Privacy-Guaranteed Distributed Optimization Algorithms for Power Network Systems

Abstract

As the smart grid becomes more decentralized with the integration of distributed energy resources (DERs), storage devices, and customers, the problems related to power network systems naturally inherits three features: large scale of components, highly variable nature of DERs, and dynamic network topology. In view of optimization, these three features make the traditional centralized optimization techniques impractical, and pose a need to develop distributed methods in grid optimization problems. Motivated by these observations, this dissertation studies the design and analysis of privacy-guaranteed distributed algorithms for the three different optimization problems which arise from power network systems.

In the first part of the dissertation, we propose a distributed algorithmic solution for the economic dispatch problem (EDP), where a group of power generators attempts to achieve power generation-demand balance while minimizing the total generation cost (i.e., sum of the individual costs) and complying with individual generation capacity constraints. The proposed algorithm not only provides the optimal solution of the EDP when it is feasible, but also enables us to detect infeasibility in a distributed sense so that individual systems may cope with such infeasible cases. Moreover, we provide a distributed adaptive method to select the design parameters used for the proposed algorithm, which enables us to implement the proposed algorithm in a fully distributed sense.

One of the key features required for distributed optimization algorithms for power network systems is the expandability since the algorithms must be properly applied to the large-scale systems. Since the large-scale power network systems naturally have hierarchical structure with multiple scales, the second part of the dissertation is devoted to develop a hierarchically distributed algorithm for the optimal generation problem of hierarchical systems (OGP-HS). The proposed distributed algorithm for such hierarchical systems also has a hierarchical structure, which can be naturally implemented in real world systems.

In the last part of the dissertation, we propose an algorithm for the optimal generation and distribution problem (OGDP), which deals with the power generation and distribution while meeting the generation-demand balance.

Since we provide algorithms based on the theory of multi-agent systems for these three problems, the goal of this dissertation is also to develop fundamental theories and techniques that can be used to the synchronization problems of heterogeneous multi-agent systems.