New Mixed-Integer Nonlinear Programming Formulations for the Unit Commitment Problems with Ramping Constraints
提出首个用多项式个变量和约束描述单台热电机组可行解凸包的混合整数非线性规划模型，并推广到多机组问题，经测试优于现有模型。
Mixed-Integer Formulations for Power Production Problems The unit commitment problem is a complex mixed-integer nonlinear program that originates in the field of power production. Although it arises in a monopolistic system, there is still great attention to this problem even in a free-market regime, where it constitutes only a subproblem of larger ones. Historically, it was usually solved by Lagrangian relaxation methods. However, the advances achieved by commercial solvers of mixed-integer (linear and convex) programming problems have made such approaches an attractive option. T. Bacci, A. Frangioni, C. Gentile, and K. Tavlaridis-Gyparakis present the first mixed-integer nonlinear programming formulation with a polynomial number of both variables and constraints that describes the convex hull of the feasible solutions of the unit commitment problem with a single thermal generation unit, comprising all typical constraints and convex power generation costs. Proving that the formulation is exact requires a new result about the convex envelope of specially structured functions that can have independent interest. This new formulation for a single power generation unit is used to derive three new formulations for the general unit commitment problem whose effectiveness has been tested against the state-of-art formulation.