Distributed Energy and Thermal Management of Buildings With High-Order RC Thermal Dynamics

Energy and thermal management of a multi-zone building equipped with photovoltaic generation, battery energy storage system, and heating, ventilation, and air conditioning system is investigated. Building thermal dynamics are modeled by a Resistance-Capacitance network accounting for shared-wall coupling between zones. A multi-objective mixed-integer linear programming (MILP) problem is formulated first to minimize electricity cost and thermal discomfort via weighted-sum scalarization, where binary variables enforce non-simultaneous grid import/export and battery charge/discharge. A formal proof of convex relaxation of the MILP into Linear Programming (LP) problem is given. Then, a convex distributed resource allocation problem solved via the Dual Consensus Alternating Direction Method of Multipliers (DC-ADMM) is studied. Simulations on a five-zone building confirm that the LP matches the MILP optimum and that DC-ADMM converges to the centralized solution, validating the convex relaxation.