Performance comparison of quadratic, nonlinear, and mixed integer nonlinear MPC formulations and solvers on an air source heat pump hydronic floor heating system

There is a gap in literature on comparisons between different MPC optimal control formulations and solver choices for the same building HVAC system. Mixed Integer Nonlinear (MINL) formulations are rarely considered, despite being the most physically accurate way to represent HVAC systems. This work compares several MPC formulations, including Quadratic, Nonlinear, and MINL, applied to a case study building and investigates benefits and challenges of MINL MPCs from practical perspectives. Ten different MPC formulations were developed and implemented using Pyomo. Then, a detailed emulator model was developed using open-source Modelica libraries and used with BOPTEST to assess the performance of each MPC. Results show that convergence and control switching behaviours of MINL MPCs are sensitive to formulations, initialization approaches, solver selections, and solver parameters. Thus, they require significant effort for tuning. However, a very well-tuned MINL MPC performed similarly to successful Nonlinear MPC formulations.