- The paper introduces a self- and coupling-damping framework that clearly distinguishes intrinsic and grid-induced oscillation mechanisms in grid-forming MTDC systems.
- A rigorous sensitivity analysis shows that q-axis AVC and PSC parameters critically affect stability, with higher active power flow increasing the risk of instability.
- Simulation results validate that adaptive AVC tuning and selective damping control loops effectively restore stability under full rated power and challenging grid conditions.
Introduction
This paper rigorously investigates the occurrence and mitigation of subsynchronous oscillations (SSOs) at the sending end of a practical Grid-Forming Multi-Terminal DC (MTDC) power system, which connects isolated renewable energy sources to the grid. The study is motivated by real-world operational events in the Zhangbei MTDC project, the world’s largest and first meshed VSC-based MTDC system, characterized by grid-forming (GFM) voltage source converters (VSC) operating without synchronous generators (SGs) at the sending end. The configuration and operational context, including control architectures and transmission characteristics, are presented in detail to highlight the distinctive dynamic phenomena and instability risks inherent to GFM control that are not encountered in conventional systems dominated by SGs or grid-following converters.
System Architecture and Modeling Framework
The Zhangbei MTDC project employs VSCs utilizing GFM control for frequency and voltage regulation, diverging from the traditional SG-led sending-end power systems. This architecture, wherein GFM-VSCs act as slack buses, is fundamentally different in small-signal stability behavior. The study comprehensively retains the dynamics of power synchronous control (PSC), AC voltage control (AVC), and inner current control (ICC) loops—contrasting with prior work that often simplifies models by disregarding sections of these loops. The theoretical model is developed in d-q coordinates, and its interaction with the AC grid is formalized to enable precise small-signal analysis.
Self- and Coupling-Damping Methodology
A core methodological contribution is the decomposition of oscillation damping into self-damping and coupling-damping:
- Self-damping quantifies the intrinsic damping contributed solely by the GFM control parameters and their loop interactions, independent of external system configuration.
- Coupling-damping captures the damping effect arising from the dynamic coupling between the GFM-VSC and the external AC grid (including transmission lines and operating conditions), potentially negative depending on parameter regimes and power flow direction.
The closed-loop system stability is shown to depend not just on the inherent GFM control design, but critically also on the coupling-damping, which can destabilize the system despite stable self-damping.
Sensitivity and Mechanistic Analysis
Rigorous sensitivity analysis delineates the specific impact of various control parameters and system variables:
- D-axis AVC parameters primarily influence self-damping.
- Q-axis AVC parameters modulate both self- and coupling-damping and are identified as the most sensitive to instability.
- PSC loop parameters mainly affect coupling-damping, dictating the strength of interaction with the external grid, in particular under high short-circuit ratio (SCR) conditions.
- Active power amplitude and flow direction are directly linked to SSO risk; higher active power transmitted from SE-GFPS to the grid increases instability risk due to negative contributions to damping.
Empirical EMT simulations confirm these findings, demonstrating the nonlinear response of SSO damping to control parameter adjustments and system operating states.
Mitigation Strategies and Practical Validation
The analysis leads to the proposal of adaptive and supplementary damping controls:
- Adaptive AVC parameter tuning based on active power output is mathematically justified and shown to effectively restore stability under increasing power transfer conditions.
- Additional damping control loops for both PSC and AVC (especially q-axis AVC) are validated in simulation, revealing that selective deployment to the q-axis AVC suffices due to its dominant influence on SSO mitigation.
- Transmission reactance augmentation is demonstrated to increase oscillation damping, favoring grid-forming operation with weak grid connections.
Numerical results substantiate these mitigation strategies, enabling stable operation even at full rated power without oscillatory instability.
Implications and Future Directions
The findings bear significant practical and theoretical implications:
- For grid-level integration of isolated RE through GFM-MTDC, rigorous retention and analysis of all control loop dynamics are imperative; simplified models cannot reliably capture risk origins or mitigation mechanisms.
- The self- and coupling-damping framework provides actionable indices for control design and system operation, facilitating targeted parameter tuning and structural interventions (e.g., series reactance installation).
- The study exposes the critical instability mechanisms in GFM-controlled systems absent SGs, informing future large-scale RE deployments and the transition to inverter-dominated grids.
Potential further research includes the application and extension of the self- and coupling-damping analysis to broader classes of GFM control strategies and variable grid environments, supporting the proper selection and optimization of GFM schemes for secure renewable integration.
Conclusion
This paper delivers a comprehensive mechanistic analysis of SSOs in practical GFM-MTDC systems for isolated renewable energy, substantiating the necessity of full-order dynamic modeling and offering validated, quantifiable mitigation strategies. The proposed self- and coupling-damping methodology and its sensitivity analysis advance the operational stability toolkit for emerging grid architectures, supporting robust transformation toward high renewable penetration and inverter-based control paradigms (2607.03104).
