峰谷分时电价借助价格信号引导用户合理分配一天中不同时段的用电量，从而实现削峰填谷，提升电网系统的稳定性。但是在电力市场中，不同行为人之间存在复杂的行为交互，给峰谷时段的划分、各时段电价的设定带来一定困难。本文研究了在包含批发市场和零售市场的电力系统中，在批发电价、分时零售电价、各时刻用户用电量三者相互影响的情况下，峰谷分时电价的定价策略。借助博弈模型建模上述电力系统：使用两人议价博弈建模发电厂与零售商之间关于批发电价的协商过程，使用斯塔克尔伯格博弈建模零售商与用户之间针对零售电价、用电需求的调整过程。对于电价时段的划分，模糊聚类方法可以较好地解决峰平谷时段边界的模糊性问题；而各时段电价的定价问题可以转化为一个带有隐函数的双层优化问题，从而求得最优闭式解。文章探究了不同用户类型、初始用电量以及峰谷电价比例限制对电价的影响，模拟实验验证了本文方法的有效性。

    Peak-valley time-of-use (TOU) pricing impacts customers’ power consumption behaviors by means of tiered pricing, incentivizing less usage during peak periods and more usage during valley ones. Not only can it optimize electricity usage efficiency, but it can also improve stability of the power grid. However, complex economic interactions among electricity generators, retailers, and users could cause difficulties in defining peak, flat, and valley periods, as well as pricing each of them. 

    This paper focuses on the electricity system consisting of both wholesale markets and retail markets, to set reasonable peak-valley TOU prices in the consideration of interrelationships among wholesale price, TOU prices and customers’ electricity demands at different time periods. Game theory is introduced to model the system: the negotiation on wholesale price between generators and retailers is modeled with a two-person bargaining game, while the adjustments on TOU retail prices and customers’ electricity demands is modeled with a Stakelberg game.

    Regarding to the problem of defining peak-valley periods, fuzzy clustering helps to solve the fuzziness in this problem. As for the pricing problem, it is solved by, transformed into a bilevel optimization problem with implicit function. And the closed-form solution can be obtained. Detailed mathematical derivation and extensive experimental results prove the effectiveness of methods proposed.