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This paper presents a methodology that extends the dynamic harmonic domain (DHD) analysis of large networks by means of the combination of DHD analysis and discrete companion circuit modeling resulting in a powerful analytic technique, called companion harmonic circuit modeling. It provides for a complete dynamic harmonic analysis of the system while preserving the advantages of discrete companion circuit models. On the other hand, the saturation effects in transformers can produce harmonics in power systems; therefore it is importance for an accurate representation of the transformer. The methodology is illustrated by its application to an unloaded transformer.