基于非光滑方程组的智能电网实时定价

Research on the real-time pricing of smart grid based on nonsmooth equations

通过研究智能电网实时定价问题,发现通过社会效益模型可以将短时段实时定价问题转化为一个互补问题.根据互补理论和经济学含义,互补问题又可以转化为包含影子价格的非光滑方程组.采用影子价格作为定价基础,通过构造光滑函数逼近非光滑方程组和拟牛顿法求解,得到基础电价.数值仿真表明,新方法下的社会效益与传统固定定价方法下的社会效益相近,但是新方法下的电价更低,计算速度快,收敛性好,数值结果稳定.

Studying the real-time pricing of smart grid, the paper discovers that real-time pricing can be transformed into a complementary problem by the social welfare model. Then, according to the complementary theory and the economic meaning, the complementary problem is transformed into a series of nonsmooth equations. This paper adopts the shadow price as the basic price. A smoothing function is constructed to approximate the nonsmooth parts and then the quasi-Newton method is used to solve for the price. The numerical simulation shows that the social profits of the new method is more but its price is cheaper compared with the traditional fixed method. Our new method is quick, reliable, stable and convergent.