2012 Poster Sessions : Message Passing for Dynamic Network Energy Management

Student Name : Eric Chu, Matt Kraning
Advisor : Stephen Boyd
Research Areas: Information Systems
We consider a network of dynamic devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and ob- jective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints. This is a large optimization problem, with variables for consumption or generation in each time period, for each device. In this paper we develop a decentralized method for solving this problem. The method is iterative: At each step, each device exchanges simple messages with its neighbors in the network, and then solves its own dynamic optimization problem, minimizing its own objective function, augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized, and needs no global coordination other than synchronizing iterations; the problems to be solved by each device can typically be solved extremely efficiently, and in parallel. The method is fast enough that even a serial implementation can solve substantial problems in reasonable time frames. We report results for several numerical experiments, demonstrating the method’s speed and scaling, including the solution of a problem instance with 107 variables in around an hour for a serial implementation; with decentralized computing, the solve time would be measured in seconds.

Matt Kraning is a fourth year Ph.D. candidate in the Electrical Engineering Department at Stanford University, advised by Professor Stephen Boyd. His research investigates applications of convex optimization for the smart grid.

Eric Chu is a fourth-year PhD candidate in the Electrical Engineering department at Stanford. He is co-advised by professors Stephen Boyd and Dimitry Gorinevsky. His research interests are in distributed optimization and large-scale data analysis.