Speaker: Steven H. Low <?xml:namespace prefix = o />

Professor, Computer Science and Electrical Engineering, California Institute of Technology, Pasadena, CA

Presentation Title: Optimal Power Flow and Demand Response

Optimal power flow (OPF) problems determine the most efficient power generations, reactive powers for voltage support, or demand response. They are well-known to be nonconvex and hence NP hard. In the first part of the talk, we propose relaxations that can be solved efficiently, focusing on radial networks.  Recently a sufficient condition is proved for general mesh network under which a semidefinite relaxation is exact. We prove that, if the network is radial (tree), then the sufficient condition is always satisfied and hence the semidefinite relaxation is always exact, provided the constraints on power flows satisfy a simple pattern. Using the branch flow model for radial networks, we propose a simple SOCP relaxation to OPF, and prove that it is exact. We apply this result to control voltage and reactive power in distribution networks, and present results from realistic simulation of a Southern California distribution circuit.

In the second part of the talk, we describe a simple model that integrates two-period electricity markets, uncertainty in renewable generation, and real-time dynamic demand response. A load serving entity decides its day-ahead procurement to optimize expected social welfare a day before energy delivery. At delivery time when renewable generation is realized, it coordinates with users, in a decentralized manner, to manage load and purchase real-time balancing power in the real-time market, if necessary. We derive the optimal day-ahead decision, propose real-time demand response algorithm, and study the effect of volume and variability of renewable generation on the optimal social welfare.

(Joint work with Subhomesh Bose, Mani Chandy, Masoud Farivar, Lingwen Gan, Dennice Gayme, Libin Jiang, Javad Lavaei, Caltech, and Chris Clarke, SCE.)