  As independent service providers shift from conventional energy to renewable
energy sources, the power distribution system will likely experience
increasingly significant fluctuation in supply, given the uncertain and
intermittent nature of renewable sources like wind and solar energy. These
fluctuations in power generation, coupled with time-varying consumer demands of
electricity and the massive scale of power distribution networks present the
need to not only design real-time decentralized power allocation algorithms,
but also characterize how effective they are given fast-changing consumer
demands and power generation capacities. In this paper, we present an Online
Decentralized Dual Descent (OD3) power allocation algorithm and determine (in
the worst case) how much of observed social welfare and price volatility can be
explained by fluctuations in generation capacity and consumer demand.
Convergence properties and performance guarantees of the OD3 algorithm are
analyzed by characterizing the difference between the online decision and the
optimal decision. The theoretical results in the paper are validated and
illustrated by numerical experiments using real data.
