"Optimal Demand Response and Power Flow"

We first propose 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.

This simple model ignores constraints from the underlying power network.  We then formulate the problem with these network constraints and consider optimal power flow (OPF) and VAR control. These problems are well-known nonconvex optimization problems and we propose relaxations that can be solved efficiently.  We prove
conditions under which the relaxations are exact.  In particular, we show that a tree network always has zero duality gap.  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.

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