Using Lumped Element Equivalent Network Model to Derive Analytical Equations for Interpretation of Transformer Frequency Responses

Frequency Response Analysis (FRA) is regarded as the most effective technique for detecting mechanical faults in transformer windings. However, the main challenge in applying the FRA technique lies in the correct interpretation of the differences between the diagnosis and the reference frequency spectra. A transformer can be modeled as an equivalent circuit network comprising inductances (L) and capacitances (C), where L and C are electrical parameters dependent on the winding geometry; a relationship exists between the winding geometry, the electrical components of the equivalent circuit network and the measured FRA spectra. Through electromagnetic circuit analysis, this paper provides a theoretical basis to develop a fundamental understanding of FRA spectra and their resulting interpretation. The FRA spectra are first explained for a single air core winding with uniform structure, and then the complexity is gradually increased by taking into consideration the iron core, the mutual inductive coupling between parts of the same winding and then between the separate windings of the transformer. Mathematical expressions are developed to represent the relationship between the FRA characteristics and the corresponding electrical components of the equivalent circuit network model.