Measurement Based Linear and Nonlinear Time Invariant Representations for High Voltage Inductive Transformer Frequency Response up to 10 kHz

Abstract

This paper presents the details of the development, evaluation process, and results of linear and nonlinear time-invariant models used to represent the frequency response of inductive high-voltage instrument transformers. The study encompasses both sinusoidal and distorted quasi-sinusoidal test waveform conditions, focusing on harmonic voltage amplitude and phase-angle measurements up to 10 kHz. A linear time-invariant model was derived using a higher-order transfer-function estimation technique that minimized the least-squares error between the measured frequency response of the transformer and the estimated transfer function across harmonic orders ranging from 50 Hz to 10 kHz. Acknowledging the limited validity of the linear time-invariant model under multi-tone distorted waveform conditions, a nonlinear timeinvariant model employing a simplified Volterra series was introduced to represent the instrument transformer frequency response under multi-tone distorted waveform scenarios. The accuracy of both models was rigorously assessed using the experimental frequency responses obtained through sinusoidal lowvoltage-frequency sweep signals and multi-tone-distorted high-voltage waveforms. This study contributes to a comprehensive understanding of the behaviour of instrument transformers at high frequencies under different input voltage conditions, providing valuable insights into the accuracy of high-frequency harmonic measurements up to 10 kHz.INDEX TERMS Frequency domain analysis, frequency response, high-voltage techniques, instrument transformers, nonlinear systems, power quality, power system harmonics, transfer functions.