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

Johns Hopkins University, Baltimore MD

Investigators

Abstract

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.