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Slow oscillations, with a period of around 15 min, were observed in an 11-kV electrical distribution system. Initial investigations were unable to reproduce the oscillations. Through the use of hybrid system modelling and analysis concepts, however, it was determined that the oscillations resulted from interactions between tap-changing transformers and switched capacitors. The hybrid systems framework was needed to account for the nonsmooth (switched) nature of these interactions. Trajectory sensitivities were used to identify influential parameters. It was found that existence of the oscillations was dependent upon factors that included system fault level, capacitor rating, and regulator deadband limits. In all cases, grazing-type conditions separated oscillatory from steady-state behavior. A system of cascaded tap-changing transformers was also investigated, with the hybrid systems framework revealing coexisting limit cycles.