THEORY OF TRANSFORMER MODELING USING MODAL-ANALYSIS

The paper proposes a new structure for transformer models aimed at compact accurate representation of multiwinding transformers under general transient conditions. The paper shows how the fundamental integro-differential equations describing a general transformer may be handled numerically, to give a matrix form corresponding to the Fredholm form of classical transformer analysis. Numerical manipulation of the matrix form, by means of straightforward linear transformations, allows general solution of the transformer equations without the limitations and restrictions of classical analysis. In particular, unlike classical work, the method allows full account to be taken of the frequency-dependent effects and losses arising from transient flux penetration into the transformer core. There is no restriction on the number of windings, and the theory is completely independent of how the windings are eventually connected. The advantage of the method is that a robust solution structure emerges that creates possibilities for very considerable reductions in computational requirements compared with existing alternatives.