Optimal ventilation systems via MILP: Duct sizing, fan placement, control strategies

Ventilation systems in buildings account for a substantial share of overall energy consumption, with fans representing one of the largest contributors. Improving energy efficiency requires considering the interaction of system components. Novel topologies, such as distributed fans integrated into the central duct network, offer promising potential for efficiency gains. At the same time, building owners demand cost-effective solutions, which depend strongly on a well-designed duct network. Meeting these requirements calls for a life-cycle–oriented planning approach that integrates component selection and duct network design.Existing planning algorithms, however, have several limitations: they often assume single load cases, rely on overly simplified fan models, neglect novel, distributed topologies, and lack guarantees of global optimality. This paper addresses these shortcomings by presenting a novel optimisation problem formulation that jointly considers topological decisions (e.g., fan and volume flow controller placement, duct sizing) and system operation under multiple load cases. The methodology enables systematic comparison of control strategies, duct limitations - in velocity and height - and analysis of cost-energy trade-offs. To reduce computation times, the non-linear optimisation problem is relaxed to a Mixed-Integer Linear Program (MILP), with proven error bounds that quantify the distance to the global optimum.The methodology is demonstrated on a case study building. Results show that the approach can compare six different central or distributed control strategies and duct constraints within seconds of computation time. This makes the method suitable for practical planning processes, providing transparent decision support through, for example, Pareto front analyses.