Gray Box Modeling of Power Transformer Windings for Transient Studies

For the fast transient study of power transformers, several types of models are available that can be categorized into three groups: white box models, black box models, and gray box models. The identification of their parameters and their usages make the models different. Since white and black box models cannot cover certain cases, such as the failure analysis of a transformer with unknown geometrical data, a new type of model has recently become important for industry and academic researchers. This model, called the gray box model, is intensely analyzed in the current paper, both theoretically and experimentally. The gray box model conceptually lies between the black and white box models. The outcomes of this work have been verified using a suitable test object. The parameter identification of the model is performed by artificial methods. Some useful new ideas, including applying the Weibull Distribution function in inductance estimation and employing an exponential function for the series resistance of windings, are developed in this paper. The number of unknown parameters to be identified in the gray box model is reduced by applying these ideas, which makes the model more simple and feasible.