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Dissipativity-Based Multiport Stability Root-Cause Identification and Mitigation for Solid-State Transformers

Xiangyu Meng, Dong Xie, Hongjian Lin, Chunxu Lin, Xinglai Ge, Zhigang Liu

arXiv:2607.09271v1eess.SY

TL;DR

SST control-loop interactions can excite low-frequency oscillations through strong AC-DC coupling, especially under weak-grid conditions. The paper develops a multiport admittance and dissipativity framework to diagnose these mechanisms, then designs DF-OSR to target the identified coupling deficiency. Experiments show that the criterion predicts coupling-induced oscillations and that the enhanced controller stabilizes operation under weak-grid conditions.

  • Problem

    Improperly designed SST control loops can excite strong AC-DC port coupling and low-frequency oscillations, while localized self-dissipativity indices may fail to detect the coupling mechanism.

  • Method

    The paper builds a three-port AC dq/DC admittance model, decomposes dissipativity into self and coupling indices, and designs dynamics-free orthogonal signal reconstruction to reshape the coupling path.

  • Results

    Experiments validate that the dissipativity criterion predicts coupling-induced oscillations and that DF-OSR suppresses oscillations and restores stable operation under weak-grid conditions.

  • Takeaways & Limitations

    The dominant instability mechanism is a coupling-dissipativity failure induced by synchronization-loop dynamics, so mitigation can target the coupling path rather than only retuning localized self-dissipativity.

  • Takeaways & Limitations

    The method assumes reference tracking and may face challenges during severe grid-side faults requiring dedicated fault-ride-through control.

Abstract

from arXiv · show

For solid-state transformers (SSTs) in high-power grid-connected applications, improperly designed control loops can excite strong inherent AC-DC port coupling, leading to low-frequency oscillation issues, especially under weak grid conditions. To address this problem, this article establishes a multiport admittance matrix for the SST, encompassing its AC dq axes and primary DC port, to characterize its inherent dynamics. Subsequently, a multiport dissipativity analysis is conducted to evaluate the robust stability of the SST. By leveraging the decomposition of passivity conditions into distinct self- and coupling-dissipativity indices, the specific root causes of instability are diagnosed. This framework reveals that a severe coupling-dissipativity failure, induced by the internal dynamics of the synchronization loop, is the dominant instability mechanism rather than a localized self-dissipativity issue. Guided by this diagnosis, a stabilizing controller featuring dynamics-free orthogonal signal reconstruction is designed to reshape the admittance characteristics of the SST. This enhancement specifically targets the identified coupling-dissipativity deficiencies, thereby resolving the root cause of the instability. Finally, the stability analysis and the effectiveness of the enhancement strategy are validated on a down-scaled SST prototype. Experimental results demonstrate that the criterion accurately predicts the coupling-induced oscillations and that the enhanced controller guarantees stable operation under challenging weak-grid conditions.

I. INTRODUCTION

The paper addresses low-frequency oscillations in SST-enabled AC-DC grids by developing a multiport stability-analysis and mitigation framework. It motivates a three-port model that captures cross-coupling in the CHB-DAB SST and supports dissipativity-based diagnosis.

  • I. INTRODUCTION: Low damping in SST-enabled hybrid AC-DC grids can produce low-frequency oscillations, overvoltages, and overcurrents that threaten reliable operation.The introduction links these oscillations to dynamic interactions among power converters.
  • I. INTRODUCTION: Existing eigenvalue methods require precise full-system models, while impedance-based methods face challenges when converter and grid parameters are unknown.The paper therefore motivates a framework that avoids dependence on an exact grid model.
  • I. INTRODUCTION: Passivity and dissipativity theory provide frequency-domain tools for stability analysis without requiring a precise grid model.The paper adopts dissipativity because practical power-electronics interactions are concentrated within critical frequency ranges.
  • I. INTRODUCTION: The proposed framework establishes and verifies a three-port CHB-DAB SST admittance model that captures cross-coupling induced by virtual signal generation.The modeled ports correspond to the AC d axis, AC q axis, and DC port.
  • I. INTRODUCTION: The SST architecture combines a CHB rectifier for medium-voltage conversion with isolated DAB modules that regulate power flow to the local LVDC bus.The analysis treats the downstream DC-AC stage as an equivalent LVDC load and uses a phase-modular single-phase representation.
  • I. INTRODUCTION: The small-signal model combines CHB dq-frame dynamics, DAB transfer functions, and control effects from the PLL, SOGI, current controller, and delays.The dq transformation introduces frequency-dependent d-q cross-coupling terms through virtual orthogonal-signal generation and frame rotation.

