[论文解读] A Game-Theoretic Method for Multi-Period Demand Response: Revenue Maximization, Power Allocation, and Asymptotic Behavior.

Khaled Alshehri, Liu Ji+2 more|arXiv (Cornell University)|Sep 30, 2017

Smart Grid Energy Management被引用 1

一句话总结

本文提出了一种基于斯塔克尔伯格博弈模型的博弈论多时段需求响应框架，其中能源公司设定动态价格，消费者通过优化其需求作出响应。该框架在收益最大化和效用优化方面建立了唯一均衡，并给出了闭式解，通过真实数据案例研究展示了最高达30%的成本节约和较低的价格波动性。

ABSTRACT

By utilizing tools from game theory, we develop a novel multi-period-multi-company demand response framework considering the interactions between companies (sellers of energy) and their consumers (buyers of energy). We model the interactions in terms of a Stackelberg game, where companies set their prices and consumers respond by choosing their demands. We show that the underlying game has a unique equilibrium at which the companies maximize their revenues while the consumers maximize their utilities subject to their local constraints. Closed-form expressions are provided for the optimal strategies of all players. Based on these solutions, a power allocation game has been formulated, which is shown to admit a unique pure-strategy Nash equilibrium, for which closed-form expressions are also provided. This equilibrium is found under the assumption that companies can freely allocate their power across the time horizon, but we also demonstrate that it is possible to relax this assumption. We further provide a fast distributed algorithm for the computation of all optimal strategies using only local information. We also study the effect of variations in the number of periods (subdivisions of the time horizon) and the number of consumers. As a consequence, we are able to find an appropriate company-to-consumer ratio when the number of consumers participating in demand response exceeds some threshold. Furthermore, we show, both analytically and numerically, that the multi-period scheme provides incentives for energy consumers to participate in demand response, compared to the single-period framework studied in the literature. In our framework, we provide a condition for the minimum budgets consumers need, and carry out case studies using real life data to demonstrate the benefits of the approach, which show potential savings of up to $30\%$ and equilibrium prices that have low volatility.

研究动机与目标

• 开发一种多时段需求响应框架，通过博弈论建模能源公司与消费者之间的战略互动。
• 在确保消费者在本地约束下实现效用最大化的前提下，最大化能源公司的收益。
• 设计一种电力分配博弈，在动态定价下存在唯一纯策略纳什均衡。
• 当消费者参与度超过某一阈值时，确定最优的公司与消费者比例。
• 提出一种分布式算法，仅通过本地信息交换即可计算最优策略。

提出的方法

• 将公司与消费者之间的互动建模为斯塔克尔伯格博弈，其中公司作为领导者，消费者作为跟随者。
• 在时变约束条件下，通过均衡分析推导出最优定价和需求策略的闭式解。
• 引入一种电力分配博弈，公司通过在不同时段分配电力以实现收益最大化。
• 证明了电力分配博弈中存在唯一纯策略纳什均衡。
• 提出一种快速分布式算法，仅通过本地信息交换即可计算最优策略。
• 分析时间跨度离散化（时段数量）和消费者数量对系统性能的影响。

实验结果

研究问题

• RQ1 能源公司如何在多个时段内动态设定价格，以在确保消费者参与的前提下最大化收益？
• RQ2 在多时段需求响应设置中，消费者对时变价格的均衡行为是什么？
• RQ3 在何种条件下，电力分配博弈存在唯一纯策略纳什均衡？
• RQ4 当消费者参与度超过临界阈值时，最优的公司与消费者比例如何确定？
• RQ5 与单时段模型相比，多时段框架在成本节约和价格稳定性方面表现如何？

主要发现

• 所提出的斯塔克尔伯格博弈框架实现了唯一均衡，公司在该均衡下实现收益最大化，消费者在本地约束下实现效用最大化。
• 电力分配博弈存在唯一纯策略纳什均衡，且最优策略具有闭式表达式。
• 多时段方案为消费者参与提供了强激励，在成本效率方面优于单时段框架。
• 基于真实数据的案例研究显示，消费者最高可实现30%的能源成本节约。
• 均衡价格表现出较低的波动性，表明在所提框架下市场具有稳定性。
• 当消费者参与度超过某一阈值时，可确定最优的公司与消费者比例，从而提升系统效率。