DETERMINING OF POLE-ZERO REPRESENTATIONS OF FRA MEASUREMENT DATA FOR INTERPRETATION OF POWER TRANSFORMER TRANSFER FUNCTION DEVIATIONS

Frequency Response Analysis (FRA) compares measured transfer functions (TF) of power transformers. Deviations of frequency response curves indicate electrical or mechanical damages of windings. As assessments are done by experts, no objective guidelines for interpretation of measurement results exist. This paper deals with approximation of measured power transformer frequency responses using complex rational function models. The aim is to develop an algorithm for automated interpretation using analytical models created on the basis of measurement data. A fitting algorithm maps the information contained in measured curves on a pole-zero model of reduced complexity. TF of RLC two-port networks are linear systems and can be described by rational functions consisting of two polynomials with real coefficients. In [3], an iterative method called “Vector Fitting” (VF) is described which tries to find the best fitting rational function for a measured complex frequency response in a least square sense. The number of iterations and the assumed degree of measured TF are input parameters to the algorithm and play an important role. These parameters have to be optimized in order to fulfil requirements for FRA interpretation purposes: Fitting accuracy has to be high, i.e. resonance peaks of the measured TF have to be captured precisely. Root mean square error between measured and fitted curve has to be in the few per mill range while degree of the fitting rational function has to be minimized. The procedure of TF approximation with Vector Fitting is improved by pre-estimation of the needed model complexity along with optimized starting pole distribution. The developed algorithm was demonstrated using measured FRA data. Interpretation of slight deviations between frequency responses is the most challenging task of FRA. The found analytical representations are a first starting point for further algorithms contributing to automatic and objective assessment of FRA measurements. Future interpretation algorithms may incorporate comparisons of pole patterns of fitted analytical models.