C. MULTIPORT ADMITTANCE MODEL OF THE SST

The SST is represented by a 3 × 3 dq-frame admittance matrix whose self- and cross-port terms are assembled from converter small-signal models and linearized power balance. This representation completes the AC-DC coupling and DC-port dynamics while defining the DC-link boundary as an external termination.

  • C. MULTIPORT ADMITTANCE MODEL OF THE SST: The AC-side admittance model supplies the first two rows of the SST’s multiport admittance matrix, including AC self-admittance and DC-to-AC coupling.These terms are obtained by integrating the CHB small-signal equations with the converter control relationships.
  • C. MULTIPORT ADMITTANCE MODEL OF THE SST: Linearized lossless power balance establishes intrinsic relationships among all AC and DC port variables.Substituting these relationships yields the remaining admittance terms.
  • C. MULTIPORT ADMITTANCE MODEL OF THE SST: The completed model captures AC-DC coupling characteristics and DC-port dynamics.The resulting terms include the remaining rows and columns needed for the multiport representation.
  • C. MULTIPORT ADMITTANCE MODEL OF THE SST: The SST admittance matrix is 3 × 3, with the AC side split into d and q ports and the DC side treated as one port.The low-voltage DC-link capacitance is external to the matrix, separating converter dynamics from DC-bus configuration.
  • C. MULTIPORT ADMITTANCE MODEL OF THE SST: The dq synchronous-frame transformation maps fundamental-frequency coupling into constant cross-coupling elements, enabling an equivalent LTI small-signal model.This supports applying the LTI passivity criterion within the control bandwidth of interest.

III. MULTIPORT DISSIPATIVITY CRITERION FOR STABILITY ASSESSMENT

The multiport dissipativity criterion evaluates the SST’s admittance model by separating individual-port dissipativity from interactive dissipativity. This enables stability assessment of both AC and DC ports and their interactions.

  • III. MULTIPORT DISSIPATIVITY CRITERION FOR STABILITY ASSESSMENT: The criterion evaluates self-dissipativity of the AC and DC ports individually and interactive dissipativity between them.The decomposition is applied to the previously established multiport admittance models.

A. MULTIPORT DISSIPATIVITY CONDITION FOR THE SST

The paper formulates SST dissipativity in the frequency domain through the Hermitian part of the admittance matrix. It also introduces an extended, weighted passivity condition to reduce conservativeness at low frequencies.

  • A. MULTIPORT DISSIPATIVITY CONDITION FOR THE SST: For a stable LTI system, passivity requires the Hermitian part of the admittance matrix to be positive semidefinite across frequencies.The matrix is formed from the admittance and its conjugate transpose.
  • A. MULTIPORT DISSIPATIVITY CONDITION FOR THE SST: The conventional passivity criterion can be conservative for grid-connected converters, particularly at low frequencies.The paper addresses this limitation using a frequency-dependent weighting matrix.

B. DECOMPOSITION OF DISSIPATIVITY PROPERTIES

The criterion decomposes the SST’s positive-semidefinite dissipativity condition into self-, coupling-, and all-port properties. These indices isolate localized port behavior from interaction-driven stability risks.

  • Principal minors of the Hermitian admittance matrix isolate self-admittance and cross-coupling contributions to stability.The decomposition follows Sylvester’s criterion for Hermitian matrices.
  • The weighting matrix R(ω) uses a low-frequency AC rotation and a high-frequency identity matrix to reduce conservatism in the passivity test.The rotation accounts for the passivating effect of grid inductance without requiring its specific impedance.
  • First-order indices Pd, Pq, and Pdc represent isolated-port self-dissipativity, while higher-order indices characterize coupling and global stability.Pdc,d and Pdc,q describe AC-DC coupling; Pall represents all-port behavior.
  • Self-Dissipativity Properties: Self-dissipativity evaluates individual AC axes, their internal interaction, and the DC port in isolation.Pd and Pq describe individual axes, Pdq describes AC-side interaction, and Pdc describes the DC port.
  • Coupling-Dissipativity Properties: Coupling-dissipativity evaluates whether energy exchange between AC and DC ports remains passive, while Pall evaluates the complete multiport system.The coupling indices address interactions between the DC port and each AC axis.
  • Satisfying all seven dissipativity conditions, especially the coupling conditions, supports robust stability against passive grid and load terminations.The framework shifts controller design from one output impedance toward complete multiport dissipativity management.

