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We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for adynamic and uncertain environment. The unpredictable supply of renewableresources and varying prices of the electricity market are a few factorsresponsible for the uncertainty. We propose to address this problem using theframework of online convex optimization, where the cost functions are not knownapriori because of the uncertainty and are revealed only incrementally overtime. We also consider a distributed setting, where each agent (generators andloads) in the power network is only privy to their own local objectives andconstraints but can communicate with their neighbours. A distributed onlinealgorithm is proposed based on the modified primal-dual approach. Theperformance of the online algorithm is evaluated using the regret (static)function, which is the difference between the actual cost incurred by employingthe proposed algorithm and the optimal fixed decision in hindsight. Since wedeal with a constrained optimization problem, analogous to the notion of regretthe accumulation of the constraint violation is also calculated at each step.We establish a sub-linear bound on the static regret and constraint violationunder suitable assumptions on step-size and cost function. Finally, we use thestandard IEEE-14 bus system to demonstrate the performance of our algorithm.

Online Distributed Algorithm for Optimal Power Flow problem with Regret Analysis