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We propose a data-driven method to solve a stochastic optimal power flow(OPF) problem based on limited information about forecast error distributions.The objective is to determine power schedules for controllable devices in apower network to balance operation cost and conditional value-at-risk (CVaR) ofdevice and network constraint violations. These decisions include scheduledpower output adjustments and reserve policies, which specify planned reactionsto forecast errors in order to accommodate fluctuating renewable energysources. Instead of assuming the uncertainties across the networks followprescribed probability distributions, we assume the distributions are onlyobservable through a finite training dataset. By utilizing the Wassersteinmetric to quantify differences between the empirical data-based distributionand the real data-generating distribution, we formulate a distributionallyrobust optimization OPF problem to search for power schedules and reservepolicies that are robust to sampling errors inherent in the dataset. A simplenumerical example illustrates inherent tradeoffs between operation cost andrisk of constraint violation, and we show how our proposed method offers adata-driven framework to balance these objectives.

Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization