Two-stage robust optimization for formulating regulation curves of smart building clusters considering multiple regulation characteristics

Accurate formulation of smart building regulation curves is essential for exploiting building-side flexibility and supporting supply–demand interaction in new power systems. However, existing methods often insufficiently consider the multiple regulation characteristics of adjustable loads, scenario-specific response requirements, and response-capability uncertainty, resulting in underused response potential and poor curve executability. This paper proposes a two-stage robust formulation method for smart building cluster regulation curves. First, five response characteristics, including response capacity, maximum response duration, minimum response interval, maximum response count, and response speed, are represented by a unified characteristic matrix to describe heterogeneous smart buildings. Second, response-demand characteristic matrices of typical scenarios are extracted from historical data, and response periods and weights are embedded into resource aggregation to obtain scenario-oriented cluster response-capability curves. Finally, a two-stage robust optimization model for regulation curves considering response-capability uncertainty is proposed. The first stage determines cluster regulation curves and response states, while the second stage adjusts individual building response quantities under different realizations of response capability. The objective function accounts for the response costs of responding entities with different response characteristics and the carbon-reduction benefits of demand-side response. Simulation results show that the proposed method better exploits the response capabilities of smart building clusters and improves the adaptability and economy of regulation curves under response-capability uncertainty.