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Summary form only given. Power transformers can fail from dielectric stresses caused by electromagnetic transients. In this paper we focus on a special phenomenon where excessive overvoltages arise due to resonance. This situation can take place when a transformer on the high-voltage side is connected to a cable and the low-voltage side is unloaded. Very high overvoltages can then result on the low-voltage side from transient events that cause a weakly attenuated overvoltage on the cable with a dominant frequency matching a resonance peak in the transformer voltage ratio. Laboratory tests on a 11 kV/230 V distribution transformer show that a step voltage excitation on a 27-m cable produces a 24 p.u. overvoltage on the open low-voltage side. The voltage waveforms are accurately reproduced by a black-box model obtained from frequency sweep measurements. Simulations show that overvoltages as high as 43 p.u. could occur with the most unfavorable cable length. It is further shown that the following situations can lead to high overvoltages on an unloaded transformer low-voltage side: 1) ground fault initiation at the far cable end, 2) cable energization from a busbar with several other cables connected, and 3) cable energization from another cable of same length.