Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems

TL;DR

This paper introduces initialization-free, scalable distributed algorithms for resource allocation that ensure feasibility and optimality, with applications to power system economic dispatch, accommodating changing environments without re-initialization.

Contribution

The paper proposes novel continuous-time distributed algorithms based on projection methods that are initialization-free and scalable, suitable for dynamic network environments.

Findings

Guaranteed convergence for strictly convex objectives.

Exponential convergence for strongly convex functions.

Successful application to power grid economic dispatch.

Abstract

In this paper, the distributed resource allocation optimization problem is investigated. The allocation decisions are made to minimize the sum of all the agents' local objective functions while satisfying both the global network resource constraint and the local allocation feasibility constraints. Here the data corresponding to each agent in this separable optimization problem, such as the network resources, the local allocation feasibility constraint, and the local objective function, is only accessible to individual agent and cannot be shared with others, which renders new challenges in this distributed optimization problem. Based on either projection or differentiated projection, two classes of continuous-time algorithms are proposed to solve this distributed optimization problem in an initialization-free and scalable manner. Thus, no re-initialization is required even if the operation environment or network configuration is changed, making it possible to achieve a "plug-and-play" optimal operation of networked heterogeneous agents. The algorithm convergence is guaranteed for strictly convex objective functions, and the exponential convergence is proved for strongly convex functions without local constraints. Then the proposed algorithm is applied to the distributed economic dispatch problem in power grids, to demonstrate how it can achieve the global optimum in a scalable way, even when the generation cost, or system load, or network configuration, is changing.