Sensitivity Analysis of Transformer Frequency Responses

Frequency response analysis (FRA), and short- circuit impedance measurements, are considered the state-of-the-art techniques, to discover mechanical deformations to transformer windings [1] . Such deformations may be the result of mechanical shock during transport to site or reduction over time of winding clamping pressure. Mechanical deformations, like "free buckling" [2] of the low voltage transformer winding, may be the result of radial short-circuit forces, acting upon the inner low voltage and the outer high voltage windings during an over-current, short-circuit event as windings tend to be more resilient to tensile, than compressive stress, hence leading to "buckling". The frequency response of a transformer winding is a signature of its distributed network parameters of frequency dependent resistances (R), capacitances (C) and inductances (L), which are unique to a specific transformer’s mechanical structure. By injecting a low voltage signal as a function of frequency into one terminal, whilst measuring the response at another, the transformer FRA signature is obtained as the signal’s voltage ratio in gain (dB) and phase (°). Should an over-current event result in winding displacements, the transformer signature will change. In order to recognize a change in signature, a comparison with previously recorded fingerprint data is required. The signatures can be compared phase-wise or with sister units of similar design, if fingerprint data is not available. Since historical fingerprint FRA data of older units is often not available, the latter case is common engineering field practice. The assessment of the FRA signature is mostly based upon visual comparison of the graphical FRA representation with the FRA reference signature by experienced engineers. Experience shows that in practice, there will always, to some degree, be differences between the actual FRA measurements and the reference FRA data. In the vast majority of cases, these deviations do not indicate winding damage, but rather reflect differences of measurement technique, state or structural features of the transformer. First of all, the frequency range must be considered. The frequency response of a transformer is distinguished by four frequency bands up to 10 MHz, which are broadly speaking dominated by the core (<1 kHz), the inter-winding space (1-10 kHz), the winding structure (10- 1000 kHz), and the leads and earthing method (>1 MHz). Differences in the low frequency range may result from different degrees of residual core magnetization. Close attention to the connection technique is required in order to make reproducible FRA measurement. Differences in the high frequency range may arise from poor or not reproducible connections (i.e. the factory acceptance signatures may be different) or poor grounding, etc. Differences in winding signatures between the phases are normal due to small geometrical differences (i.e. connection leads from windings to terminals). Small structural differences between sister units may result in slightly different FRA signatures. Such structural variations are a natural consequence of updated or improved transformer designs as well as differences in the workmanship during manufacture.