Modern energy systems increasingly combine thermal and electrical infrastructure—such as district heating networks, heat pumps, combined heat and power units, and battery storage—requiring controllers that balance economic efficiency with real-time computational demands. Researchers have developed an Economic Model Predictive Control (EMPC) framework that unifies the operation of these hybrid systems under a single optimization model.
The key innovation is cyclic-terminal EMPC, which incorporates hybrid thermal-electrical dynamics alongside network constraints and time-varying electricity prices. By representing both heat and power flows within a mixed-integer state-space framework, the controller jointly optimizes dispatch of combined heat and power generators, heat pumps, thermal storage tanks, batteries, and grid interactions—all subject to convex economic objectives.
Critically, the authors address computational tractability by employing reduced-order models of district heating networks and DC power flow grids, enabling the optimization to run fast enough for online deployment. Testing on a campus-scale system revealed important tuning insights: the prediction horizon and terminal penalty weight act as substitutes rather than independent parameters. Without terminal anchoring, closed-loop costs approach optimal performance only when the prediction horizon spans multiple daily cycles. However, with appropriate terminal weighting, near-optimal performance is achieved even at shorter horizons, effectively decoupling computational requirements from economic performance.
The framework also revealed previously undocumented behavior: a residual receding-horizon drift in thermal storage state that remains cost-neutral but warrants operational attention. Beyond a critical activation threshold, closed-loop behavior remains insensitive to terminal weight across multiple orders of magnitude, providing operators a robust tuning plateau.
This research advances the practical deployment of model predictive control for integrated energy systems. By enabling campus and district-level energy managers to simultaneously optimize thermal and electrical resources while responding to dynamic market signals, the approach supports grid stability, reduces operational costs, and facilitates deeper renewable energy penetration through coordinated demand-side flexibility.
