Applications of multi-point Arnoldi algorithms to linear lumped transformer model simplifications

The study of electro-magnetic transient of power transformers requires different models at different levels. Comprehensive models are essential in design level while only simplified models are required for system level simulations. Since different model characteristics in different levels, it is beneficial to develop a practical and efficient model simplification tool which can simplify the design level models into the system level models and capture essential characteristics prior to transformer constructions. In this paper, a new moment-matching-based algorithm will be adopted for power transformer model reductions. This algorithm, called the multi-point Arnoldi algorithm, is an iterative method which can recursively generate a reduced-order orthonormal basis from the corresponding Krylov space. The parameters of the reduced system and those of the original system will be related by the congruence transform of the system matrix. The resulting simplified systems still retain some network characteristics of the original systems. Fundamental developments of this algorithm will be discussed in details. Applications of proposed techniques to comprehensive transformer models will be given to illustrate the accuracy and tractability of proposed techniques.