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

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.