求解大规模机组组合问题的二阶锥规划方法

Solution of Large Scale Unit Commitment by Second-order Cone Programming

基于混合整数二阶锥规划(mixed integer second-order cone programming,MI-SOCP)提出一种求解电力系统计及爬坡约束机组组合问题(unit commitment,UC)的新方法。利用UC问题的混合整数二次规划(mixed integer quadratic programming,MI-QP)模型和一个简单混合整数集合的凸包表示,产生UC问题一个更紧的MI-SOCP模型。将最小覆盖不等式作为割平面,应用内点割平面法求解MI-SOCP以获得不计爬坡约束UC问题的机组启停状态。为满足爬坡约束,提出一种简单易行的机组启停状态修正方法。100机组96时段等多个系统的仿真结果表明,利用内点割平面法求解2种模型时,MI-SOCP能比MI-QP获得质量更好的次优解,所提方法能有效处理爬坡约束,适用于大规模的UC问题。

A new algorithm based on mixed integer second-order cone programming （MI-SOCP） was presented to solve ramp rate constrained unit commitment （UC） problem of power system. The proposed method involves reformulating the UC problem into a tighter MI-SOCP model by integrating the traditional mixed integer quadratic programming （MI-QP） model and the convex hull description of a simple mixed integer set. Using the minimal cover inequality as cutting plane, the proposed approach applied interior point cutting plane method for the MI-SOCP in order to obtain the on/off status of units without ramp rate constraints. To meet the ramp rate constraints, a simple correction technique for the on/off status of the units was introduced. The simulation results for systems up to 100 units and 96 hours not only show that the MI-SOCP can get better sub-optimal solutions of the UC problem than the MI-QP when interior point cutting plane method is used, but also show that the proposed method can handle the ramp rate constraints efficiently and is suitable for large scale UC problems.