Duality Derived Transformer Models for Low-Frequency Electromagnetic Transients—Part I: Topological Models

The objective of this two-part paper is to provide clarity to physical concepts used in the field of transformer modeling, to dispel common misconceptions regarding numerical instabilities, and to present unified modeling techniques for low-frequency transients. This paper focuses on proper modeling of nonlinearities (magnetizing branches) since these components are critical to determine the low-frequency behavior. A good low-frequency model should properly represent: normal operation, inrush currents, open and short circuit, out-of-phase synchronization transient of step-up transformers, geomagnetic-induced currents, ferroresonance, and harmonics. This paper discusses the derivation of electrical dual models from the equivalent (magnetic) reluctance networks and the direct application of the principle of duality. It is shown that different dual models need to be derived for different transformer geometries and the advantages and disadvantages of each method are discussed. This paper also compares double-sided versus single-sided dual models, and shows that the double-sided model is a more general approach. The mathematical equivalency of several leakage models (negative inductance, mutual coupling, and BCTRAN) is demonstrated for three-winding transformers. It is also shown that contrary to common belief, a negative inductance is not the source of numerical oscillations, but they occur due to the use of noncorrect topological models for representing the core.