A shadow-cost-based long-term model predictive controller for a solar-based district heating system with tank thermal energy storage

Model predictive control (MPC) is a promising candidate for controlling district heating (DH) networks. Future DH networks should include more renewable heat sources like solar thermal collectors (STCs). However, these require seasonal thermal energy storage (STES) to bridge the seasonal mismatch between solar heat supply and heat demand. MPC typically operates with a prediction horizon of a few hours or days, suitable for real-time control, but this is inadequate for optimally managing the STES operation. Therefore, a long-term MPC methodology is required to optimally control the DH system and STES without compromising real-time control capabilities.

Previous studies on long-term MPC for (thermal) energy systems can be categorised into three strategies: (1) adding a heuristic term to the MPC’s cost function [1]; (2) adding a shadow cost to the MPC’s cost function [2]; (3) using a hierarchical controller [3]. Only the first strategy is applied to a DH network [1], specifically a solar-based DH network with a borefield, but the heuristic is very case-specific. The shadow-cost and hierarchical control approaches are more generic and can incorporate detailed long-term dynamics, but this requires long-term predictions of the system disturbances (heat demand and weather conditions), which typically lack accuracy.

This paper introduces a simple shadow cost formulation that depends solely on the system states within the short-term prediction horizon, avoiding the need for a long-term controller model and associated predictions. To evaluate the accuracy of this long-term MPC (LTMPC), a full-year simulation is performed in which LTMPC is applied to a small-scale (12 houses) solar-based DH network with tank thermal energy storage (TTES). The performance of LTMPC is compared to both a theoretical optimum (a full-year optimal control problem with perfect predictions, FYOCP) and a short-term MPC that does not account for long-term effects (STMPC).

Simulation results indicate that LTMPC outperforms STMPC by effectively storing solar heat during warm months and using it to meet the space heating demand in the cold months. However, LTMPC uses 18% more electrical energy than FYOCP, though this difference reduces to 5% when accounting for the heat stored in the TTES at the end of the simulation period. The remaining performance gap between LTMPC and FYOCP is due to LTMPC’s lack of knowledge about future solar heat availability and building heat demand. Extending LTMPC with a long-term controller model that incorporates these predictions could potentially bridge this gap, provided that good long-term predictions are available.