Mixed-Integer Nonlinear Differentiable Predictive Control for Underground Pumped Hydro Energy Storage Systems

Hydrogen supply chains are expected to play a central role in future low-carbon energy systems by enabling renewable energy integration, long-duration storage, and decarbonization of industrial and transportation sectors. However, their operation is challenged by renewable generation variability, electricity price fluctuations, uncertain hydrogen demand, and engineering constraints associated with electrolyzers, energy storage, and grid interaction. As hydrogen infrastructure expands toward commercial deployment, operational strategies must balance economic performance, reliability, and sustainability under dynamic and uncertain conditions. This paper investigates and compares four control approaches for a renewable-powered hydrogen supply chain: a rule-based controller (RBC), model predictive control (MPC), reinforcement learning without forecasts (RL-NF), and reinforcement learning with forecast-augmented observations (RL-F). All methods are evaluated within a unified, physically realistic framework incorporating electrolyzer minimum-load and ramp-rate constraints, battery and hydrogen storage dynamics, grid import limits, and consistent economic assumptions, enabling a fair comparison under identical operating conditions. Simulation results show that MPC achieves the highest economic performance by exploiting short-term forecasts to coordinate storage, reduce grid dependence, and improve efficiency. RL-NF demonstrates robust and competitive performance without future information, highlighting the capability of learning-based methods to discover effective policies from experience. RL-F does not consistently outperform its no-forecast counterpart, suggesting that forecast uncertainty and increased state complexity can limit forecast-augmented learning. The results provide guidance for selecting operational control strategies in future hydrogen energy systems.

Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale Mixed-integer Linear Programming (MILP) problem that is strictly and heavily governed by the grid physical constraints. As grid integrate variable renewable sources, and new technologies such as long duration storage in the grid, UC must be optimally solved for multi-day horizons and potentially with greater frequency. Therefore, traditional MILP solvers increasingly struggle to compute solutions within these tightening operational time limits. To bypass these computational bottlenecks, this paper proposes a novel framework utilizing a transformer-based architecture to predict generator commitment schedules over a 72-hour horizon. Also, because raw predictions in highly dimensional spaces often yield physically infeasible results, the pipeline integrates the self-attention network with deterministic post-processing heuristics that systematically enforce minimum up/down times and minimize excess capacity. Finally, these refined predictions are utilized as a warm start for a downstream MILP solver, while employing a confidence-based variable fixation strategy to drastically reduce the combinatorial search space. Validated on a single-bus test system, the complete multi-stage pipeline achieves 100% feasibility and significantly accelerates computation times. Notably, in approximately 20% of test instances, the proposed model reached a feasible operational schedule with a lower overall system cost than relying solely on the solver.

Buildings are expected to shift cooling loads in response to grid conditions. Thermal energy storage (TES) enables this shift, but scheduling it well requires planning hours ahead under storage constraints. Model predictive control (MPC) and reinforcement learning are difficult to scale across buildings. This study instead adapts an open-weight reasoning model through reinforcement learning with verifiable rewards (RLVR). We convert exact offline dynamic-programming (DP) action values into dense rewards for every candidate action. Using only 30 training prompts, reinforcement fine-tuning (RFT) trains the model as an upper-level scheduler that outputs hourly heat-pump setpoints from text-based states and forecasts. Evaluation uses a deliberately simple office-building TES benchmark where exact DP is tractable and the optimum is known. RFT reduces the open-weight model's emissions from 70.5 to 61.2 kg-CO2, close to the DP optimum of 60.8 kg-CO2. GPT-5 nearly matches DP and MPC without task-specific training, while GPT-4o, a non-reasoning LLM, produces higher emissions than the no-storage baseline, so inference-time reasoning appears important. Trace analysis shows that RFT mainly stabilizes observable planning patterns (candidate comparison, look-ahead, and feasibility checking) rather than creating a new strategy. Robustness and generalization tests clarify what transfers: the reinforced planning patterns persist under forecast errors and an unseen TES condition and carry over to a battery task, but its different structure limits the gains. DP-based verifiable rewards offer a practical way to adapt open-weight reasoning models to building storage scheduling. These results motivate higher-fidelity tests of whole-building control and scalable verifiers for city-scale energy management.