Admittance Identification of Grid-Forming Inverters Using Time and Frequency-Domain Techniques

TL;DR

The paper tackles the challenge of identifying the $dq$ admittance of grid-forming inverters without access to internal firmware, enabling robust EMT studies. It compares three system identification approaches—Eigensystem Realization Algorithm (ERA), Step Excitation Method (SEM), and Sweep Frequency Response Analysis (SFRA)—to estimate the admittance matrix $Y(s)$ of grid-forming inverters from input-output data, covering the $1$–$100$ Hz range (with SFRA extending into higher frequencies). ERA and SEM operate in the time domain, while SFRA uses frequency-domain excitations; all three produce consistent estimates of the four transfer functions $Y_{dd}, Y_{dq}, Y_{qd}, Y_{qq}$. The key finding is that ERA and SEM closely match SFRA at low frequencies and offer faster, simpler identification, whereas SFRA provides superior accuracy for high-frequency dynamics, guiding method selection for practical stability analysis and controller design in IBR-dominated grids.

Abstract

The increasing integration of inverter-based resources (IBRs) into the power grid introduces new challenges, requiring detailed electromagnetic transient (EMT) studies to analyze system interactions. Despite these needs, access to the internal firmware of power electronic devices remains restricted due to stringent nondisclosure agreements enforced by manufacturers. To address this, we explore three system identification techniques: sweep frequency response analysis (SFRA), step excitation method (SEM), and eigensystem realization algorithm (ERA). SFRA employs sinusoidal signals of varying frequencies to measure the system's frequency response, while SEM and ERA utilize step functions to derive time-domain responses and transform them into Laplace-domain transfer functions. All three approaches are shown to provide consistent results in identifying the dq admittance of grid-forming inverters (GFM) over a frequency range of 1 Hz to 100 Hz.

Figures (7)

• Figure 1: dq-frame admittance measurement testbed.
• Figure 2: Reference scenario for the ERA experiment. a) Discrete impulse. b) Discrete step. c) Continuous step. d) Continuous step of amplitude $g$.
• Figure 3: Step change of 1% at $v_{gd}$ and resulting effect on $i_{od}$ and $i_{oq}$.
• Figure 4: Step change of 1% at $v_{gq}$ and resulting effect on $i_{od}$ and $i_{oq}$.
• Figure 5: Percentage of accuracy between the measurement time domain data and the estimation employing SEM.