C. DISSIPATIVITY-ORIENTED CONTROLLER DESIGN WORKFLOW

The workflow uses a baseline controller, frequency-limited dissipativity assessment, diagnosis-specific redesign, and final validation. It distinguishes acceptable minor violations from significant failures that trigger redesign.

  • The workflow iterates from initial specifications to a controller validated for multiport stability and dynamic performance.It is organized into four stages.
  • Stage 1. Initialization and Baseline Design: Stage 1 establishes system requirements and baseline performance targets, then uses a conventionally tuned controller as the benchmark.Assessment focuses on a critical frequency range Ω rather than the full spectrum.
  • Stage 2. Dissipativity Analysis: Stage 2 formulates the SST admittance matrix and calculates seven decomposed dissipativity properties across the selected frequency range.These properties determine whether the design meets the dissipativity criterion.
  • Stage 2. Dissipativity Analysis: Small negative values over a narrow band may be accepted using predefined margins and engineering judgment, whereas large critical-band violations trigger redesign.The workflow treats the magnitude and frequency extent of violations as decision criteria.
  • Stage 3. Diagnostic-Based Controller Redesign: Self-dissipativity failures suggest localized tuning or delay problems, while coupling failures require strategies such as feedforward decoupling or virtual impedance emulation.After enhancement, the system returns to dissipativity assessment.
  • Stage 4. Final Validation and Tradeoff Analysis: Stage 4 validates the redesigned controller against both stability and dynamic-performance requirements while managing their tradeoff.

IV. DISSIPATIVITY-BASED ANALYSIS AND CONTROLLER ENHANCEMENT

This section applies the multiport dissipativity framework to a baseline SST controller and its hardware parameters. The baseline is built with conventional loop-tuning methods for subsequent diagnostic assessment.

  • The analysis assesses a baseline SST controller, identifies dissipativity deficiencies, and develops a targeted control enhancement from the diagnosis.
  • The baseline controller is tuned using classical frequency-domain specifications, including bandwidth and phase margin.
  • CHB Control Loop Tuning: The CHB rectifier inner current loop uses a PI regulator tuned by the modulus optimum criterion for fast response and input-filter-pole compensation.Its target current-loop bandwidth is 200 Hz.
  • CHB Control Loop Tuning: The outer DC-link voltage loop uses the symmetrical optimum criterion with a target bandwidth of 10 Hz.Its gains are derived from the DC-side capacitance.
  • DAB Voltage Loop Tuning: The DAB output-voltage loop is tuned with the symmetrical optimum criterion to achieve a bandwidth of 35 Hz.The DAB is treated as a controlled current source charging the output capacitor.
  • SOGI-PLL Parameter Tuning: The SOGI-PLL is designed for a 5 Hz bandwidth, yielding an optimal SOGI gain of approximately 0.5.

B. DISSIPATIVITY ASSESSMENT OF THE INITIAL DESIGN

The baseline assessment combines admittance-model verification with seven dissipativity responses to identify how synchronization-loop tuning and the active DAB affect SST stability. It finds both coupling-related and DC-port vulnerabilities.

  • The diagnostic framework applies the multiport admittance model to the baseline controller and remains applicable to alternative control laws through their corresponding admittance matrices.The same seven dissipativity indices are calculated for each control strategy.
  • Model Accuracy Verification: Analytical admittance elements align with frequency-scanning measurements from the detailed switching model across the frequency range, validating the coupling model.Three independent perturbations identify the 3 × 3 admittance matrix.
  • Reducing the SOGI gain lowers DC-q coupling and all-port dissipativity indices in the 10–50 Hz range, eroding the stability margin.Reduced filtering damping causes phase-angle fluctuations that degrade AC-DC dynamic coupling.
  • The active DAB shifts DC-port self-dissipativity negatively across the low-frequency spectrum.Its voltage loop makes the stage behave as a constant-power load with negative incremental impedance.
  • The baseline has two vulnerabilities: intrinsic DC-port nondissipativity from DAB constant-power behavior and conditional AC-DC coupling instability worsened by SOGI-gain tuning.

C. DIAGNOSTIC-BASED CONTROLLER ENHANCEMENT

The diagnosed instability is traced to severe coupling-dissipativity failure, so the enhancement replaces delay-inducing current-loop filtering with dynamics-free orthogonal signal reconstruction. This reshapes AC–DC coupling characteristics while retaining measured-current feedback and voltage synchronization.

