Impedance Modeling and Stability Analysis of HVDC Systems
Summary
High-voltage direct current (HVDC) transmission systems have emerged as a cornerstone for long-range power transfer and integration of large-scale renewable energy sources. Central to their reliable operation is the accurate modelling of system impedance and rigorous stability analysis. Impedance modelling provides a frequency-domain representation of converter and grid dynamic interactions, enabling the identification of resonant modes and damping margins. It encompasses both black-box approaches—where converter terminals are characterised by measured or fitted impedance spectra—and detailed physics-based methods that derive small-signal impedance from component-level dynamics. These representations serve as the foundation for impedance-based stability criteria, such as Nyquist or generalized Nyquist approaches, which assess the resilience of interconnected AC and DC networks to oscillatory perturbations. Modern voltage source converter (VSC) technologies, particularly those employing modular multilevel converters (MMCs), introduce complex frequency-coupling effects and multiple control loops, necessitating multi-input multi-output impedance models for accurate stability prediction. The global significance of these analyses is evident in offshore wind integration, intercontinental grid interties and the reinforcement of weak AC systems. Robust impedance-based design and control strategies help mitigate subsynchronous and high-frequency oscillations, ensure secure operation under grid contingencies and facilitate the seamless incorporation of low-inertia generation. By bridging theoretical advances and practical implementations, impedance modelling and stability analysis continue to underpin the development of resilient, efficient HVDC infrastructures.
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Impedance Modeling and Stability Analysis of HVDC Systems publication trend
The graph below shows the total number of articles in impedance modeling and stability analysis of hvdc systems across all publications each year (not limited to Nature Index journals).
Technical terms
High-voltage direct current (HVDC): A power transmission technology that uses direct current at high voltage levels for long-distance and bulk power transfer.
Impedance-based stability analysis: A frequency-domain method that assesses the dynamic interactions of interconnected converters and networks by examining impedance spectra and employing Nyquist-type criteria.
Voltage source converter (VSC): A type of power electronic converter that controls voltage and current independently, used in modern HVDC links.
Modular multilevel converter (MMC): An advanced VSC topology composed of multiple sub-modules, offering scalability, modularity and improved harmonic performance.
Eigenvalue-based stability analysis: A small-signal technique that derives system eigenvalues from linearised state-space models to predict oscillatory modes and damping characteristics.
Nodal admittance matrix: A representation of a network’s dynamic behaviour that incorporates both AC and DC connections, allowing modal impedance extraction for stability assessment.
Frequency coupling: The phenomenon in which different harmonic components of a converter system interact, requiring multi-input multi-output modelling for accurate stability evaluation.
References
- Wideband Oscillation Mechanism Analysis in VSC-HVDC Systems With Virtual Synchronous Machine in Master-Slave Mode. IEEE Access (2025).
- Generalized MIMO Sequence Impedance Modeling and Stability Analysis of MMC-HVDC With Wind Farm Considering Frequency Couplings. IEEE Access (2020).
- State Space Modeling of an Offshore Wind Power Plant With an MMC-HVDC Connection for an Eigenvalue-Based Stability Analysis. IEEE Access (2022).
- Extended Nodal Admittance Matrix Based Stability Analysis of HVDC Connected AC Grids. IEEE Access (2022).
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