UC Berkeley

Contemporary power systems are characterized by increasing penetrations of renewable and distributed energy resources (DERs), which present both opportunities and challenges for reliable system operation. Uncertainty in renewable generation must be managed over both shorter and longer timescales, necessitating greater flexibility in the supply and demand of electricity. Fortunately, this rise in renewables has been accompanied by the growth of flexible energy resources such as energy storage and aggregated demand flexibility. However, these assets are generally not adequately integrated into existing electricity market structures leading to many benefits of their flexibility going unrealized. Additionally, distributed energy resources, such as rooftop solar and electric vehicles, present a challenge to the traditional top-down management of power systems, requiring new decentralized control and market architectures to ensure their safe operation and to maximize their value.

This dissertation tackles a range of questions relating to the integration of flexible and distributed resources into electricity markets in the presence of uncertainty, using techniques from control theory, game theory, multiparametric programming, and distributed optimization.

The main contributions of this dissertation encompass novel analysis and design of markets, both centralized and decentralized, that explicitly integrate distributed and flexible resources, numerical methods providing exact solutions to multi-leader follower equilibrium problems among strategic bidders, and insights into the role of virtual bidders in managing demand uncertainty in two-stage markets.

Chapter 1 introduces the context for the dissertation, describing trends driving the energy industry and the challenges and opportunities they pose. Current practice and existing literature are described with regard to uncertainty, flexibility, and decentralized markets and control. Chapter 2 lays out the mathematical background for the dissertation, describing models for power flow, electricity markets, and market participants, in addition to the theory of multiparametric programming. Chapter 3 demonstrates the equivalence of virtual bidding and stochastic optimization in two-stage markets under certain conditions. It also characterizes the equilibrium of a crowd of virtual bidders with heterogeneous beliefs and explores simple learning strategies for virtual bidders to reach equilibrium. Chapter 4 studies robust Cournot-Bertrand equilibria among generation firms. Firms anticipate demand and renewable uncertainty and optimize their actions to ensure their profits are robust to this uncertainty. The chapter concludes by discussing the effects on market outcomes of this behavior. Chapter 5 addresses the more general topic of strategic bidding by generation firms in electricity markets. This question involves solving non-convex bilevel optimization problems, which form part of the wider class of multi-leader follower problems. Both the single firm problem, constituting an MPEC, and the multi-firm equilibrium problem, constituting an EPEC, are solved exactly using techniques from multiparametric programming. This latter contribution, in particular, represents a significant advance over current methods, generalizing the solution of supply function equilibrium problems to cases with asymmetric players and transmission constraints. Chapter 6 analyzes a number of regulatory models for the integration of energy storage into wholesale electricity markets, including Open Access Storage, and investigates the implications and incentives of a variety of storage ownership structures under each model. Chapter 7 demonstrates the potential of load flexibility for congestion relief, defining the notion of a congestion-free dispatch. Chapter 8 describes the design of a decentralized coordination mechanism for DERs in a microgrid using blockchain technology. The implementation uses ADMM with a smart contract on the blockchain serving as the ADMM coordinator. Chapter 9 illustrates the design of an open-gate forward market with specific flexibility products for DERs, allowing users to hedge better against uncertainty and correctly express and maximize the value of their flexibility. A number of algorithms are presented to address the combinatorial scheduling and pricing problem involved with flexible loads.