Definition of Simplified Frequency-Domain Volterra Models With Quasi-Sinusoidal Input

Abstract

The Volterra approach to the modeling of nonlinear systems has been employed for a long time thanks to its conceptual simplicity and flexibility. Its main drawback lies in the number of coefficients, which rapidly grows with memory length and nonlinearity order. In some important cases, such as power system applications, the input signal is periodic and contains a fundamental component that is much larger with respect to the others. This peculiarity can be exploited in order to dramatically reduce the number of coefficients defining the frequency-domain Volterra model with slight drawbacks in terms of accuracy. A systematic procedure for the definition of simplified, frequency-domain models of arbitrary order is proposed. Thanks to the simplification, very high orders of nonlinearity can be managed. The proposed approach has been employed to model the behavior of two electrical devices with different amount of nonlinearity, and that of a power grid containing linear and nonlinear loads. Accuracy is discussed and compared with that obtained with a conventional Volterra model defined by a similar number of coefficients. Results show the effectiveness of the approach, which is particularly suitable to model and test voltage and current transducers as well as other ac power system devices

Overcoming Frequency Response Measurements of Voltage Transformers: An Approach Based on Quasi-Sinusoidal Volterra Models

“…As pointed out in the introduction, the authors already presented in [18], [19] a simplification of frequency-domain Volterra models devoted to the behavioral representation of power system devices. In particular, the number of coefficients can be greatly reduced thanks to the peculiar spectral content of electrical quantities in AC power systems, consisting of a strong fundamental tone, and harmonics that are much smaller in amplitude.…”

“…In [19] the authors have validated the proposed simplification that has been applied to the behavioral representation of several nonlinear power system devices by means of numerical simulations. In this paper, the approach has been experimentally tested to model the steady-state behavior of medium voltage (MV) instrument transformers, namely to predict their secondary voltage harmonics (system output) produced by a known primary voltage (system input).…”

“…The main drawback of such Volterra models is that they are defined by a number of coefficients that rapidly grows with the number of input harmonics and with the selected nonlinear degree; this unavoidably results in a long a complex identification procedure. By exploiting the large ratio between fundamental and harmonics in typical voltage signals, simplified frequency domain Volterra models can be obtained [18], [19] thus allowing a dramatic reduction of the number of coefficients without significant impact on the accuracy. In this work, these models are employed to represent the behavior of medium voltage inductive transformers.…”

A Simple Method for Compensating Harmonic Distortion in Current Transformers: Experimental Validation

“…Similar to the case of CTs, also the metrological performance of conventional voltage transformers (VTs) employed for harmonic measurement is strictly related to their dynamic and nonlinear behavior [ 23 ]. In this respect, the authors of the present paper have shown that nonlinear behavioral models based on a simplified Volterra representation [ 24 , 25 ] can be used to accurately predict the secondary voltage spectrum from the primary side [ 26 ]. This enables a thorough characterization of VTs: linear and nonlinear effects can be separated, nonlinearities can be classified, and their individual impact on the overall metrological performance can be studied.…”

A New Test Procedure to Measure Power Electronic Devices’ Frequency Coupling Admittance

“…Different methods for harmonic analysis in the frequency domain and time domain are currently present in the relevant literature; hybrid frequency and time-domain methods have also been developed [2]- [14]. Medina et al [2] present a review with a concise description and analysis of the fundamentals, characteristics, analytical details, merits, and drawbacks associated with existing methods in frequency and time domains for harmonic analysis in practical power networks.…”