Chapter 6 - Decomposition Methods for Distributed Optimal Power Flow: Panorama and Case Studies of the DC Model

Abstract

Efficient and well-designed optimization tools are necessary to determine an economically efficient operating point of the power systems in a timely fashion, while maintaining the generation-load balance in the system. In this regard, the optimal power flow (OPF) analysis is widely used by system operators to minimize the grid-wide generation cost and active power losses subject to the physical and operational constraints of the underlying network. The OPF problem can suffer from high computational complexity in large power networks. Hence, centralized optimization techniques are not the proper choice to deal with large-scale OPF problems with thousands of decision variables and constraints. Moreover, centralized approaches require real-time information on the decision-making parameters of the generators and load demands, which are not generally available to the system operators due to privacy concerns. In this chapter, we focus on distributed/decentralized approaches to solve the OPF problem in a power system. To this end, we take advantage of the widely used DC power flow formulation, which is a simplified power flow model with an acceptable approximation for transmission networks. We first review the state-of-the-art decomposition techniques to address the scalability of the OPF analysis in the general case. Then, we discuss the application of the Lagrangian relaxation (LR) decomposition and augmented LR in designing decentralized OPF algorithms for the DC model. We also introduce a consensus-based distributed optimization method to deal with the OPF problem.