It is well known that power transformers inevitably suffer the impacts of short-circuit electromagnetic forces in service. For precise diagnosis investigation of winding mechanical deformation, this paper presents a double-ladder circuit model of transformer winding with lumped parameters for frequency response analysis. This advanced model includes the axial and radial ladder network with regard to the winding discs and the eddy current paths of magnetic core, respectively. In the radial ladder network, the nonlinear behavior of frequency-dependent parameters and core loss are considered. Relevant equivalent parameters in this double-ladder circuit model are calculated by using three-dimensional finite element method (FEM). The energy balance method is applied to obtain the frequency-dependent inductances and resistances. In order to verify the effectiveness of this model, the frequency response of voltage ratio at a wide frequency range from a few tens of hertz up to megahertz are simulated and measured.

It is inevitable for power transformers to suffer from multiple impacts of short-circuit (SC) current and huge dynamic electromagnetic force in service which may cause large elastic and plastic deformations. Under the SC fault, the distribution of flux leakage and the amplitude of electromagnetic force may be disturbed by winding deformations or displacement. This paper analyzes the cumulative strain-stress characteristics of transformer windings using coupled electromagneticstructural analysis solution. The dynamic electromagnetic force, mechanical stress, and plastic deformation are calculated by 3-D finite element method (FEM). An example of two-winding, 110kV transformer is simulated. It is found that an initial and little deformation in windings may influence the magnetic flux distribution. The changed flux density may enlarge the applied electromagnetic force in the windings. The cumulative model and simulation results of this paper may be useful for investigating the winding deformation state prediction.  Index Terms-transformer winding; magnetic-structural coupling; short-circuit force; cumulative deformation; finite element method.

To study the fast modelling of dynamic characteristics caused by power electronic switching, the dynamic phasor (DP) theory based on the time-varying Fourier decomposition and frequency shifting is firstly applied to the modelling of various multipulse rectifiers. The DP model for symmetrical 12-pulse phase-shifting reactor rectifier unit (PSR-RU) is derived with model order reduction, relations between ac and dc terminals, and Taylor series expansion. The DP model of asymmetrical 18-pulse autotransformer rectifier unit (AT-RU) is proposed based on the switching functions expressed in the DP domain. Meanwhile, the DP model of voltage source inverter (VSI) fed by asymmetrical 18-pulse AT-RU is built with the harmonic state-space (HSS) equations. Under both balanced and unbalanced conditions, the good calculation accuracy and rapid simulation speed of the developed DP models are validated by the detailed time-domain (TD) simulation.