Two-stage robust optimization for space heating loads of buildings in integrated community energy systems

Abstract

A two-stage robust optimization (RO) method for buildings’ space heating loads (SHLs) in an integrated community energy system (ICES) is proposed. At the first stage, a bi-level optimization is deployed to formulate the hierarchical relationship between the ICES operator and consumers in buildings to enable the optimal heating pricing strategy between them. Thermal inertia of SHLs, which is modelled utilizing the Resistor-Capacitor thermal network, is used to provide heating demand response according to the optimal heating sale prices released by the ICES operator. At the second stage, the ICES operator decides the optimal energy purchase schedules from the upper energy systems after the heating sale prices are decided at the first stage. Since the day-ahead energy prices differ from the real-time ones, a RO method is adopted. The original min–max RO problem is converted into its dual problem to cooperate with the bi-level optimization. Finally, the whole optimization model is transformed into a mixed integer linear programming (MILP) based on Karush-Kuhn-Tucker conditions, duality theory, big-M method and piecewise linearization. Numerical results show that the proposed model can balance the interests between the ICES operator and consumers. And the profit of the ICES operator is 5.10% higher using RO method, compared to the deterministic optimization under energy prices uncertainties. Compared to the benchmark solution method, the computation efficiency of the final MILP model in this paper is highly improved and the convergency of the MILP model can be guaranteed.