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Comparative Assessment of Frequency Scans using EMT and RMS Models

Clea Bürgel, Gustavo Valverde, Gabriela Hug

arXiv:2608.26851v1eess.SY

TL;DR

Frequency scans are important for assessing stability and system strength, but evidence comparing EMT and RMS scans remains limited. The paper systematically compares matched generator and inverter models, then relates PCC impedance features to system dynamics. RMS models capture low-frequency behavior up to approximately 10 Hz, while CC-GFMI accuracy improves when inner voltage-control loops are included.

  • Problem

    Differences between EMT- and RMS-based frequency scans are limited in prior work, despite their relevance to stability and system-strength assessment.

  • Method

    The paper compares dq-frame EMT and RMS frequency scans for matched synchronous-generator, grid-following, and grid-forming inverter models, and analyzes PCC impedance and singular values.

  • Results

    RMS models capture low-frequency dynamics up to approximately 10 Hz, but can mask high-frequency interactions and instability; CC-GFMI accuracy improves with inner voltage-control loops.

  • Takeaways & Limitations

    Typical RMS models represent VC-GFMI low-frequency behavior more accurately than CC-GFMI behavior, while PCC impedance is dominated by the lower generator or grid impedance.

Abstract

from arXiv · show

Frequency scans of inverter and grid impedances are crucial for assessing small-signal stability and system strength in inverter-dominated power systems. This paper compares frequency-scan results for several generating units, including a synchronous generator, grid-following, and grid-forming inverters, using fully dq electromagnetic transient and root-mean-square (RMS) models in Simulink. The scans are performed for the same device rating and operating point. Frequency scans and time-domain simulations show that the RMS models are valid only at low frequencies. We find that the current-controlled grid-forming inverter is more difficult to represent in RMS than the voltage-controlled grid-forming inverter. However, including the inner voltage-control loops improves the accuracy of the RMS representation. The paper also investigates the influence of generator and grid impedance on the total system impedance seen from the point of common coupling and relates the oscillatory modes and zeros of the system to peaks and dips in the first and second singular values of the system impedance, respectively.

I. INTRODUCTION

The paper addresses limited evidence comparing EMT and RMS frequency scans for generators and inverters. It systematically evaluates these models and examines how impedance relationships shape PCC scans.

  • Motivation: RMS simulations are computationally efficient but cannot capture the broader frequency range represented by high-fidelity EMT simulations.The paper notes that RMS models remain widely used despite increasing inverter-based-resource penetration.
  • Motivation: Frequency scans support dynamic-interaction, resonance, small-signal-stability, and frequency-dependent system-strength assessments.At the PCC, frequency-dependent impedance indicates voltage sensitivity to current changes.
  • Research gap: Prior work compared IBR and synchronous-generator impedances, but differences between EMT- and RMS-based frequency scans remained insufficiently studied.
  • Approach: The study compares a synchronous generator, a grid-following inverter, and two grid-forming inverter variants at the same rating, transformer, and operating point.It also investigates RMS limitations, PCC impedance composition, and interpretations of frequency-scan features.

A. Frequency Scan

The frequency-scan method derives a dq-frame system impedance from a linearized state-space model and evaluates its singular values across frequency. These singular values quantify directional voltage amplification and support system-strength assessment.

  • Impedance derivation: Linearizing the nonlinear system around an operating point produces state-space matrices A, B, C, and D for a white-box impedance model.Current perturbations are selected as inputs and voltage perturbations as outputs.
  • Frequency scan: Setting s = jω converts the dq-frame transfer function Zdq(s) into a frequency scan.
  • Singular-value analysis: The first and second singular values of the 2-by-2 impedance matrix provide the upper and lower bounds on voltage gain from current perturbations.A single scalar cannot characterize the response because gain depends on perturbation direction in the dq plane.
  • System strength: The first singular value captures worst-case amplification and serves as a system-strength metric, with lower values indicating a stronger system.
  • Impedance composition: The method also separates generator impedance Zgen_dq(s) and grid impedance Zgrid_dq(s) to analyze their dependence on the total system impedance.The overall behavior of the equivalent parallel impedances is governed by the smaller impedance.

B. Generator Models

The study uses detailed EMT models and corresponding RMS simplifications to represent the generator and its fast and slow dynamics. The synchronous-generator model includes electrical, mechanical, excitation, and stabilization components.

  • Model framework: The EMT models and their RMS simplifications are defined before the device-specific generator descriptions.
  • Synchronous generator: The synchronous generator uses an eighth-order model covering stator, field, damper-winding, and rotor-motion dynamics.A second-order turbine, first-order automatic voltage regulator, and tuned power-system stabilizer complement the machine model.

1) Synchronous Generator:

The inverter-based resources are voltage-sourced converters connected through LC filters and step-up transformers, with control structures distinguishing grid-following, current-controlled grid-forming, and voltage-controlled grid-forming operation. RMS models omit several fast dynamics and assume inner controls are ideal.

