This paper describes three different ways of transformer modeling for inrush current simulations. The developed transformer models are not dependent on an integration step, thus they can be incorporated in a state-space form of stiff differential equation systems. The eigenvalue propagations during simulation time cause very stiff equation systems. The state-space equation systems are solved by using A- and L-stable numerical differentiation formulas (NDF2) method. This method suppresses spurious numerical oscillations in the transient simulations. The comparisons between measured and simulated inrush and steady-state transformer currents are done for all three of the proposed models. The realized nonlinear inductor, nonlinear resistor, and hysteresis model can be incorporated in the EMTP-type programs by using a combination of existing trapezoidal and proposed NDF2 methods.
COBISS.SI-ID: 17118486
Purpose – The investigation was aimed at magnetically-nonlinear dynamic model of a single-phase transformer, where the effects of dynamic hysteresis losses are accounted for by a simplified model. Such a modelling could be applied when the transient operating conditions are analysed or the impact of nonlinear and unbalanced loads on the transformer operation is investigated. Design/methodology/approach – An inverse form of the Jiles-Atherton hysteresis model was applied for the calculation of hysteresis losses in the transformer. In that sense this paper compares and evaluates both hysteresis models, where the possible errors caused by simplified model application are exposed. Findings – The Jiles-Atherton model can be applied when more accurate hysteresis models are required, however, at the cost of increased model complexity and required computational effort. It is impossible to use such a model, when some input parameters are unknown. On the other hand the simplified hysteresis model does not increase the required computational effort substantially. Originality/value – Both methods have been modified in such a way that they can be used when the magnetizing curve of the iron-core material is not available, whilst the magnetically-nonlinear characteristic of the entire device can be determined experimentally. The aforementioned characteristic can be given in the form of an approximation polynomial or in the form of a look-up table.
COBISS.SI-ID: 17030166
Purpose – The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies. Design/methodology/approach – The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards. Findings – The quasi-static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency-independent quasi-static hysteresis loop. Research limitations/implications – The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1?kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue. Practical implications – The combined Takács-Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies. Originality/value – The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non-standard excitation conditions.
COBISS.SI-ID: 17065750