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

Abstract

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 modelled 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. INDEX TERMS Transformer Modelling, Frequency Response Analysis (FRA), Interpretation, Electrical Circuit Analysis NOMENCLATURE Real part of permeability of electrical steel in per unit value Imaginary part of permeability of electrical steel in per unit value Winding series capacitance Winding shunt capacitance to ground α Space coefficient Magnetizing inductance of winding Air core inductance of winding Magnetic coupling factor between parts of winding with iron core present Magnetic coupling factor between parts of air core winding Equivalent series capacitance of winding seen from tested winding terminals in a transformer Equivalent winding shunt capacitance to ground seen from tested winding terminals in a transformer n Number of stages/sections in a lumped element equivalent circuit network model Angular frequency N Voltage ratio of high voltage to low voltage windings of transformer

Analytical formulas for calculating the electrical characteristics of multiparameter arbitrary configurational homogenous ladder networks

“…The parameters of the winding can be determined based on the constructional specifications of the transformer and listed in Table 4. 40 The estimated winding parameters can be used to calculate the persection series and shunt impedances of the ladder network. The HV winding is represented by a 140-section ladder network for 140 discs, while the LV winding is represented by a 74-section ladder network for 74 turns.…”

“…To illustrate the application, the simulation results of a 144/13 kV, 60 MVA, single‐phase, two‐winding transformer with 140‐disc interleaved HV (144 kV) winding and 74‐turns layer LV (13 kV) winding are presented. The parameters of the winding can be determined based on the constructional specifications of the transformer and listed in Table 4 40 . The estimated winding parameters can be used to calculate the per‐section series and shunt impedances of the ladder network.…”

Parameter identification of transformer lumped element network model through genetic algorithm‐based gray‐box modelling technique

“…[24]. This is a typical FRA curve for a winding with small series capacitance and air-core inductance [18].…”

Power Transformer Winding Deformation Diagnosis Based on the Sum of Two‐Way Shortest Distance

“…The idea of FRA is originated from that the winding deformation fault will cause the change of the equivalent electrical parameters, and result in the change of the frequency response signature of the transformer. By comparing the FRA signatures before and after the transformer winding deformation fault, the differences can be used to detect inner faults and deformation [4].…”