带阀点效应水火联合调度问题的一种半定凸松弛求解法

A Semidefinite Convex Relaxation Method for Hydrothermal Coordination with Valve Point Effect

水火联合调度问题是电力系统中一类复杂的优化问题。合理安排调度周期内的水火电出力,确定一个最优发电计划,可以带来巨大的经济效益。在实际系统中,汽轮机调汽阀开启时出现的拔丝现象会使机组耗量特性产生阀点效应。忽略阀点效应,在一定程度上降低求解的精度。本文考虑带阀点效应的水火联合调度问题。该问题非凸非光滑,且带有非线性约束,直接使用确定性全局优化方法求解是相当困难的。本文使用高效的半定规划求解此问题。首先用耗量特性函数的初始周期代替其余有限的周期,并对其进行二次拉格朗日插值拟合。再通过引进0-1变量,得到整个耗量特性函数的近似,进而把问题松弛为半定规划模型。最后,采用凸规划应用软件包CVX求解一个仿真算例,得到一个近似全局最优解。

Hydrothermal coordination is one of optimization problems with complexity in power system.If we can well arrange the hydro and thermal resources during a scheduling period and determine an optimal generation scheduling,it can bring huge economic benefits.In reality,the wire drawing effect,occurring as each steam admission valve in a turbine starts to open,produces a valve point effect on the cost curve.Ignoring the valve point effect,to a certain extent,the accuracy of solution will be reduced.In this paper,we consider the problem about hydrothermal coordination problem with valve point effect.That is a non-convex and non-smooth with non-linear constraints issue.It is very difficult to solve it by deterministic global optimization methods.This paper uses the efficient semidefinite programming to solve this problem.Firstly,the limited periods of cost function are replaced by its primitive period.Then it is interpolated by quadratic Lagrange function.By introducing 0-1 variables,one can get the approximation of the whole cost function.Thus the problem can be relaxed into a semidefinite programming model.Finally,a convex programming application package CVX is used to solve a simulation example.Then an approximate global optimal solution is obtained.