A Numerical Matrix-Based Method for Stability and Power Quality Studies Based on Harmonic Transfer Functions

Abstract

Abstract-Some couplings exist between the positive-and negative-sequence impedances of a voltage sourced power converter especially in the low frequency range due to the nonlinearities and low bandwidth control loops like the PLL. In this paper, a new numerical method based on the Harmonic Transfer Function for analysis of the Linear Time Periodic systems is presented, which is able to handle these couplings. In a balanced three-phase system, there is only one coupling term, but in an unbalanced (asymmetrical) system, there are more couplings, and therefore, in order to study the interactions between these couplings a matrix based method should be used. No information about the structure of the converter is needed and elements are modelled as black boxes with known terminal characteristics. The proposed method is applicable for both power quality (harmonic and inter-harmonic emissions) and stability studies, which is verified by simulations in this paper.

DQ impedance‐decoupled network model‐based stability analysis of offshore wind power plant under weak grid conditions

“…Stability assessment under unbalanced grid conditions has been a hot topic recently [54–58]. Harmonic transfer functions are used in [54, 55] to derive the impedance model of unbalanced three‐phase grid, which is able to capture all the possible frequency couplings. Based on the harmonic transfer‐function‐based model, it's found that the GCI‐grid system exhibits a greater capability of maintaining stability if the grid asymmetry is more serve.…”

“…Therefore, the presented stability analysis method in this paper for balanced systems provides a conservative stability conclusion, i.e. if the system is assessed as stable for a balanced system using the proposed method in this paper, the stability performance will be even better in the unbalanced system [54, 55].…”

Introduction to the Analysis of Harmonics and Resonances in Large Offshore Wind Power Plants

“…These newly created frequencies will further create other frequencies that will also have a reflection on the grid, thus creating a feedback loop in between elements that "couples" the frequencies in the system. Further explanation can be found in [3,30].…”

“…Introduction to the Analysis of Harmonics and Resonances in Large Offshore Wind Power Plants I. INTRODUCTION The concern for power quality has been on the rise in recent years for all kinds of electric power systems [1,2,3]. Several examples can be found in literature on real-life systems which have been driven into failure or instabilities due to a high presence of harmonic distortions [4,5,6].…”

Improving the Impedance-Based Stability Criterion by Using the Vector Fitting Method

“…The eigenvalues can be obtained by an analytical evaluation of the whole system [13] or by approximating the driving point impedance, which is indeed the equivalent impedance of that node as a frequency response, into state equations using the Vector Fitting method [11], [12]. However, the former leads to a very complicated study and it also needs analytical models of all components that might not be available due to the confidentiality or difficulty in the modeling [14]- [16]. The latter can also not identify the problematic subsystem because it only measures the driving point impedance.…”