Initial Parameter Estimates and Constraints to Support Gray Box Modeling of Power Transformers

An accurate transformer model is an important tool for use in the study of power transformers. However, a manufacturer's proprietary restrictions will generally make access to the detailed design specifications of a transformer difficult. Therefore, in order to construct a physically representative transformer model, it is often necessary to estimate the model parameters. One approach is to fit the model to data obtained from tests, such as frequency-response analysis. However, during the process of fitting a model to a data set, it is critical that the estimated parameters appropriately represent the transformer under test. An estimator that is not constrained can converge on a parameter set which may satisfy the objective function but is not physically representative of the transformer. It is therefore important to constrain the model parameters. The aim of this paper is to formulate a methodology to obtain initial estimates and constraints for several fundamental transformer parameters. To demonstrate applicability, the initial parameter estimates and constraints are applied to a range of distribution transformers of varying age and manufacture, ranging in size from 200 kVA to 18 MVA.