Generalised Harmonic Domain Analysis for Transformer Core Hysteresis Modelling

TL;DR

The paper addresses the challenge of analysing harmonic interactions in power systems with nonlinear devices by proposing a general harmonic-domain linearisation method that derives a Norton equivalent with frequency coupling matrices from a time-domain model. It adapts the Preisach hysteresis model to time-periodic inputs and develops a data-driven fitting workflow, including cubic-spline representations and approximate splitting functions, to build accurate Y^(1) and Y^(2) admittance matrices. The authors demonstrate substantial accuracy gains in transformer open-circuit characteristics, notably improving odd-harmonic couplings and phase, compared with simpler saturation-only models. They also reveal practical constraints when data symmetry limits even-harmonic resolution, and discuss future extensions to asymmetric and more complex Preisach variants. The approach enables efficient harmonic power-flow studies and iterative linearisation in EMT simulations with nonlinear devices.

Abstract

This work identifies the general approach for linearising any power system component in the harmonic domain, that is with respect to its Fourier series coefficients. This ability enables detailed harmonic analysis, and is key as more power electronic devices inject harmonic currents into the power system to its shared detriment. The general approach requires a time domain model of the component, and is most applicable where a conversion to the frequency domain is impractical prior to linearisation. The outcome is a Norton equivalent current source, which expresses linear coupling between harmonic frequencies with admittance matrices. These are the so-called frequency coupling matrices. The general approach is demonstrated for magnetic hysteresis, where a Preisach model has been developed for this purpose. A new data driven approach is used to fit the test results of a small physical transformer to the Preisach model. Results show an improved accuracy in the frequency coupling matrices over models that only considered magnetic saturation. Maximum improvement is observed in the odd harmonic current to odd harmonic voltage couplings.

Figures (20)

• Figure 1: Ideal Relay.
• Figure 2: Example domain of $p(\beta, \alpha)$.
• Figure 3: (a) Example magnetizing current waveform showing the different times major and minor hysteresis loops are created. (b) Example hysteresis loop for the current from (a) with minor loops shown within the major loop.
• Figure 4: Regions of $p(\beta, \alpha)$ for calculating the centred test data from the time periodic Preisach model.
• Figure 5: Test current waveforms to specify internal minor loops condition.