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

With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, the penetration of renewable energy sources has significantly increased --primarily due to their inexhaustible nature. In this context, integrating photovoltaic (PV) modules with energy storage systems offers a means to mitigate the inherent variability of solar energy. This paper proposes an optimal methodology for power management and market bidding strategies tailored to PV power producers. To achieve this, the PV system, electricity price dynamics, and battery storage behavior are modeled using a system of stochastic differential equations (SDEs), resulting in a stochastic optimal control problem with state constraints. The corresponding optimality conditions are derived from the Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations. Additionally, a simplified formulation of the control problem is introduced, which substantially reduces computational complexity by decreasing the dimension of the problem.