On the Equivalence and Impact on Stability of Impedance Modeling of Power Electronic Converters in Different Domains

Abstract

Abstract-Small-signal analysis of power electronic converters and systems is often carried out by impedance-based methods. At the core of these methods lies the impedance modelling, which can either be obtained through analytical calculations, simulations or measurements. The impedance models can be obtained into two main domains -the dq-domain and the sequence domain. In the dq-domain the impedance model is a 2x2 matrix, while in the sequence domain it is composed by the positive and negative sequence impedance. Recently, a third domain called the modified sequence domain was defined as an extension to the sequence domain, but also with clear similarities to the dq-domain. The objective of this paper is to unambiguously relate to each other the impedances in these three domains, and to show how this equivalence translates into their respective stability assessments. It is also proven that the sequence domain impedance has the same marginal stability condition as the dq-domain impedance matrix.The three-phase Voltage Source Converter is used as an example converter in this paper, as its impedance model in all three domains is well established and reported by previous research. The results in this paper shows that the modified sequence domain model can be derived from the dq-domain model (and vice versa), and that the stability analysis will be identical in these two domains. It is also shown how the original sequence domain model can be derived from the two other models through a model reduction. However, a small discrepancy between the two Nyquist plots is observed in the presence of components such as phase lock loop or DC-link control.

Effect of Reactive Power Characteristic of Offshore Wind Power Plant on Low-Frequency Stability

“…The impedance models of GCIs and transmission cable should also be represented in phasor-domain and dq-domain, respectively, to investigate the impedance interaction. The phasordomain impedance model of the GCI can be obtained as follows [44].…”

Stability margin definition for a converter-grid system based on diagonal dominance property in the sequence-frame

“…Hence, it is necessary to calculate theL(s) matrix, which in turns requires the calculation of both the small-signal converter admittance Y c (s) = Z −1 c (s) and the small-signal impedance Z Th (s). The former has been calculated based on the following equation [18] ∆i…”

“…The terms y c,pp (s), y c,pn (s), y c,np (s), y c,nn (s) are the elements of Y c (s). These have been calculated from the small-signal converter admittance in the qd-frame, and applying a methodology inspired by [9], [18], [12] to refer it to the sequence-frame. By shifting the second equation of (3) by −2ω 0 , the following formulation is obtained for Y c (s)…”

Reduced-Order Modelling Method of Grid-Connected Inverter with Long Transmission Cable

“…The impact of PLL on the output impedance of the GCI can be ignored if the bandwidth of PLL is small enough [16]. The output impedance equivalent is shown as follows, which is just like the formula for single-phase power system, simplifying the following analysis.…”