Mitigating short-sightedness of MPC for district heating networks using dual dynamic programming

In this paper, we use dual dynamic programming to address the myopic nature of MPC for scheduling of district heating networks by designing value functions that can approximate the effects of time-varying elements on the objective function beyond the initial prediction horizon. To this end, we formulate the control problem as a two-level MPC. More precisely, in the first-level, we consider a short-horizon nonlinear MPC equipped with a terminal cost approximating the value function. Subsequently, a long-horizon linear MPC is solved in the second-level to establish a lower bound on the terminal cost function from the first-level, thereby improving the value function approximation. Specifically, we consider scheduling of thermal and hydraulic components within district heating networks. Our numerical example demonstrates that our method can anticipate demand variations beyond the prediction horizon while maintaining computational efficiency.