Measurement of Utility Harmonic Impedance Based on Gaussian Mixture Model

In the context of accurately measuring harmonic contributions, it is essential to assess both the overall stable harmonic responsibilities and the transient fluctuations to determine if short-term harmonic emissions exceed established standards. Traditional methods often assume that utility-side impedance remains constant in the short term, leading to measurement inaccuracies and inadequate tracking of impedance variations, which are inherently dynamic. This paper introduces a novel approach that models utility impedance using a Gaussian mixture model (GMM). Through this approach, we derive the probability distribution of harmonic voltage at the point of common coupling (PCC). The parameters of this model are estimated using the expectation maximization (EM) algorithm, and utility impedance is subsequently recovered with a least mean squares (LMS) estimator. Our method not only demonstrates superior measurement precision and effective tracking of impedance fluctuations but also surpasses conventional methods by eliminating assumptions such as stable and minimal background harmonics and significantly higher customer-side harmonic impedance compared to the utility-side. Additionally, the proposed GMM method offers a comprehensive measurement scheme capable of accurately calculating average values while dynamically following short-term harmonic impedance fluctuations.

I. Introduction

As power systems evolve, the increasing prevalence of nonlinear loads has heightened the demands on power quality, particularly concerning harmonics [1], [2]. To manage harmonic distortion in power grids, IEEE Standard 519 [3] establishes limits on the levels of harmonic currents and voltages that customers can generate. Consequently, accurately determining the harmonic responsibilities of customers has emerged as a critical issue.