Practical transfer function estimation and its application to wide frequency range representation of transformers

A widely applicable, general methodology for estimation of transfer function parameters from frequency response data is presented. The procedure is based on the solution of a linear least squares problem by the singular value decomposition (SVD). The condition of the problem is discussed and approaches referred to as shifting and scaling are introduced in order to reduce the condition number. To extend the application to practical cases with measurement errors and/or a large number of poles, a partitioned estimation method with Gauss-Seidel iterations is developed. An iterative improvement process with constraints on the poles is applied to increase the accuracy and to avoid the possibility of obtaining unstable poles. The application of the suggested method of estimation to the representation of transformers is presented with practical examples. Either transfer function or state equation representation can be obtained for transformers described by their terminal frequency responses.>