Convex Hull Model for Optimal Self‐Scheduling of the Thermal Unit Considering Deep Peak Regulation

ABSTRACT Optimal self‐scheduling of the thermal unit (OSSTU) is typically formulated as a mixed‐integer linear programming (MILP), which is NP‐hard. When deep peak regulation (DPR) is considered, additional integer variables are introduced, significantly increasing the computational burden. To address this challenge, this paper proposes a convex hull formulation to precisely and efficiently solve the OSSTU considering DPR. To be more specific, we prove that the optimal power outputs of the DPR‐constrained OSSTU lie within a finite discrete set. Based on this structure, the original MILP can be reformulated as a backward dynamic programming problem, which is further transformed into a tractable linear programming (LP). Then, the optimal self‐scheduling strategy is obtained from the dual solution of the LP, ensuring that the proposed method can solve this problem in polynomial time. Numerical experiments validate its effectiveness.