Modelagem caixa preta de transformadores de potência em amplo espectro de frequências

Abstract

This dissertation focuses on the construction of linear wideband black box models for single-phase and three-phase transformers that are able to reproduce the behavior of such equipment in a frequency range of 10 Hz to 2 MHz. Three different transformers are considered, namely a 75 MVA and 240/ 3 ±2x2,5% / 13,8 kV single-phase power transformer, a 12 VA and 127/12 V single-phase transformer, and a 3 kVA and 220/110 V three-phase transformer with Dyn5 connection. In order to characterize these transformers terminal behavior, their admittance matrices are used and obtained in one of the following conditions: (a) inversion of the impedance matrix that is measured with the transformers terminals open; (b) direct measurement in tests with the transformers terminals short-circuited; or (c) modification of the measured admittance matrix by the inclusion of the transformer voltage ratios or, in the particular case of the three-phase transformer, by the correction of the zero sequence components. In all cases, for the purpose of mathematically representing the input/output behavior of the evaluated transformers, the procedure of systems identification known as vector fitting is employed in which each element of the measured admittance matrix is approximated by a series of partial fractions. The developed models based on this technique are implemented in a computing platform by means of two distinct approaches, depending on the situation assessed. In the first approach, the resulting model is represented as a RLGC equivalent circuit. In the second approach, the resulting model is represented as state equation matrices. In order to validate the implemented models, three comparative studies on theoretical and measured results are presented both in frequency domain and in time domain. In frequency domain, the ability of the implemented models to reproduce the frequency responses of the real transformers is evaluated. In time domain, a practical study of transferred voltages is presented, where resistive loads are connected to the low voltage (LV) terminals and impulsive voltage waves of distinct time characteristics are applied to the high voltage (HV) terminals of the transformers. The obtained results show that the proposed models are able to accurately represent the behavior of the evaluated transformers in different conditions. They also show that the adopted technique of system identification can be readily extended to transformers of any size and rating, as long as proper attention is given to the frequency response measurements.