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Fast inverter control is a desideratum towards the smoother integration ofrenewables. Adjusting inverter injection setpoints for distributed energyresources can be an effective grid control mechanism. However, finding suchsetpoints optimally requires solving an optimal power flow (OPF), which can becomputationally taxing in real time. This work proposes learning the mappingfrom grid conditions to OPF minimizers using Gaussian processes (GPs). ThisGP-OPF model predicts inverter setpoints when presented with a new instance ofgrid conditions. Training enjoys closed-form expressions, and GP-OPFpredictions come with confidence intervals. To improve upon data efficiency, weuniquely incorporate the sensitivities (partial derivatives) of the OPF mappinginto GP-OPF. This expedites the process of generating a training dataset asfewer OPF instances need to be solved to attain the same accuracy. To furtherreduce computational efficiency, we approximate the kernel function of GP-OPFleveraging the concept of random features, which is neatly extended tosensitivity data. We perform sensitivity analysis for the second-order coneprogram (SOCP) relaxation of the OPF, whose sensitivities can be computed bymerely solving a system of linear equations. Extensive numerical tests usingreal-world data on the IEEE 13- and 123-bus benchmark feeders corroborate themerits of GP-OPF.

Fast Inverter Control by Learning the OPF Mapping using Sensitivity-Informed Gaussian Processes