  • Inverter-based resources: The IBR models use voltage-sourced converters with LC filters, ideal DC sources, neglected switching dynamics, and step-up transformers.The GFLI and CC-GFMI structures are shown in the dq reference frame of the generator.
  • Grid-following inverter: The GFLI controls current and synchronizes through a PLL, while outer loops generate current references for active-power and voltage setpoints.Inner current-control loops track current and generate the internal-voltage command.
  • Current-controlled grid-forming inverter: The CC-GFMI imposes its own voltage waveform, with active-power and outer-voltage loops determining terminal-voltage angle and reference.Inner voltage-control loops generate the reference current for terminal-voltage tracking, while inner current-control loops match those of the GFLI.
  • Voltage-controlled grid-forming inverter: The VC-GFMI is considered separately, using single-loop controls, because the CC-GFMI is more commonly adopted.
  • RMS simplifications: RMS simplifications neglect fast line, transformer, filter, and stator dynamics and omit idealized inner current- and voltage-control loops.

3) Simplifications in RMS:

Figure 3 presents the one-line diagram of the three-bus system modeled in Simulink.

  • The figure depicts the three-bus system used for Simulink modeling.

III. RESULTS

The study compares frequency scans from EMT and RMS models in a radial three-bus Simulink system, using consistent operating conditions and scan definitions.

  • Simulation Setup: The test system is a radial three-bus network with one generator, two resistive loads, transmission elements, and an infinite bus.
  • Simulation Setup: The generator can be modeled as an SG, GFLI, CC-GFMI, or VC-GFMI in the same dq-reference-frame system.
  • Simulation Setup: All simulations use the same operating point, with uk = 1 pu, 0.6 pu generator active-power injection, and 0.15 pu consumption per resistive load.
  • Simulation Setup: The study computes PCC, generator, and grid impedances using specified Simulink linear-analysis inputs and outputs.
  • Simulation Results: Figure 4 reports PCC Zdq(s) frequency scans for the SG, GFLI, CC-GFMI, and VC-GFMI using EMT and RMS models.

B. EMT vs. RMS Models

EMT and RMS frequency scans agree mainly at low frequencies, while RMS models conceal higher-frequency behavior and represent voltage-controlled GFMI more accurately than current-controlled GFMI.

  • The first and second singular values bound voltage responses to current perturbations and describe their frequency-dependent variation.
  • RMS models capture low-frequency dynamics up to approximately 10 Hz but hide potential high-frequency interactions above that range.
  • At very low and very high frequencies, EMT scans are similar across devices because grid impedance dominates.
  • The VC-GFMI RMS scan matches EMT exactly at low frequencies, whereas the CC-GFMI scan shows small deviations.
  • Including inner voltage-control loops significantly improves the CC-GFMI RMS scan at low frequencies, while adding inner current-control loops has negligible effect.

C. Time-Domain Validation

Time-domain validation demonstrates that an RMS simulation can remain stable while EMT reveals a high-frequency instability under a poorly tuned PLL.

  • The validation increases the GFLI PLL proportional gain and applies active-power and terminal-voltage reference steps.
  • Figures 5 and 6 provide the scan and time-domain validation contexts for the CC-GFMI and poorly tuned-PLL GFLI cases.
  • The EMT simulation becomes unstable at approximately 190 Hz after the voltage-reference step, while the RMS simulation remains stable.
  • The EMT oscillation frequency closely matches the unstable linearized-system mode and a peak in the first singular value.

D. Interpretation of EMT Frequency Scans

EMT frequency scans show that generator and grid impedances dominate the total impedance in different frequency regions, while system modes and zeros appear as peaks and dips in its singular values.

  • At very low and high frequencies, the grid impedance dominates the total impedance for all three generator types.
  • Generator influence is strongest from 3 Hz to 1000 Hz for the SG, 500 Hz to 3000 Hz for the GFLI, and 0.5 Hz to 3000 Hz for the CC-GFMI.
  • At high frequencies, generator-impedance influence becomes negligible as transformer and stator inductances increase its impedance in the SG case.
  • Each peak in the first singular value of Zdq(s) can be associated with an oscillatory mode, with peak height depending on modal residue and the inverse real-part magnitude.
  • Dips in the second singular value correspond to system zeros; nearby poles and zeros can mask oscillatory modes, and visibility depends on selected inputs and outputs.

IV. CONCLUSION

The conclusions show that RMS frequency scans represent low-frequency behavior but can miss high-frequency generator-grid interactions, with CC-GFMI representation remaining inaccurate even at low frequencies.

  • RMS frequency scans capture low-frequency dynamics up to 10 Hz but can mask high-frequency interactions between the generator and grid.
  • The typical RMS model of a GFMI captures the low-frequency behavior of a VC-GFMI, whereas inaccuracies arise for a CC-GFMI even at low frequencies.
  • Including inner voltage-control loops reduces the mismatch in the RMS model of the CC-GFMI.
  • The system impedance is dominated by the lower of the grid and generator impedances, while frequency-scan peaks correspond to oscillatory modes and some modes can be masked by zeros.
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