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Model-Free Output-Admittance Reshaping for Stability Enhancement of Grid-Connected Inverters

Runnan Wang, Wanrong Li, Huawei Yuan, Sinan Li

arXiv:2610.32095v1eess.SYcs.SY

TL;DR

Grid-connected inverters can become unstable through interactions with uncertain external networks, while reshaping admittance with existing controls can alter current tracking. This paper adds a local MFC loop that reshapes admittance while closely preserving tracking, and reports reduced admittance and greater GNC-stable grid-impedance coverage.

Abstract

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Grid-connected inverters can be unstable when their current-control loops interact with an uncertain external network. Returning the existing controller to improve damping also alters current tracking because tracking dynamics and output admittance are coupled. This paper adds a local model-free control (MFC) loop around the existing current controller to reduce output admittance while closely preserving nominal current-tracking dynamics. The added loop uses local inverter parameters without an external grid or neighbouring converter model. A Norton formulation separates reference tracking from the current response to terminal-voltage disturbances and establishes a tracking-preservation condition for admittance reshaping. Reducing the disturbance response makes the inverter behave more like an ideal controlled current source. Averaged-model simulations show reductions exceeding 65% in the magnitudes of all four dq output-admittance elements over 10-200 Hz, with closely preserved current-tracking dynamics. Generalised Nyquist analysis predicts small-signal stability for all sampled grid-impedance cases with MFC, compared with 90.0% without MFC.

I. INTRODUCTION

Converter–network interactions can destabilize grid-connected inverters even when local current loops are stable, while existing approaches can require external-system information or compromise current tracking. The paper adds local model-free control for admittance reshaping, using a representative grid-following inverter model.

I. INTRODUCTION

  • Stable local current loops do not prevent instability from converter–network interactions, motivating stability enhancement that requires limited information about the surrounding network.Network impedance varies with configuration, and neighboring converters introduce operating-point-dependent dynamics.Source: §I · p. 1
  • Conventional approaches motivate a separate admittance-shaping degree of freedom because some require model-based coordination or grid-impedance estimation, while current-error compensation lacks an explicit independent admittance control.Conventional grid-current-feedback designs also face a bandwidth–robustness compromise.Source: §I · p. 1
  • The proposed local MFC loop reshapes output admittance while preserving nominal current tracking, without an external-grid or neighboring-converter model.A synchronous-frame Norton formulation establishes a tracking-preservation condition; generalized Nyquist analysis and time-domain simulations assess interaction stability.Source: §I · p. 1

A. System Configuration and Current Controller

  • The representative case is a PLL-synchronized grid-following inverter with synchronous-frame current control; its small-signal model assumes balanced operation and neglects dc-link-voltage and PLL dynamics.The current-control model includes a PI controller, inductor decoupling, PCC-voltage feedforward, and total digital delay.Source: A. System Configuration and Current… · pp. 1–2

B. Norton Representation and Coupled Tracking–Admittance Dynamics

The Norton representation separates reference-driven current tracking from voltage-disturbance response, but the original controller couples tracking and output admittance. This coupling motivates an additional degree of freedom for reshaping admittance while preserving tracking.

B. Norton Representation and Coupled Tracking–Admittance Dynamics

  • The Norton form separates the current response into a reference-driven tracking path and a terminal-voltage-driven disturbance path.The nominal current-tracking matrix describes operation with terminal-voltage perturbation set to zero; the output-admittance matrix describes voltage sensitivity with reference perturbation set to zero.Source: B. Norton Representation and Coupled… · p. 2
  • An ideal controlled current source has zero output admittance, so reducing the voltage-disturbance channel moves the inverter toward that behavior.The reduced channel represents lower sensitivity of current to terminal-voltage perturbations.Source: B. Norton Representation and Coupled… · p. 2
  • A common inverse factor in the tracking and admittance expressions means retuning the existing current controller or decoupling changes both dynamics.Conventional active damping faces a bandwidth–robustness compromise, while robust admittance shaping requires model-based coordination.Source: B. Norton Representation and Coupled… · p. 2

A. Control Structure and Admittance Shaping

An outer MFC feedback loop adds a local degree of freedom for output-admittance shaping. Selecting it to approximately preserve nominal current tracking attenuates admittance without an external-network model.

A. Control Structure and Admittance Shaping

  • The MFC transfer matrix Co converts the error between the external current reference and measured current into the existing current-controller input.The existing current controller, decoupling, and feedforward remain in the local subsystem.Source: A. Control Structure and Admittance… · pp. 2–3
  • Selecting Co so that MFC tracking approximately matches nominal tracking yields an admittance-shaping relation while preserving current dynamics.This provides an additional control degree of freedom through an outer current-feedback loop.Source: A. Control Structure and Admittance… · p. 3
  • Suitable Co attenuates output admittance while closely preserving tracking, reducing PCC-voltage sensitivity without requiring an external-network model.Lower voltage sensitivity approaches ideal controlled-current-source behavior and weakens inverter–network interaction.Source: A. Control Structure and Admittance… · p. 3

B. Generalized Nyquist Stability Assessment

The analysis constructs the inverter–grid return ratio with and without MFC and applies the generalized Nyquist criterion to classify interconnection stability.

