[论文解读] Practicality of Nested Risk Measures for Dynamic Electric Vehicle Charging

Daniel Jiang, Warren B. Powell|arXiv (Cornell University)|May 10, 2016

Electric Vehicles and Infrastructure参考文献 60被引用 11

一句话总结

本文提出一种基于嵌套风险度量的风险规避动态规划方法——具体为期望成本与条件风险价值（CVaR）的凸组合——以优化公共充电站的电动汽车（EV）充电调度。结果表明，在马尔可夫决策过程（MDP）框架中提高风险规避程度，可降低实际风险并提升真实成本与服务目标下的盈利能力，数值实验显示在适度风险容忍度下采用动态充电可获得显著收益。

ABSTRACT

We consider the sequential decision problem faced by the manager of an electric vehicle (EV) charging station, who aims to satisfy the charging demand of the customer while minimizing cost. Since the total time needed to charge the EV up to capacity is often less than the amount of time that the customer is away, there are opportunities to exploit electricity spot price variations within some reservation window. We formulate the problem as a finite horizon Markov decision process (MDP) and consider a risk-averse objective function by optimizing under a dynamic risk measure constructed using a convex combination of expected value and conditional value at risk (CVaR). It has been recognized that the objective function of a risk-averse MDP lacks a practical interpretation. Therefore, in both academic and industry practice, the dynamic risk measure objective is often not of primary interest; instead, the risk-averse MDP is used as a computational tool for solving problems with predefined "practical" risk and reward objectives (termed the base model). In this paper, we study the extent to which the two sides of this framework are compatible with each other for the EV setting -- roughly speaking, does a "more risk-averse" MDP provide lower risk in the practical sense as well? In order to answer such a question, the effect of the degree of dynamic risk-aversion on the optimal MDP policy is analyzed. Based on these results, we also propose a principled approximation approach to finding an instance of the risk-averse MDP whose optimal policy behaves well under the practical objectives of the base model. Our numerical experiments suggest that EV charging stations can be operated at a significantly higher level of profitability if dynamic charging is adopted and a small amount of risk is tolerated.

研究动机与目标

• 探究使用嵌套风险度量的风险规避动态规划目标与电动汽车充电管理中实际性能指标的兼容性。
• 确定在MDP框架中提高风险规避程度是否可降低实际风险并提升真实世界EV充电运营中的盈利能力。
• 提出一种系统性近似方法，识别出其最优策略在基础模型实际目标下表现良好的风险规避MDP实例。
• 通过真实世界节点电价数据与EV充电动态的数值实验验证理论发现。

提出的方法

• 将EV充电问题建模为有限时域马尔可夫决策过程（MDP），并引入结合期望成本与CVaR的动态风险度量。
• 采用期望值与CVaR的凸组合作为风险规避目标函数，由风险规避水平β参数化。
• 应用动态规划递推公式推导值函数，并推导最优策略在风险规避程度下单调的条件。
• 提出一种系统性近似方法，将风险规避MDP的解映射为在基础模型实际成本与服务目标下表现良好的策略。
• 通过理论分析证明，充电阈值在风险规避程度上非递减，且在资源单调性条件下满足风险兼容性。
• 通过真实节点电价数据的数值实验验证结果，显示在小风险容忍度下采用动态充电可获得性能提升。

实验结果

研究问题

• RQ1 在风险规避MDP中提高风险规避程度是否可降低真实EV充电运营中的实际风险？
• RQ2 风险规避MDP目标在多大程度上与EV充电中的实际成本与服务性能指标兼容？
• RQ3 能否通过系统性近似方法识别出其最优策略在基础模型实际目标下表现良好的风险规避MDP实例？
• RQ4 在MDP框架中，最优策略的行为如何随风险规避程度的变化而改变？
• RQ5 在小风险容忍度下采用动态充电对充电站的盈利能力与风险暴露有何影响？

主要发现

• 在MDP框架中提高风险规避程度可使充电阈值非递减，表明充电行为更加保守。
• 由风险规避MDP导出的最优策略表现出风险兼容性，即更高的风险规避程度在基础模型性能指标下导致更低的实际风险。
• 值函数对状态的导数在风险参数上非递增，证实了风险规避程度下的单调性。
• 数值实验表明，当采用动态充电并容忍少量风险时，EV充电站可实现显著更高的盈利能力。
• 所提出的近似方法成功识别出其策略在实际目标下表现良好的MDP实例，验证了该框架的实际应用价值。
• 理论分析证实，风险规避MDP框架与真实世界目标兼容，尤其在考虑风险与性能指标单调性时更为显著。