基于分片线性效用函数的实时电价定价策略

Real-time Pricing Strategy for Smart Grid with the Piecewise Linear Utility Function

智能电网社会福利最大化模型中,目前主要使用二次效用函数,对数效用函数等来刻画用户的用电满意程度。这些效用函数对不同的用户偏好来说不具备一般性,在求解时需要分类进行讨论。针对此问题,提出一个具有一般性质、更加贴近实际的分片线性效用函数。对分片线性效用函数进行光滑化,将社会福利最大化模型转化为可微的凸优化问题。针对此问题设计对偶次梯度算法求出实时电价,并通过数值仿真验证了所建模型的合理性以及算法的有效性和可行性。

In the social welfare maximization model of smart grid,the quadratic utility function and logarithmic utility function are used to describe the satisfaction degree of users’ power consumption.These utility functions are not general for different user preferences,and they need to be discussed in classification when solving.To overcome this problem,apiecewise linear utility function with general property and more closer to reality is proposed in social welfare maximization model.Furthermore,smoothing the piecewise linear utility function can transform the social welfare maximization model into a differentiable convex optimization problem.In order to solve this problem,a dual sub-gradient algorithm is proposed.The rationality of the model and the validity and feasibility of the algorithm are verified by numerical simulation.