AMPS: Financial Mathematics to Identify Optimal Electricity Distribution Pricing under Risk, High Photovoltaics Penetration, and Consumer Aggregation

随着分布式发电（如屋顶太阳能光伏发电）的日益普及，消费者和公用事业公司面临着新的运营和规划挑战。这些挑战来自于这一代人的性质，他们的个人设施非常小，不受运营商的控制，以及它的位置，要么在电表的消费者一侧，要么在低压电网上。这个项目的目标是，一方面，计算消费者对分布式发电的最佳投资，同时允许在负荷聚合计划中登记的可能性。另一方面，我们的目标是为电力公司提供一种有效和透明的方法来计算他们的分配费用，用于收回他们的网络投资，并了解这些费用的水平和形式如何影响消费者投资分布式能源的决定，甚至可能与电网脱节。除了在应用数学课程中开设一门额外的课程外，预计该项目还将使公用事业和监管机构了解费率监管与未来需求和分布式发电之间的相互作用，从而为他们带来机会和联系。从消费者的角度出发，将使用具有随机动态需求的可处理的、前瞻性的收入轨迹框架来构建优化问题。这些问题将在使用和不使用分布式发电的不同场景中得到解决。对于每个场景，将找到具有多个异构消费者的系统的平衡解决方案。与公用事业费率制定政策的动态互动，包括反馈，如著名的“死亡螺旋”，都是有代表性的。将从稳定性、经济效率、客户阶层之间的公平性以及零售利率监管的其他目标等方面对融资分销投资和运营的替代利率政策进行评估。任何一项利率监管政策都不太可能在所有目标中都是最佳的，因此有必要考虑权衡。由此产生的见解将有用地为有关电力公用事业分配函数的监管和定价的政策讨论提供信息。拟议的框架将包括基本的、简单的但易于处理的模型，从中可以得出一般的分析结果。这些反过来将为更精细的模拟模型提供基础，这些模型将根据历史准确性进行校准，并允许更复杂和更现实的假设，例如考虑长期技术、财产价值、政策不确定性和次优决策行为。该项目将展示如何使用现代金融数学、效用优化、动态规划、整合实物期权和模拟，来建立更现实的模型，以了解在风险规避和短期价格波动下，配电充电与消费者决策的动态交互作用。此外，该框架将包括诸如技术和政策变化等较长期的不确定性。

With an increase in popularity of distributed generation, such as rooftop solar Photovoltaics, consumers and utilities are faced with new operations and planning challenges. These challenges arise from the nature of this generation, whose individual facilities are very small and not controlled by the operator, and where it is sited, either on the consumer's side of the power meter or on the low-voltage grid. The goal of this project is, on the one hand, to calculate the optimal investment by consumers in distributed electricity generation, while allowing for possibility of an enrollment in a load aggregation program. While on the other hand, the goal is to provide a way for the power utilities to efficiently and transparently calculate their distribution charges used to recover their network investment, and to understand how the level and form of those charges affects consumer decisions to invest in distributed energy and perhaps disconnect from the grid. In addition to the creation of an additional course in the applied mathematics curriculum, it is expected that this project will also lead to opportunities and connections with both utilities and regulators, by informing their understanding of interactions of rate regulation and future demand and distributed generation.A framework of tractable, forward-looking revenue trajectories with stochastic, dynamic demand will be used to construct optimization problems from a consumer's point of view. These will be solved in different scenarios with and without distributed generation. For each scenario, an equilibrium solution for a system with multiple heterogeneous consumers will be found. Dynamic interactions with utility ratemaking policies, including feedbacks such as the famous 'death spiral', are represented. Alternative rate policies for financing distribution investment and operations will be evaluated for their stability, economic efficiency, fairness among customer classes, and other objectives of retail rate regulation. It is unlikely that any one rate regulation policy will be best in all objectives, so it will be necessary to consider tradeoffs. The resulting insights will usefully inform policy discussions about regulation and pricing of the distribution function of electric utilities. The proposed framework will include basic, simple but tractable models for which general analytical results can be derived. These in turn will provide the basis for more elaborate simulation models that will be calibrated for historical accuracy and allow for a more complicated and realistic assumptions, such as consideration of long run technology, property value, and policy uncertainties and sub-optimal decision behavior. The project will demonstrate how modern Financial Mathematics, utility optimization, dynamical programming, integrating real options, and simulation, can be used to build more realistic models of the dynamic interaction of electric distribution charging with consumer decision making under risk aversion and short-run price volatility. In addition the framework will include longer-run uncertainties about, e.g., technology and policy changes.