An Online Gradient Algorithm for Optimal Power Flow on Radial Networks

8 years 13 days ago

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—We propose an online algorithm for solving optimal power ﬂow (OPF) problems on radial networks where the controllable devices continuously interact with the network that implicitly computes a power ﬂow solution given a control action. Collectively the controllable devices and the network implement a gradient projection algorithm for the OPF problem in real time. The key design feature that enables this approach is that the intermediate iterates of our algorithm always satisfy power ﬂow equations and operational constraints. We prove that the proposed algorithm converges to the set of local optima and provide sufﬁcient conditions under which it converges to a global optimum. We derive an upper bound on the suboptimality gap of any local optimum. This bound suggests that any local minimum is almost as good as any strictly feasible point. We explain how to greatly reduce the gradient computation in each iteration by using approximate gradient derived from linearized power ﬂow...

Lingwen Gan, Steven H. Low

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