Single-level MILP incentive pricing for customer directrix load-based demand response in smart buildings

Abstract

With the high penetration of renewable energy, tapping the regulation potential of smart buildings in distribution networks plays a pivotal role in enabling orderly renewable energy accommodation. Customer directrix load-based demand response serves as an effective mechanism for guiding smart building interaction. However, its incentive price, derived as the equilibrium point of a leader-follower game between the operator and load entities, relies on a corresponding bilevel optimization model that suffers from low computational efficiency. To address this limitation, an efficient incentive pricing method is proposed. The proposed linear similarity metric and incentive revenue formulation ensure the linearity of the lower-level optimization problem. Subsequently, based on primal-dual feasibility, an aggregated strong-duality equality, and a discrete-price reformulation, the original bilevel model is accurately reformulated into a single-level mixed-integer linear programming problem, enabling a one-shot determination of the incentive price. Simulation results demonstrate that the proposed linear metric is highly consistent with traditional nonlinear metrics in terms of ranking monotonicity. Compared with time-of-use-only demand response and fixed incentive pricing strategies, the proposed method can identify an economically balanced incentive price that effectively guides smart building energy consumption behavior, improves renewable energy accommodation, and maintains favorable economic performance for both the distribution system operator and smart buildings. These findings support the use of the proposed single-level MILP framework for balancing renewable energy accommodation with the economic interests of the distribution system operator and smart buildings.