Nonlinear modeling of magnetic saturation and hysteresis in an electromagnetic device

The cores of most electromagnetic devices, in their normal operating regions, enter saturation by design or otherwise. Some devices, such as ferroresonant transformers, utilize the saturating properties of their core materials to perform their intended tasks. In other devices, such as power transformers, saturation is an undesirable phenomenon imperative to their economically competitive designs. A second phenomenon, known as hysteresis, associated with the operation of electromagnetic devices is the non-uniqueness of the core magnetic flux for a given excitation. That is, core flux is a multivalued function depending on the excitation as well as its own previous states. Computer simulation of a saturable electromagnetic device requires mathematical models for the device saturation and hysteresis characteristics. A general approach to modeling saturation and hysteresis is proposed in this paper. A model which is nonlinear in a parameter is proposed; however, a linearizing transformation is used to allow the estimation of the model parameters by linear estimators. The results of modeling saturation and hysteresis for a two-winding ferroresonant transformer are given. The hysteresis loop obtained from simulation is compared with the actual loop for a given operating condition. These results indicate that accurate modeling of the hysteresis loop is possible with the proposed technique.