UC San Diego

The share of renewable energy generation in meeting our electricity needs is growing by the day. A majority of these renewables have small generation capacity and they are geographically distributed. It is for this reason that they are often termed as distributed energy resources (DERs). In addition to the capacity constraint, DERs' generation is highly variable and uncertain. The current electricity grid, on the other hand, was designed for centralized bulk generation. Therefore, regulating authorities like the Independent System Operator (ISO) or the Regional Transmission Organization (RTO) find it quite challenging to seamlessly integrate these DERs into the current grid, without affecting the quality of service to consumers. As one of the measures of tackling this issue, regulating authorities envision a hierarchical architecture where, at the lower layer, different sets of distributed energy resources (DERs) coordinate their response under an aggregator and, at the upper layer, the ISO interacts (through a market) with the aggregators to solve the optimal dispatch problem. In this scenario, aggregators function as virtual, large-capacity generators. While the DERs under one aggregator can cooperate among themselves, the aggregators compete with each other in the market. Given this context, this thesis designs and analyzes coordination among DERs and competition among aggregators.

Specifically, the thesis can be divided into three parts. The first part focusses on the static and the dynamic optimal dispatch problems, where the aim for a set of DERs is to plan their generation so as to meet a particular load, minimize the total cost of generation, and respect individual constraints. For these optimization problems we design a suit of Laplacian-gradient based distributed algorithmic solutions and study their performance. The second part studies the asymptotic convergence and robustness properties of the saddle-point dynamics. This dynamics serves as the backbone of numerous distributed algorithms for network constrained optimization problems, including the dispatch problem. Finally, the third part investigates an electricity market designed for optimal dispatch among the aggregators. We design and analyze an iterative bid update scheme for the aggregators, discussing the advantages of this scheme using rationality and robustness arguments.