A Dynamic Similarity Index for Assessing Voltage Source Behaviour in Power Systems

TL;DR

This paper tackles the challenge of evaluating voltage source behavior in inverter-based resources within power systems by introducing the Dynamic Similarity Index (DSI), a frequency-domain, MIMO metric that quantifies how closely a system matches a reference voltage-source behind an impedance (vsbi). The method hinges on linearizing a nonlinear model, forming admittance/impedance representations, and computing the maximum singular value of the difference between reference and system responses across frequencies, $DSI(oldsymbol{comega})=\sigma_{max}(Y^{diff}(oldsymbol{comega}))$ or $Z^{diff,b}(oldsymbol{comega})$ for buses. The authors derive the vsbi dynamics from impedance analysis, map $(R/L)$ to the damping ratio $\xi$ and $X/R$, and apply DSI at both component and system levels, illustrated on gfor/gfol converters and benchmark networks (IEEE 9-bus and 118-bus). The results identify buses with low voltage stiffness and show how control tuning affects dynamic similarity, providing a practical tool for converter manufacturers and system operators to diagnose, design, and optimize grid resilience. Validation via Matlab/Simulink confirms correspondence between frequency-domain DSI measures and time-domain responses, highlighting the approach’s relevance for planning and operation of modern power systems.

Abstract

Due to the fundamental transition to a power electronic dominated power system, the increasing diversity of dynamic elements underscores the need to assess their similarity to mature electrical engineering models. This article addresses the concept of the Dynamic Similarity Index (DSI) for its use in, power electronics-dominated networks. The DSI is a multipurpose tool developed to be used by different stakeholders (e.g., converter manufacturers and system operators). Such an index is calculated per frequency, which serves to anticipate potential differences in particular frequency ranges of interest between the model under study and the reference model. Within the scope of this study, the dynamic similarity of inverter-based generators to an ideal voltage source behind an impedance is assessed, due to the relevance of this fundamental circuit in the representation of generation units in power system studies. The article presents two potential applications based on this mathematical framework. First, for manufacturers to evaluate control performance compared to a reference model and second, it enables operators to diagnose buses with voltage vulnerability based on a user-defined reference Short-Circuit Ratio (SCR) value. The DSI results for these two case studies are validated using Matlab Simulink simulations.

Figures (14)

• Figure 1: Single-line diagram of a simple radial system with 2 voltage sources behind an impedance. Z (System Under Study) and (External Grid)
• Figure 2: Bode diagrams of the admittance matrix of the system under study with $|Z|$= 0.05 pu (left) and $|Z|$= 0.5 pu (right) with $X/R$ ratio of 10.
• Figure 3: Flowchart of the methodology
• Figure 4: System under study by choosing $u_{qd}^{POC}$ (as input) and $i_{qd}^{tr}$ (as output) as an example
• Figure 5: Fictitious current source addition to each bus and comparison of the system with the reference by using DSI