The occurrence and mechanism of hysteresis between axial deformation and short-circuit electromagnetic force during the vibration of power transformer windings

Mechanical stability is one of the core capabilities of power transformers. External short-circuit accidents are the main cause of winding instability. International Electrotechnical Commission 60076-5 standard recommends a method to calculate the short-circuit strength of power transformer windings by comparing the stress within windings under the effect of the maximum electromagnetic force with the critical stress of the winding. This method assumes that the maximum deformation will be produced by the maximum electromagnetic force, which corresponds to the first peak of the waveform. However, owing to the interactions between disks during the vibration process, the maximum deformation may occur after the occurrence of the maximum electromagnetic force. The hysteresis phenomenon between disk deformation and electromagnetic force is studied. The definition of the hysteresis phenomenon during the vibration process is first demonstrated, and the mechanism of the hysteresis phenomenon is investigated. The vibration model is established. By decoupling analysis, the conditions for the formation of hysteresis are proposed, and the mechanism of the hysteresis phenomenon is validated by the experiment, which is conducted on a winding sample. In the deformation formula, the term that determines the time-varying characteristic is found. The waveform-determining term is the difference between the two cosine components, whose frequencies are the natural vibration frequency and the electromagnetic force frequency. When the two frequencies are close, the maximum deformation lags behind the maximum force, and the hysteresis phenomenon occurs.