We present two recent results. In the first result, we use a continuous linearized power flow model for distribution networks and derive the optimal sizing of distributed energy storage devices to minimize power loss and prove several monotonicity properties of the optimal solution when all loads have the same shape. We show through simulations that these structural properties hold approximately in standard discrete nonlinear power flow models, even when loads have different shapes. In the second result, we describe a recent method for computing power flow solutions using monotone operators. The basic idea is to embed an operationally relevant space in a domain of voltages over which the power flow operator is monotone. Such domains are non unique and we show that at most one power flow solution exists in each of these domains. Efficient algorithms, based on solving an associated monotone variational inequality, can compute power flow solutions in the monotonicity domain or certify that none exists in the monotonicity domain. (Joint work with Yujie Tang (Caltech), Krishnamurthy Dvijotham (PNNL), Michael Chertkov (ANL))
About the SmartGrid Seminar:
Our speakers will discuss exciting new ideas and technologies that are changing the electricity industry. The theme of the seminar series is on smart grids and energy systems, with speakers from academic institutions and industry. The hour-long seminars, including ample time for discussion, are held at 1:30 pm every Thursday. Open to all Stanford students, faculty and staff.
Steven Low is a Professor of the Department of Computing & Mathematical Sciences and the Department of Electrical Engineering at Caltech. Before that, he was with AT&T Bell Laboratories, Murray Hill, NJ, and the University of Melbourne, Australia. He was a co-recipient of IEEE best paper awards, is Senior Editors of IEEE transactions, and an IEEE Fellow. He was a member of the Networking and Information Technology Technical Advisory Group for the US President's Council of Advisors on Science and Technology (PCAST) in 2006. He received his B.S. from Cornell and PhD from Berkeley, both in EE.
Steven would love to meet undergrads who might be intreated in doing Ph.D. in the energy direction at Caltech. If you have an interest, please contact Yang Weng (firstname.lastname@example.org) for an arrangement.