Valuing operational flexibility in hybrid energy systems: A neural solution to the Hamilton–jacobi–bellman equation

This paper develops a continuous-time stochastic control framework for the joint operation of gas-fired generation, wind power, and energy storage under correlated electricity and gas price uncertainty. The operator’s decision problem is formulated as a finite-horizon Hamilton–Jacobi–Bellman (HJB) equation, capturing the trade-off between immediate revenues and the continuation value of storage under physical and operational constraints. To address the resulting high-dimensional control problem, we employ a mesh-free neural approximation based on physics-informed and Deep Galerkin methods. An analytical linear–quadratic (LQ) formulation is derived as a benchmark, providing structural insight and a reference point under simplified assumptions. Numerical experiments demonstrate stable convergence of the neural HJB solver and recovery of economically interpretable policy structures. When calibrated to historical electricity and gas price data and evaluated under realistic transaction costs, the learned policy exhibits sparse, threshold-driven storage operation with extended no-trade regions. In these regimes, optimal behavior leaves the storage inactive despite ongoing generation, reflecting the option-like and highly state-dependent value of operational flexibility. Overall, the results show that neural HJB solvers provide an economically consistent and transparent framework for analyzing hybrid energy systems. By linking stochastic price dynamics, operational constraints, and realized storage decisions, the approach clarifies when flexibility is actively exercised and when it remains economically dormant in low-carbon power systems. • Integrated stochastic control of hybrid gas-wind–storage assets under correlated price uncertainty. • Neural HJB solver enables scalable solutions to high-dimensional control problems with non-linear operating frictions. • Empirical calibration and backtesting using historical 2019–2024 European electricity and gas price data. • Diagnostic benchmarking against analytical linear-quadratic models and classical finite-difference schemes. • Learned policies reveal sparse, threshold-driven storage operations with extended no-trade regions.