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发电的性质，其单个设施非常小，不受运营商控制，并且位于电表的消费者侧或低压电网上。该项目的目标是，一方面，计算消费者在分布式发电中的最佳投资，同时允许在负荷聚合计划中注册的可能性。另一方面，我们的目标是为电力公司提供一种有效和透明地计算用于收回网络投资的配电费用的方法，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策，以及可能与电网断开连接。除了在应用数学课程中创建额外的课程外，预计该项目还将通过告知他们对费率监管与未来需求和分布式发电的相互作用的理解，为公用事业和监管机构带来机会和联系。动态需求将被用来从消费者的角度构造优化问题。这些问题将在有和没有分布式发电的不同情况下得到解决。对于每一种情况下，一个系统的多个异质consumers.Dynamic相互作用与公用事业ratemaking政策，包括反馈，如著名的“死亡螺旋”的均衡解将被发现。将评估为分销投资和运营融资的替代利率政策的稳定性、经济效率、客户类别之间的公平性以及零售利率监管的其他目标。任何一种利率管制政策都不可能在所有目标中都是最好的，因此有必要考虑权衡。由此产生的见解将有益地告知政策讨论的监管和定价的配电功能的电力公用事业。拟议的框架将包括基本的，简单的，但易于处理的模型，一般的分析结果可以得出。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。该项目将展示如何现代金融数学，效用优化，动态规划，集成真实的期权和模拟，可以用来建立更现实的模型，在风险规避和短期价格波动下，配电收费与消费者决策的动态相互作用。此外，该框架将包括长期不确定性，例如，技术和政策的变化。

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.