Mixed-integer non-linear model predictive control of district heating networks

The use of model predictive control (MPC) to optimally control district heating (DH) networks can support the transition to a carbon-neutral heating sector. DH systems are inherently subject to non-linear physics and integer controls, which results in a mixed-integer non-linear program (MINLP). In this work, an MINLP-based MPC strategy is developed for the optimal control of a DH network, building upon an existing decomposition approach (combinatorial integral approximation). The main novelty of this work is the application of an integrated MINLP-based MPC to a DH network and its comparison to a non-linear program (NLP)-based MPC. To successfully develop this MINLP-based approach, the pycombina tool is efficiently integrated in the existing NLP-based MPC toolchain (TACO) and the concept of an augmented time horizon is introduced to manage dwell time constraints. The MINLP-based MPC is applied to two use cases: a relatively simple nine-zone terraced house and a more complex fourth generation DH network. The simulation study shows that the MINLP-based MPC yields a comparable control performance to that of a previously developed NLP-based MPC, but the CPU time is approximately eight times higher. However, the absence of a post-processing step (which requires ample engineering practice and time) and the improved match between the MPC’s controller model and the actual system show promise for the MINLP-based MPC to control complex DH networks.