Economics, 80, 123-131. [ DOI:10.1016/j.eneco.2018.12.022] 14. Li, W., Du, P., & Lu, N. (2018). Design of a new primary frequency control market for hosting frequency response reserve offers from both generators and loads. IEEE Transactions on Smart Grid, 9(5), 4883-4892. [ DOI:10.1109/TSG.2017.2674518] 15. Liang, Z., Mieth, R., & Dvorkin, Y. (2023). Inertia Pricing in Stochastic Electricity Markets. IEEE Transactions on Power Systems, 38(3), 2071-2084. [ DOI:10.1109/TPWRS.2022.3189548] 16. Lin, Y., Eto, J. H., Johnson, B. B., Flicker, J. D., Lasseter, R. H., Villegas Pico, H. N., Seo, G.-S., Pierre, B. J., Ellis4, A., Miller, J., & Yuan, G. (2020). Research Roadmap on Grid-Forming Inverters With editing and support from Hariharan Krishnaswami. www.nrel.gov/publications. [ DOI:10.2172/1721727] 17. Markovic, U., Chu, Z., Aristidou, P., & Hug, G. (2019). LQR-Based Adaptive Virtual Synchronous Machine for Power Systems With High Inverter Penetration. IEEE Transactions on Sustainable Energy, 10(3), 1501-1512. [ DOI:10.1109/TSTE.2018.2887147] 18. P. Kundur, N. B. and M. L. (1994). Power System Stability and Control., 1st ed. New York, NY,USA: McGraw Hill. 19. Paturet, M., Markovic, U., Delikaraoglou, S., Vrettos, E., Aristidou, P., & Hug, G. (2020). Economic Valuation and Pricing of Inertia in Inverter-Dominated Power Systems. http://arxiv.org/abs/2005.11029 20. Poolla, B. K., Bolognani, S., Li, N., & Dörfler, F. (2020). A Market Mechanism for Virtual Inertia. IEEE Transactions on Smart Grid, 11(4), 3570-3579. [ DOI:10.1109/TSG.2020.2969518] 21. Qiu, D., Baig, A. M., Wang, Y., Wang, L., Jiang, C., & Strbac, G. (2024). Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach. Applied Energy, 361. [ DOI:10.1016/j.apenergy.2024.122929] 22. Raman, Gurupraanesh, Raman, Gururaghav, & Peng, J. C. H. (2022). Coupled power generators require stability buffers in addition to inertia. Scientific Reports, 12(1). [ DOI:10.1038/s41598-022-17065-7] 23. Roy, N. K., Islam, S., Podder, A. K., Roy, T. K., & Muyeen, S. M. (2022). Virtual Inertia Support in Power Systems for High Penetration of Renewables - Overview of Categorization, Comparison, and Evaluation of Control Techniques. IEEE Access, 10, 129190-129216. [ DOI:10.1109/ACCESS.2022.3228204] 24. Sajadi, A., Kenyon, R. W., & Hodge, B. M. (2022). Synchronization in electric power networks with inherent heterogeneity up to 100% inverter-based renewable generation. Nature Communications, 13(1). [ DOI:10.1038/s41467-022-30164-3] 25. Salman, D., & Kusaf, M. (2022). Day Ahead Unit Commitment for IEEE-30 Bus System Application Taking into Consideration the Uncertainty of Wind Power Performance. In Prime Archives in Sustainability. Vide Leaf, Hyderabad.
https://doi.org/10.37247/PAS.2.2022.30 [ DOI:10.37247/pas.2.2022.30] 26. Wang, S., Li, J., Riaz, S., Zaman, H., Hao, P., Luo, Y., Mohammad, A. S., Aziz Al-Ahmadi, A., & Ullah, N. (2022). Duplex PD inertial damping control paradigm for active power decoupling of grid-tied virtual snchronous generator. Mathematical Biosciences and Engineering, 19(12), 12031-12057. [ DOI:10.3934/mbe.2022560] 27. Zhang, C., Li, C., & Zhang, R. (2024). The Application Method of Karush-Kuhn-Tucker Condition for Judging Boundary Extremum Points. Proceedings - 2024 China Automation Congress, CAC 2024, 1368-1371. [ DOI:10.1109/CAC63892.2024.10865144] 28. Zhang, Z., Du, E., Teng, F., Zhang, N., & Kang, C. (2020). Modeling Frequency Dynamics in Unit Commitment with a High Share of Renewable Energy. IEEE Transactions on Power Systems, 35(6), 4383-4395. [ DOI:10.1109/TPWRS.2020.2996821] |
|
Zaremansouri F, Rashidinejad M, Abdollahi A, Dorahaki S, Pirmoradi E. Presenting an optimization method for inertia pricing in power systems based on renewable energy sources, with the aim of improving efficiency and reducing operational costs. ieijqp 2025; 14 (4) :16-33 URL: http://ieijqp.ir/article-1-1037-en.html
|