B. Generalized Nyquist Stability Assessment

  • The external-network impedance at the point of common coupling is derived from the grid branch and PCC-capacitor models.The grid-voltage perturbation is suppressed for this derivation.Source: B. Generalized Nyquist Stability… · p. 3
  • The return-ratio matrix is constructed separately for the inverter–grid interconnection without and with MFC.Source: B. Generalized Nyquist Stability… · p. 3
  • With converter and grid subsystems individually stable, the interconnection is classified as stable when the return-ratio eigenloci do not encircle −1.Case-study calculations use inverter admittance matrices including PLL dynamics.Source: B. Generalized Nyquist Stability… · p. 3

IV. CASE STUDY AND STABILITY VALIDATION

The case study uses averaged inverter simulations and compares MFC and non-MFC cases under matched conditions. The outer controller is selected to preserve nominal current-tracking dynamics without requiring external-grid parameters.

IV. CASE STUDY AND STABILITY VALIDATION

  • Within each comparison, cases share the same power circuit, current controller, delay, grid, operating point, and event.The case study uses a three-phase averaged inverter model.Source: §IV · p. 3
  • The outer controller is selected so MFC closely preserves nominal current-tracking dynamics over the current-control bandwidth.The design uses the listed system parameters and a first-order Padé delay model.Source: §IV · p. 3
  • The d- and q-axis outer loops apply the controller separately to their current errors, without requiring an external-grid parameter.Source: §IV · p. 3

A. Reference-Tracking Preservation

Under nominal grid conditions, separate 5-A reference steps test whether MFC preserves current tracking; the reported response differences are small on both axes.

A. Reference-Tracking Preservation

B. Output-Admittance Reduction

At SCR = 1 and X/R = 10.5, MFC reduces all four dq output-admittance magnitudes over 10–200 Hz, while the high-frequency relation describes the shaping mechanism.

B. Output-Admittance Reduction

C. Stability-Boundary Validation

MFC enlarges the GNC-predicted stable grid-impedance region and preserves stability in the tested weakened-grid condition. Averaged-model responses corroborate the predicted boundary crossing.

C. Stability-Boundary Validation

  • GNC maps stability boundaries across grid-impedance and current-operating-point variations, with representative predicted crossings checked in averaged-model simulations.Source: C. Stability-Boundary Validation · p. 4

1) Grid-Impedance Boundary:

  • At SCR = 1, the baseline eigenlocus encircles (−1, j0), while MFC loci do not encircle it at SCR = 1 or 2.The GNC prediction is loss of stability for the baseline after the SCR reduction and stability with MFC under both conditions.Source: 1) Grid-Impedance Boundary · p. 4, Figure 7 · p. 4, Figure 6 · p. 4
  • 90.0% to 100% GNC-stable coverage results with MFC over 1 ≤ SCR ≤ 10 and 0.5 ≤ X/R ≤ 14.The mapped region is shown in Fig. 8.Source: 1) Grid-Impedance Boundary · p. 4, Figure 8 · p. 4
  • In the averaged model, an SCR step from 2 to 1 produces sustained coupled oscillation without MFC, while MFC damps it and restores both currents to reference.The response validates the predicted weakened-grid boundary crossing.Source: 1) Grid-Impedance Boundary · p. 4

2) Operating-Point Boundary:

At SCR = 1.2 and X/R = 14, MFC expands the predicted stable current-reference region, and an averaged-model response corroborates a tested boundary crossing. The conclusion reports enlarged stability regions under both grid-impedance and current-reference variations.

2) Operating-Point Boundary:

  • 68.3% to 100% predicted stable coverage results with MFC across sampled dq-current-reference pairs at SCR = 1.2 and X/R = 14.Fig. 10 shows the operating-point map.Source: 2) Operating-Point Boundary · p. 4, Figure 10 · p. 5
  • At id,ref = 19 A, an iq,ref step from −2 to −1 A produces growing oscillations without MFC and decaying oscillations with MFC.The averaged-model responses corroborate the GNC classifications at the tested operating point.Source: 2) Operating-Point Boundary · pp. 4–5

V. CONCLUSION

  • The conclusion reports lower dq-frame output-admittance magnitudes, closely matched tracking, and enlarged stability regions under grid-impedance and current-reference variations.Time-domain responses corroborate both stability assessments.Source: §V · p. 5
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