Enhanced Dynamic Programming Optimization for Real-Time Model Predictive Control in Heat Pump Driven Residential HVAC Systems

Abstract The increasing volatility of power prices, driven by the integration of renewable energy sources into the electricity mix, requires more efficient control strategies for electrified residential heating and cooling systems. This paper proposes an enhanced dynamic programming (EDP) algorithm designed for real-time model predictive control (MPC) of heat pump-driven HVAC systems with integrated thermal energy storage (TES). The EDP introduces a brute-force initialization and a smart cutoff approach to significantly reduce computational requirements, while preserving the global optimality of standard dynamic programming (DP). The proposed method is benchmarked against standard DP, particle swarm optimization (PSO), and genetic algorithms (GA) in a residential use case based on a German home and time-varying electricity prices. The results show that the EDP finds the same cost-optimal control trajectories as the conventional DP but with up to 75% less computational time. Compared to metaheuristic methods, the EDP delivers superior cost savings while being up to two orders of magnitude faster, particularly for extended prediction horizons, hence enabling effective real-time MPC applications. The method is not limited to HVAC applications, but can be used for any DP-solvable MPC problem, enabling more intelligent and resource-efficient energy management under dynamic operating conditions.