UC Berkeley

This dissertation focuses on the problem of designing rates in the utility sector. It is motivated by recent developments in the electricity industry, where renewable generation technologies and distributed energy resources are becoming increasingly relevant. Both technologies disrupt the sector in unique ways. While renewables make grid operations more complex, and potentially more expensive, distributed energy resources enable consumers to interact two-ways with the grid. Both developments present challenges and opportunities for regulators, who must adapt their techniques for evaluating policies to the emerging technological conditions.

The first two chapters of this work make the case for updating existing techniques to evaluate tariff structures. They also propose new methods which are more appropriate given the prospective technological characteristics of the sector. The first chapter constructs an analytic tool based on a model that captures the interaction between pricing and investment. In contrast to previous approaches, this technique allows consistently comparing portfolios of rates while enabling researchers to model with a significantly greater level of detail the supply side of the sector. A key theoretical implication of the model that underlies this technique is that, by properly updating the portfolio of tariffs, a regulator could induce the welfare maximizing adoption of distributed energy resources and enrollment in rate structures. We develop an algorithm to find globally optimal solutions of this model, which is a nonlinear mathematical program. The results of a computational experiment show that the performance of the algorithm dominates that of commercial nonlinear solvers. In addition, to illustrate the practical relevance of the method, we conduct a cost benefit analysis of implementing time-variant tariffs in two electricity systems, California and Denmark. Although portfolios with time-varying rates create value in both systems, these improvements differ enough to advise very different policies. While in Denmark time-varying tariffs appear unattractive, they at least deserve further revision in California. This conclusion is beyond the reach of previous techniques to analyze rates, as they do not capture the interplay between an intermittent supply and a price-responsive demand.

While useful, the method we develop in the first chapter has two important limitations. One is the lack of transparency of the parameters that determine demand substitution patterns, and demand heterogeneity; the other is the narrow range of rate structures that could be studied with the technique. Both limitations stem from taking as a primitive a demand function. Following an alternative path, in the second chapter we develop a technique based on a pricing model that has as a fundamental building block the consumer utility maximization problem. Because researchers do not have to limit themselves to problems with unique solutions, this approach significantly increases the flexibility of the model and, in particular, addresses the limitations of the technique we develop in the first chapter. This gain in flexibility decreases the practicality of our method since the underlying model becomes a Bilevel Problem. To be able to handle realistic instances, we develop a decomposition method based on a non-linear variant of the Alternating Direction Method of Multipliers, which combines Conic and Mixed Integer Programming. A numerical experiment shows that the performance of the solution technique is robust to instance sizes and a wide combination of parameters. We illustrate the relevance of the new method with another applied analysis of rate structures. Our results highlight the value of being able to model in detail distributed energy resources. They also show that ignoring transmission constraints can have meaningful impacts on the analysis of rate structures. In addition, we conduct a distributional analysis, which portrays how our method permits regulators and policy makers to study impacts of a rate update on a heterogeneous population. While a switch in rates could have a positive impact on the aggregate of households, it could benefit some more than others, and even harm some customers. Our technique permits to anticipate these impacts, letting regulators decide among rate structures with considerably more information than what would be available with alternative approaches.

In the third chapter, we conduct an empirical analysis of rate structures in California, which is currently undergoing a rate reform. To contribute to the ongoing regulatory debate about the future of rates, we analyze in depth a set of plausible tariff alternatives. In our analysis, we focus on a scenario in which advanced metering infrastructure and home energy management systems are widely adopted. Our modeling approach allows us to capture a wide variety of temporal and spatial demand substitution patterns without the need of estimating a large number of parameters. We calibrate the model using data of appliance ownership, census household counts, weather patterns, and a model of California's electricity network. The analysis shows that the average gains of implementing time-varying rates with respect to a simple flat rate program are rather mild, not greater than 2 dollars per month, even in the scenario in which volumetric charges are allowed to vary freely from hour to hour. Our results also show that factors such as the presence of an air conditioning system and the exterior temperature profile can have a meaningful impact on the surplus gains that different rates generate on households. These two results combined suggest that defaulting all residential customers into a time-of-use rate structure, which is the current path California is following for the residential sector, may not be an optimal strategy. Targeting different rates to households with different appliance stocks and in different locations will likely be a superior policy.