Passivity of Electrical Transmission Networks modelled using Rectangular and Polar D-Q variables

TL;DR

This paper investigates the passivity properties of electrical transmission networks using D-Q and polar variables, providing analytical results and examples to assess stability criteria for systems with distributed energy resources.

Contribution

It introduces alternative formulations using polar variables to analyze passivity, addressing limitations of D-Q based passivity conditions in low-frequency ranges.

Findings

Polar variable formulation can better capture passivity in certain conditions.

D-Q impedance passivity is restrictive and not always indicative of stability.

Analytical results demonstrate the effectiveness of polar variables in stability assessment.

Abstract

The increasing penetration of converter-interfaced distributed energy resources has brought out the need to develop decentralized criteria that would ensure the small-signal stability of the inter-connected system. Passivity of the D-Q admittance or impedance is a promising candidate for such an approach. It is facilitated by the inherent passivity of the D-Q impedance of an electrical network. However, the passivity conditions are generally restrictive and cannot be complied with in the low frequency range by the D-Q admittance of devices that follow typical power control strategies. However, this does not imply that the system is unstable. Therefore, alternative formulations that use polar variables (magnitude/phase angle of voltages and real/reactive power injection instead of the D-Q components of voltages and currents) are investigated. Passivity properties of the electrical network using these different formulations are brought out in this paper through analytical results and illustrative examples.