Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries
Although renewable energies are beneficial to reduce carbon emissions, its intermittent characteristics may result in power-supply issues in distribution grid. Battery energy storage system is generally regarded as an effective tool to deal with them. On the other hand mathematical modelling, numeri...
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| Language: | English |
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Académie des sciences
2024-02-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.236/ |
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| author | Bermúdez, Alfredo Padín, Iago |
| author_facet | Bermúdez, Alfredo Padín, Iago |
| author_sort | Bermúdez, Alfredo |
| collection | DOAJ |
| description | Although renewable energies are beneficial to reduce carbon emissions, its intermittent characteristics may result in power-supply issues in distribution grid. Battery energy storage system is generally regarded as an effective tool to deal with them. On the other hand mathematical modelling, numerical simulation, optimization and control theory are nowadays of paramount importance to handle this kind of problems and related issues. In this paper we present a methodology for the development of bidding strategies and real-time control for electricity producers in a competitive electricity marketplace. Firstly, a stochastic model of a wind power plant with battery storage is stated in the framework of stochastic differential equations (SDE). Then, a stochastic control problem with state constraints is introduced and the corresponding optimality conditions involving the Hamilton–Jacobi–Bellman equation are deduced. For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation. |
| format | Article |
| id | doaj-art-eeedb8de745b454e923c18aff91b742c |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-eeedb8de745b454e923c18aff91b742c2025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-02-01351S18911010.5802/crmeca.23610.5802/crmeca.236Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteriesBermúdez, Alfredo0https://orcid.org/0000-0002-1865-6804Padín, Iago1CITMAga and Universidade de Santiago de Compostela, SpainDepartment of Applied Mathematics. Universidade de Santiago de Compostela. SpainAlthough renewable energies are beneficial to reduce carbon emissions, its intermittent characteristics may result in power-supply issues in distribution grid. Battery energy storage system is generally regarded as an effective tool to deal with them. On the other hand mathematical modelling, numerical simulation, optimization and control theory are nowadays of paramount importance to handle this kind of problems and related issues. In this paper we present a methodology for the development of bidding strategies and real-time control for electricity producers in a competitive electricity marketplace. Firstly, a stochastic model of a wind power plant with battery storage is stated in the framework of stochastic differential equations (SDE). Then, a stochastic control problem with state constraints is introduced and the corresponding optimality conditions involving the Hamilton–Jacobi–Bellman equation are deduced. For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.236/Renewable energy plantoptimal energy biddingsstochastic controlFokker–Planck equationHamilton–Jacobi–Bellman equation |
| spellingShingle | Bermúdez, Alfredo Padín, Iago Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries Comptes Rendus. Mécanique Renewable energy plant optimal energy biddings stochastic control Fokker–Planck equation Hamilton–Jacobi–Bellman equation |
| title | Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries |
| title_full | Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries |
| title_fullStr | Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries |
| title_full_unstemmed | Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries |
| title_short | Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries |
| title_sort | stochastic control with state constraints via the fokker planck equation application to renewable energy plants with batteries |
| topic | Renewable energy plant optimal energy biddings stochastic control Fokker–Planck equation Hamilton–Jacobi–Bellman equation |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.236/ |
| work_keys_str_mv | AT bermudezalfredo stochasticcontrolwithstateconstraintsviathefokkerplanckequationapplicationtorenewableenergyplantswithbatteries AT padiniago stochasticcontrolwithstateconstraintsviathefokkerplanckequationapplicationtorenewableenergyplantswithbatteries |