Performance Assessment of Nonconvex MINLP Formulations for District Heating Model Predictive Control

This study evaluates the performance of nonconvex Mixed-Integer Nonlinear Programming formulations for optimizing district heating systems under model predictive control. A novel methodology is introduced to assess operational optimization results by benchmarking them with a complex transient thermo-hydraulic simulation model replicating real-world operational conditions with high temporal and spatial detail. The analysis focuses on a low-temperature, multi-source district heating system operating with supply temperatures between 55 and 80 °C. Two optimization approaches, a full problem formulation and a partial problem formulation, are compared against traditional rule-based controls. The case study reveals that optimization-based control strategies achieve cost savings of 1-10 €/MWh over rule-based methods. The full problem formulation delivers additional reductions of 2 €/MWh during winter by optimizing all mass flows and temperatures. Meanwhile, the partial problem formulation, despite its simplified fixed-temperature approach, consistently delivers high-quality solutions in seconds, making it well-suited for real-time applications. The detailed simulations validate the feasibility of the optimization control strategies, showing their potential to address computational challenges and enhance district heating system performance. Future research should prioritize improving scalability, addressing uncertainties in forecasting, and exploring hybrid approaches that combine machine learning with optimization techniques.