Power Transformer Frequency Response Analysis: Examination of Resonance Influences on Frequency Response Analysis Signals as The Traveling Wave is Transmitted Through a Power Transformer

Abstract

Understanding the physics associated with power transformer frequency response analysis (FRA) is required to properly interpret FRA traces for correct diagnostics of a power transformer. Events occurring within a power transformer to influence FRA test traces are explained. A complex Lorentzian curve shape is acquired by combining the solution of the electromagnetic wave equation with a resonance equation. The resultant solution provides a new definition of resonance observed within power transformer FRA traces. The windings in a power transformer are a transmission system to the FRA signal traveling electromagnetic wave. The traveling wave is the electro-motive force causing movement of charge within a resonant circuit. The moving charge within that resonant circuit emits its own traveling wave, which combines with the initial incident wave. The FRA traces demonstrate this influence of resonance on the original injected FRA signal. A new mathematical model of the power transformer FRA traces is developed utilizing the complex Lorentzian curve. The influence of each resonant frequency is catalogued with three parameters: resonant frequency; spectral width; and, coefficient of influence. The developed mathematical model sums the influence of each resonance to a base trace to emulate the actual test trace. Exploratory tests were conducted on a Delta - Grounded Wye power transformer to prove the developed concept and further explain FRA test results. Actual resonance within a power transformer was measured. Measured resonances were applied to the developed mathematical model, which resulted in a very close fit to FRA test results. Multiple types of resonance were observed and other non-resonant influences on the FRA traces are explained.