We present pmuGE (phasor measurement unit Generator of Events), one of the first data-driven generative model for power system event data. We have trained this model on thousands of actual events and created a dataset denoted pmuBAGE (the Benchmarking Assortment of Generated PMU Events). The dataset consists of almost 1000 instances of labeled event data to encourage benchmark evaluations on phasor measurement unit (PMU) data analytics. The dataset is available online for use by any researcher or practitioner in the field. PMU data are challenging to obtain, especially those covering event periods. Nevertheless, power system problems have recently seen phenomenal advancements via data-driven machine learning solutions -solutions created by researchers who were fortunate enough to obtain such PMU data. A highly accessible standard benchmarking dataset would enable a drastic acceleration of the development of successful machine learning techniques in this field. We propose a novel learning method based on the Event Participation Decomposition of Power System Events, which makes it possible to learn a generative model of PMU data during system anomalies. The model can create highly realistic event data without compromising the differential privacy of the PMUs used to train it. The dataset is available online for any researcher to use at the pmuBAGE Github Repository.Part I -This is part I of a two part paper. In part I, we describe a high level overview of pmuBAGE, its creation, and the experiments used to test it. Part II will discuss the exact models used in its generation in far more detail.