With the growing share of inverter-based resources (IBRs) in electric power systems, the risk of oscillatory events in the sub-, supersynchonous and harmonic frequency range increases. Various methods have been proposed to identify critical network conditions and calculate margins in the mentioned frequency ranges for system stability based on power system network models. As part of the publicly funded project “SysStab2030”, the following selection of the methods is evaluated regarding their comparability and usability for network studies.

The impedance-based stability analysis is an emerging methodology to evaluate system stability based on the Nyquist criterion. It allows to evaluate the stability of singular network connection points through a SISO analysis or multiple connection points through a MIMO analysis. The SISO analysis also provides stability margins in the form of the phase and gain margin.

Matrix-Valued Vector Fitting is a numerical identification technique used to obtain a rational Linear Time Invariant (LTI) model from measured MIMO frequency response data. Applied to the whole system admittance, it allows the closed-loop poles of the power system to be approximated directly from the fitted frequency-domain admittance model. These poles form the basis for eigenvalue-based system-strength methods. In this work, we specifically investigate the Impedance Margin Ratio (IMR) as one such metric.

A direct method for evaluating the small-signal stability of a white-box system involves time-domain state-space modeling and eigenvalue analysis of the system matrix. The converter control and grid dynamics can be represented as a state-space model, which often results in a nonlinear system; linearization around equilibrium operating points yields a set of LTI models for analysis. Each model corresponds to a specific grid-device operating point. The eigenvalues of the system matrices then provide concrete insights into system modes and stability margins. Additionally, participation factors quantify the contribution of each state variable to specific eigenmodes, with high values identifying critical states that most influence (and are influenced by) the mode's dynamics, thus aiding the identification of critical components in power grid and control systems.

A recently proposed quantifying mode damping method (denoted as QMD) is adopted to assess the oscillatory stability of power systems using only frequency-domain impedance data. The QMD approach can provide quantitative results comparable to closed-loop poles or state-space based eigenvalues. Starting from collecting impedance data and constructing a system admittance matrix, which is then inversed and decomposed into individual eigen-impedances for discrete frequency points, the modes with a damping ratio of |ζ| ≤ 0.1 can be extracted by screening each eigen-impedance.

Two existing metrics - generalized short circuit ratio (gSCR) and equivalent-SCR (eSCR) - are widely used for assessing the small signal grid strength at the system and bus level respectively. By comparing the device critical SCR (cSCR) with the grid strength, the risk of weak-grid oscillations in sub- and super-synchronous ranges can be effectively evaluated.

The proposed paper provides a comparison of the methods by applying them to exemplary networks. It discusses the advantages and challenges of each method regarding the modelling requirements, the input data, as well as format and preparation of results.