  • Severe coupling-dissipativity failure, rather than a localized self-dissipativity issue, is identified as the primary stability risk.The failure is associated with adverse AC–DC coupling dynamics that simple PI tuning cannot resolve.
  • DF-OSR algebraically synthesizes the quadrature current signal from dq-frame command references instead of estimating it with a dynamic SOGI filter.The inverse Park transformation maps idref and iqref into the stationary β-axis current frame.
  • The reconstructed iβ(t) replaces the conventional filter output, while the α-axis signal remains the measured ac-side current to preserve real-system feedback.This changes the quadrature-signal path without removing measured-current feedback from the control loop.
  • The SOGI-PLL remains in the voltage synchronization loop, but SOGI dynamics in the current-feedback loop are replaced because they caused the diagnosed Pdc,q < 0 failure.The separation preserves phase-angle generation for coordinate transformations while removing the problematic current-loop dynamics.
  • By eliminating resonant dynamics and phase lag from the current path, DF-OSR improves AC–DC coupling dynamics and mitigates adverse port interactions.The targeted modification reshapes coupling admittances such as Yd,dc(s).

D. DISSIPATIVITY RE-ASSESSMENT OF THE ENHANCED

Dissipativity re-assessment shows that DF-OSR reduces the previously severe coupling-index deficits and improves AC-side self-dissipativity. Prototype experiments then validate the diagnosed instability mechanisms and the controller’s operation under weak-grid conditions.

  • D. DISSIPATIVITY RE-ASSESSMENT OF THE ENHANCED: DF-OSR reduces the severe negative dips in the DC–d and DC–q coupling indices, confirming weaker adverse AC–DC interactions.The reassessment focuses on the coupling channels previously identified as the primary instability source.
  • D. DISSIPATIVITY RE-ASSESSMENT OF THE ENHANCED: The AC-side self-dissipativity indices Pd, Pq, and Pdq become positive, while the active DAB’s slightly negative Pdc remains.The enhancement neutralizes the DAB’s detrimental overall impact through improvements in other dissipativity properties.
  • Experimental validation: A down-scaled laboratory prototype with programmable grid emulation and series inductance was used to test the analysis under different grid-strength conditions.The setup uses a physical Lg to emulate grid impedance, with Cg connected in parallel with the series grid-inductance/source combination.
  • Experimental validation: With DAB active control enabled under a weak grid, approximately 13 Hz oscillations grow; replacing it with passive impedance rapidly damps them.The result links the experimentally observed instability to the negative self-dissipativity property Pdc.
  • Experimental validation: Theoretical vulnerability at 11 Hz aligns with the approximately 13 Hz oscillation measured experimentally, supporting the predicted coupling-driven mechanism.The comparison is reported for Case 1, where the experimental oscillation frequency was approximately 13 Hz.
  • Experimental validation: The enhanced controller suppresses instability during switching from SOGI-PLL control to DF-OSR and maintains dynamic performance during DC-voltage, load, and grid-impedance changes.During the load step, THD changes from 6.23% to 5.58%.
  • Experimental validation: Experiments also show that instability can be triggered by either negative DC-port dissipativity Pdc < 0 or AC-port dynamic deficiency Pdq < 0.These tests isolate contributions from the SST’s internal characteristics and external grid impedance.

C. VALIDATION OF THE ENHANCEMENT STRATEGY AND ITS ROBUSTNESS

The DF-OSR strategy stabilizes the SST under weak-grid conditions, including prior oscillatory cases, while retaining robust transient and stiff-grid performance. It also simplifies stabilization by avoiding additional parameter tuning and reducing model dependency.

  • Weak-grid validation: The DF-OSR controller suppresses sustained low-frequency oscillations under the weak-grid condition that previously caused instability.The experiment switched from SOGI-PLL control to DF-OSR during operation under Lg = 3.8mH.
  • Dynamic performance: DF-OSR provides fast, well-damped responses to DC-voltage-reference and load steps without observable oscillations.
  • Robustness: The controller remains stable with low ripple when grid inductance changes from Lg = 3.0mH to Lg = 3.8mH, confirming no stiff-grid performance degradation.The reported grid strengths are SCR ≈3.32 and SCR ≈2.62, respectively.
  • Design implications: The proposed method avoids additional stabilization-loop parameter tuning and reduces model dependency, simplifying design while enhancing robustness.
  • Experimental validation: Hardware experiments validate the diagnostic accuracy and effectiveness of the DF-OSR enhancement strategy.
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