On Distributed Optimization Methods for Solving Optimal Power Flow Problem over Electricity Grids

Open Access
Zhang, Jinwei
Graduate Program:
Industrial Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 08, 2016
Committee Members:
  • Necedt Serhat Aybat, Thesis Advisor
  • Optimal Power Flow
  • Multi-agent Consensus Model
  • Distributed Optimization
  • Composite Convex Function
  • linearized ADMM
  • augmented Lagrangian
The optimal power flow (OPF) problem seeks to find the optimal settings of a given power system network that optimize particular system objectives such as minimizing the generation cost or power loss in the network. The OPF problem is nonconvex and generally hard to solve. Numerous mathematical optimization methods have been studied and the conditions on the power networks that ensure the OPF can be solved in polynomial time have been analyzed. Because of the improvements in acquisition and storage technologies, distributed collection of huge amounts of data in power system is possible; and there is increasing awareness that the statistical and computational algorithms should be designed to work in a decentralized manner so that they can be implemented on problems with distributed data, not stored at a central location, due to memory issues and/or privacy requirements. In this thesis, the OPF network is modeled as a graph G={N, E} of buses N={1,..,n} connected with branches in E. The objective function is modeled as composite convex functions {F(i)=xi(i)+f(i):i=1,...,n} with non-smooth part xi(i) and smooth part f(i), respectively. We show that the distributed first-order augmented Lagrangian (DFAL) and distributed linearized alternating direction method of multipliers with proximal gradient (PG-ADMM) can effectively solve OPF problem under the simple assumption that only the buses connected by a branch can exchange state information. These two methods are implemented in MATLAB to solve OPF consensus formulations. The numerical computation results are given to examine the convergence behavior of each algorithm.