Stability of axial vibration of power transformer windings

This paper deals with the electromechanical coupled vibration problem in transformer. A new dynamic model for the axial vibration of transformer's winding is presented. The transformer leakage magnetic field is simplified to a 2-dimensional magnetic field, and analytic formulation of the transformer leakage field is obtained. Base on the Lagrange equation of electromechanical coupled system, the nonlinear and simplified linear electromechanical coupled axial vibration equations of windings are obtained. The stability of the axial vibration of the transformer windings is analyzed by means of the dynamics theory. Using designed transformer model as an example, it is shown that instability occurs during high currents, and the stability and instability regions of design parameters are obtained.