Solving Optimal Power Flow on a Data-Budget: Feature Selection on Smart Meter Data

How much data is needed to optimally schedule distributed energy resources (DERs)? Does the distribution system operator (DSO) have to know load demands at each bus of the feeder to solve an optimal power flow (OPF)? This work exploits redundancies in OPF's structure and data to minimize the communication of such a data deluge, and explores the trade-off between data compression and the grid's performance. We propose an OPF data distillation framework involving two steps: The DSO first collects OPF data in near-real-time from only a subset of nodes. It subsequently reconstructs the complete OPF data from the partial ones, and feeds them into the OPF solver. Selecting and reconstructing OPF data may be performed to maximize the fidelity of the reconstructed data or the associated OPF solutions. Under the first objective, OPF data distillation is posed as a sparsity-regularized convex problem. Under the second objective, it is posed as a sparsity-regularized bilevel program. Both problems are solved using proximal gradient algorithms. The second objective is superior in approximating OPF solutions at the expense of increased complexity. Numerical tests show that it enhances the fidelity and feasibility of the reconstructed OPF solutions, which can be approximated reasonably well even from partial data.