The use of the Least Squares Method to estimate the model parameters of a transformer

Abstract

Due to the importance of transformers to power systems, investments in studies are justified in order to develop mathematical models to better understand equipment characteristics. The methodology used in this study consisted of the traditional open and short-circuit tests of the transformer to determine the equivalent circuit parameters and the frequency response of the system. The task was then to find the approximate polynomial functions that may satisfactorily represent the behavior of parameters of the developed model. The solution of the associated equation systems was characterized as a Linear Least Squares Problem, since the residual function, which represents the error between the real value of the parameter and the estimates obtained by the approximation functions, must be minimized. The use of Least Squares Method allowed the determining of the best approximation functions for the transformer equivalent circuit parameters. The analysis of the results obtained for the experimental 5 kVA transformer chosen leads to the conclusion that the developed models do constitute good representations of the transformer, given the little relative error between the real experimental values of the tests and those estimated with the use of estimation polynomials. The major conclusion was that the parameters associated to the Joule losses and to the dispersion and magnetizing fluxes are reasonably represented by third degree polynomial functions and, in addition, the core losses are well represented by second degree polynomial functions. Finally, the model obtained for the 5 kVA transformer was applied to two transformers of 1 kVA and 3 kVA in order to verify the robustness of the new equivalent circuit. The results showed that the model properly represents the characteristics of the original transformer, but may not be generalized to other similar equipment.