Sustainable design and control of a multi-sourced radiant heating system: Non-linear optimization under thermal comfort constraints

Abstract

The demand for energy-efficient heating solutions in buildings is increasing consistently, necessitating tools to determine the system’s optimal design and operation, while ensuring occupant comfort. This study develops a novel thermal comfort-constrained capacity-operation optimization framework for a multi-source (solar collectors, a biomass boiler, and a gas boiler) radiant floor heating system, addressing the limitations of existing literature that typically focus on non-linear optimization of single-source systems. The system incorporates two forms of thermal storage, namely a water tank and a thermally active floor slab, which magnifies the system’s non-linearities. Hence, a non-linear interior-point optimization algorithm (Ipopt) is implemented in MATLAB® to minimize lifecycle costs (LCC). Unlike conventional approaches, the developed optimization framework has three novel features: i) it captures the dynamics and complex interactions between heat generation, storage, and consumption components, ii) it constrains temperature levels to ensure energy quality while simultaneously solving thermal comfort equations at each time step, accounting for the dynamic response of the building in subsequent steps, and iii) it balances various operational and sizing decision variables, capturing the bi-directional impacts of optimal system capacity and management. The results reveal that the tri-source system achieves an LCC of approximately 0.42 mil. CAD (Canadian dollars), equivalent to 0.3 mil. USD, and a competitive levelized cost of heat (LCOH) of 0.143 CAD kWh−1 (0.1 USD kWh−1), maintaining a stable operative temperature between 19 °C and 25 °C, with an average predictive mean vote (PMV) of −0.12, and total lifecycle CO2 emissions of 330.15 tons. Comparative analyses with simpler design variations indicate that the gas-only system incurs the lowest LCC at 0.302 mil. CAD (0.21 mil. USD), yet its emissions are nearly twice those of the tri-source system. Among renewable options, the solar-biomass system offers the best balance of economic (LCC of 0.506 mil. CAD or 0.36 mil. USD), environmental (110.9 tons of CO2), and comfort metrics (mean PMV of −0.12).