State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations

[2506.11765] State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2506.11765 (math) [Submitted on 13 Jun 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations Authors: Alfredo Bermúdez , Iago Padín View a PDF of the paper titled State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations, by Alfredo Berm\'udez and Iago Pad\'in View PDF HTML (experimental) Abstract: With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, photovoltaic (PV) generation is playing an increasingly important role in modern power systems, while its intrinsic variability poses challenges for real-time operation and electricity market participation. This paper proposes a continuous-time stochastic optimal control framework for the joint optimization of real-time battery management and day-ahead market bidding of PV plants with energy storage. Solar irradiance, electricity prices, and battery dynamics are modeled through stochastic differential equations (SDEs), leading to a constrained stochastic control problem characterized by a coupled Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) formulation. To mitigate the associated computational burden, a dimension-reduction strategy is introduced by decomposing the state space into controllable and uncontrollable components, yielding lower-dimensional optimality systems while preserving the continuous-time Dynamic Programming structure. Numerical results show that the reduced formulations achieve substantial computational savings, enabling real-time applicability without significant loss of performance. The proposed methodology is benchmarked against two rule-based strategies and a stochastic Model Predictive Control (MPC) approach, highlighting a favorable trade-off in terms of economic performance, computational efficiency, and suitability for day-ahead market participation. Comments: 43 pages, 15 figures Subjects: Optimization and Control (math.OC) Cite as: arXiv:2506.11765 [math.OC] (or arXiv:2506.11765v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2506.11765 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1016/j.apenergy.2026.128108 Focus to learn more DOI(s) linking to related resources Submission history From: Iago Padín Domínguez [ view email ] [v1] Fri, 13 Jun 2025 13:20:26 UTC (229 KB) [v2] Sat, 11 Apr 2026 09:33:52 UTC (274 KB) Full-text links: Access Paper: View a PDF of the paper titled State constrained stochastic optimal control of a PV system with battery storage via Fokker-Planck and Hamilton-Jacobi-Bellman equations, by Alfredo Berm\'udez and Iago Pad\'in View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-06 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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