Wideband Oscillation Analysis and Robust Stabilization Control for Grid-Tied Converter Systems

The large-scale integration of renewable energy through power electronic converters has introduced wideband oscillation phenomena across sub-synchronous to super-synchronous frequencies, posing critical challenges to modern power grid stability. This tutorial presents a systematic framework for analyzing and mitigating wideband oscillations in grid-tied converter systems, structured into four interconnected parts.

Part I establishes fundamental modeling and stability analysis of single grid-tied converters using state-space eigenvalue analysis and impedance-based methods with Nyquist stability criteria. Part II introduces a frequency-domain adaptive parametric model order reduction method for multi-converter-fed systems, overcoming traditional Krylov subspace limitations through three indicators—convergence error, cumulative error, and projection matrix rank—enabling accurate and efficient oscillatory stability analysis across varying system scales. Part III presents robust stabilization control strategies including margin balancing control via phase correction, virtual damping and virtual element control for wideband dissipativity shaping, voltage feedforward-based coordinated damping, and gap metric-based robust stability assessment for ultra-weak grid support. Part IV introduces a Physics-Guided Deep Reinforcement Learning-based Multi-Objective Controller for online broadband oscillation prevention in power electronic-dominated regional power systems, combining an impedance network perception module with a TD3 reinforcement learning engine to achieve rapid optimal control decisions.

By integrating analytical methods, model reduction, robust control theory, and AI-driven adaptive control, this tutorial equips attendees with a holistic toolkit for tackling wideband oscillation challenges in modern renewable-rich power systems.

Outline and Schedule (3-hour duration)

Duration	Topic	Presenter
45 min	Part I: Modeling and Oscillatory Stability Analysis of Grid-Tied Converters	Bao Xie
45 min	Part II: Modeling and Oscillatory Stability Analysis of Multi-Converter-Fed Systems	Meiqin Mao
15 min	Coffee Break	—
45 min	Part III: Robust Stabilization Control of Grid-Tied Converters	Zhiqing Yang
30 min	Part IV: Adaptive Wideband Oscillation Mitigation of Multi-Converter-Fed Systems	Xun Jiang
15 min	Q&A and Open Discussion	All

Part I – Modeling and Oscillatory Stability Analysis of Grid-Tied Converters

This part covers output impedance modeling of single grid-tied converters in the dq-frame and sequence domains, incorporating the effects of phase-locked loops, current control loops, DC-side dynamics, and digital control delays. The Nyquist and generalized Nyquist criteria are introduced for converter–grid stability assessment, and key oscillatory modes including subsynchronous and supersynchronous resonances are analyzed under varying control parameters, grid short-circuit ratios, and operating points. Impedance measurement validation via perturbation injection methods and time-domain simulation case studies are presented to verify the theoretical analysis.

Part II – Modeling and Oscillatory Stability Analysis of Multi-Converter-Fed Systems

This part addresses the computational challenges of oscillatory stability analysis in multi-converter-fed systems. It identifies the limitations of traditional Krylov subspace-based parametric model order reduction methods, which struggle to construct precise reduced-order impedance models due to complicated and coupled error factors. A frequency-domain adaptive PMOR method is then introduced, driven by three indicators—convergence error, cumulative error, and projection matrix rank—enabling adaptive selection of the optimal reduced order to balance accuracy and computational efficiency. The method is validated across small-scale, medium-scale, and large-scale multi-converter systems, demonstrating scalability and effectiveness in constructing precise parametric reduced-order impedance models for rapid oscillatory stability analysis.

Part III – Robust Stabilization Control of Grid-Tied Converters

This part presents robust stabilization control methods under weak grid conditions. It begins with oscillation mechanism analysis using state-space eigenvalue-based and impedance-based modeling validated through frequency sweep measurements. Margin balancing control using phase correction is introduced to enhance internal symmetry of the converter system, significantly extending the stable operating region under weak grid conditions. Virtual damping control via virtual admittance design and virtual element control constructing virtual resistors, inductors, and capacitors are presented for wideband damping coordination. Voltage feedforward-based wideband dissipativity enhancement is discussed across low, medium, and high frequency bands using PLL compensation, proportional feedforward, and multi-sampling derivative feedforward, respectively. Active voltage and frequency support strategies for ultra-weak grids are introduced using asymmetric PLL compensation and frequency feedforward with improved integral design. Future directions include gap metric-based robust stability frameworks and generalized internal model two-degree-of-freedom control to reduce conservatism and improve dynamic performance under parameter uncertainties.

Part IV – Adaptive Wideband Oscillation Mitigation of Multi-Converter-Fed Systems

This part addresses online broadband oscillation active prevention control in power electronic-dominated regional power systems. The problem is formulated as a multi-objective optimization balancing gain margin maintenance and power curtailment minimization. A Physics-Guided Deep Reinforcement Learning-based Multi-Objective Controller with a two-stage architecture is introduced: the first stage embeds a physics-guided impedance network perception module to sense real-time broadband oscillation risk, while the second stage employs a twin delayed deep deterministic policy gradient reinforcement learning engine to generate optimal control decisions rapidly. This framework overcomes two critical bottlenecks—the challenge of accessing potential oscillation information in conventional reinforcement learning-based methods and the computationally intensive iteration-based decision making in model-based approaches. The controller's performance is validated on a representative power electronic-dominated regional power system with grid-forming and grid-following renewable energy stations, demonstrating reliable online broadband oscillation prevention.