A general method for determining resonances in transformer windings

This paper presents a method for calculating terminal and internal impedance versus frequency for a lumped parameter model of a transformer. The transformer's total frequency response can be accurately determined from this impedance data directly, i.e., the terminal resonance and anti-resonance and internal amplification factor characteristic can be calculated for a single or three-phase transformer model. Since most equipment associated with power system operation can be accurately modeled with lumped parameter networks, this method also provides an accurate, straightforward method for determining the resonance characteristic of those systems. An additional significance of this method is that the accuracy of the calculation is limited only by the user's ability to represent the equipment or system. Heretofore, the accuracy of this calculation was limited by the simplifying assumptions required of the network model by each solution method. This paper presents the definitions and mathematical theory underlying the method. Two examples are presented in which comparisons are made between measured and calculated values for a helical air core coil and a 200 MVA single-phase autotransformer. The agreement is excellent.