Application of singular-perturbation-based model reduction techniques to neglect saliency in synchronous machines

A common approximation used in the analysis of power systems is the neglect of the dynamic saliency in synchronous machines. In this research, it is shown that eliminating the error associated with neglecting dynamic saliency can be considered as a model-order reduction problem. By considering the elimination of error in such a way, singular-perturbation-based model-order-reduction techniques are used to derive detailed- and reduced-order models of synchronous machines in which dynamic saliency is eliminated with zero error and no added numerical cost. To facilitate model-order reduction, a method of partitioning time scales by careful selection of state variables has been introduced for detailed models in which stator transients are included, and reduced-order models, in which stator transients are neglected. The techniques require little work on the part of the system analyst and are directly applicable to machine models with an arbitrary number of damper windings in the q- and d-axes, thereby eliminating traditional concerns of neglecting dynamic saliency when an unequal number of rotor windings are used in each axes. Comparisons of models of both wound-rotor and buried-permanent-magnet machines are used to provide validation of the methods. Means of extending the techniques to simplify average-value models of synchronous machine-converter systems are also considered.