Grid-Compatible Flexibility from Multi-Energy Systems via Cyclic-Terminal Economic MPC with Hybrid Thermal-Electrical Dynamics

Abstract

Coupled electrical and thermal infrastructures need controllers that respond to market prices and still solve fast enough to run online. This paper presents a unified Economic Model Predictive Control (EMPC) framework for the coordinated operation of integrated thermal and electrical energy networks. Building on cyclic-terminal EMPC, the proposed approach incorporates hybrid thermal-electrical dynamics, network constraints, and time-varying economic signals within a single mixed-integer state-space representation, jointly optimizing combined heat and power units, large-scale heat pumps, thermal energy storage, batteries, and grid interactions under a convex economic stage cost. Computational tractability is ensured by reduced-order models of district heating networks and DC power flow grids. The framework is demonstrated on a campus-scale energy system under time-varying prices and demand profiles. A joint sweep of the prediction horizon against the terminal penalty weight shows that the two act as substitutes rather than as independent tuning knobs. Without terminal anchoring, the closed-loop cost approaches the periodic-reference average-performance bound only once the horizon spans several diurnal cycles. With a sufficiently large terminal weight, the bound is attained essentially tightly at every tested horizon, including the shortest one, so the horizon ceases to be a performance-critical parameter and becomes a purely computational one. The result reproduces on a second, independent price week. Beyond the weight at which the soft terminal constraint activates, closed-loop behavior is insensitive to the weight over a wide multi-decade plateau; below activation, cost and storage tracking both degrade markedly. A residual receding-horizon drift of the cost-neutral thermal-storage state is also documented and interpreted.