智能电网光滑化逼近实时定价  

Real-Time Pricing of Smart Grid Based on Smooth Approximation

作　　者：屈德强 李军祥[1] 尚有林[2] 李媛媛 罗世昌 QU Deqiang;LI Junxiang;SHANG Youlin;LI Yuanyuan;LUO Shichang(Business School&School of Intelligent Emergency Management,University of Shanghai for Science and Technology,Shanghai 200093;School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023)

机构地区：[1]上海理工大学管理学院和智慧应急管理学院,上海200093 [2]河南科技大学数学与统计学院,洛阳471023

出　　处：《系统科学与数学》2025年第1期145-156,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(72071130,71871144,12071112);河南省高等学校重点科研项目计划基础研究专项(20ZX001);上海理工大学大学生创新训练计划项目(XJ2024137)资助课题。

摘　　要：智能电网实时定价是维护电力系统稳定,引导用户合理用电,进而达到削峰填谷、节能减排目的的重要手段.在追求社会福利最大化的基础上,建立了商业用户的实时定价模型.由于模型是凸优化问题,其与相应的KKT系统同解.借助非线性互补函数可将KKT系统等价转化为非线性方程组,但非线性互补函数通常非光滑,导致等价的非线性方程组非光滑,难以应用基于梯度信息的高效求解算法.非线性互补函数的光滑逼近可以克服这一难题,但逼近误差会影响解的精度.为了减小逼近误差,提出一个新的光滑逼近函数光滑化方程组,并利用光滑牛顿算法进行求解.同已有算法进行比较,文章算法求解速度更快且解的精度更高,和固定电价机制的对比表明文章提出的实时定价机制是合理的.In smart grid,as an important way to maintain the stability of power system,real-time pricing guides users to use electricity reasonably,and then achieves the purposes of peak shaving,valley flling,energy conservation and emission reduc-tion.On the basis of pursuing the maximization of social welfare,a real-time pricing model for commercial users is established.Since the model is a convex optimiza-tion problem,it is solved identically to the corresponding KKT system,which can be equivalently transformed into a system of nonlinear equations via nonlinear com-plementary functions.However,the nonlinear complementary functions are usually non-smooth,which results in a non-smooth system of equivalent nonlinear equations,and it is difficult to apply efficient solving algorithms based on the gradient informa-tion.Smooth approximation of the nonlinear complementary functions can overcome this dificulty,but the approximation error affects the accuracy of the solution.To reduce the approximation error,a new smooth approximation function for smoothing the equivalent system of equations is proposed,and the smooth Newton algorithm is used to solve the smooth equation system.Compared with the existing algorithm,the proposed algorithm has faster solution speed and higher solution accuracy,and the comparison with the fixed electricity price mechanism indicates that the proposed real-time pricing mechanism is reasonable.

关 键 词：实时定价 KKT条件 非线性互补函数 光滑逼近函数 光滑牛顿算法 

分 类 号：TM76[电气工程—电力系统及自动化] O224[理学—运筹学与控制论]