Analysis of VSC-based HVDC systems
Doktorsavhandling, 2016

The main objective of this thesis is to perform stability and control studies in the area of VSC-HVDC systems. A major part of the investigation focuses on the development of procedures, whose aim is to understand, explain and avoid poorly-damped conditions or instability that may appear due to dc-side resonances, which stem from the interaction of converters and passive elements in such systems. An analytical approach is initially considered, where the eigenvalues of VSC-HVDC systems are approximated by analytical closed-form expressions. The Similarity Matrix Transformation (SMT) method is introduced and applied to the reduced 4th order state-space model of a two-terminal VSC-HVDC system. The results show that the SMT offers improved accuracy in approximating the actual eigenvalues of the system, compared to the already established LR method. Nevertheless, the two analytical methods are not free of limitations. The increase in modeling accuracy of a system renders the analytical approach impractical or impossible to use. A frequency-domain approach proves ideal in performing a stability analysis in such cases, and is therefore considered and applied to a detailed two-terminal, two-level converter-based VSC-HVDC system. The latter is modeled as a Single-Input Single-Output (SISO) feedback system, where the VSC-system and dc-grid transfer functions are defined and derived. The passivity analysis and the net-damping criterion are separately utilized and assessed on their potential to be adequate analysis tool in VSC-HVDC stability studies. In contrast with the typical Two-Level Converter (2LC), the Modular Multilevel Converter (MMC) has a fundamentally different structure that introduces internal dynamics and requires additional control for the converter to operate properly. The dc-side input admittance of the MMC is analytically derived, allowing the dynamic impact of MMCs in two-terminal VSC-HVDC systems to be analyzed from a frequency-domain perspective. The contribution of the MMC's circulating-current control to the closed-loop system stability is investigated and the differences of the MMC and the 2LC in terms of their passivity characteristics are highlighted. Finally, studies are performed in VSC-based Multiterminal grids, with the objective of proposing advanced control strategies that can offer robust performance during steady-state and transient conditions, with improved power flow and direct-voltage handling capabilities. The properties of the proposed controllers are assessed through simulations of four- and five-terminal grids, where their benefits compared to those of their conventional counterparts are shown.




Poor damping

Symbolic eigenvalue expressions

Droop control

Passivity Analysis

Net damping

Frequency Domain Analysis


EA, Hörsalsvägen 11, Chalmers University of Technology.
Opponent: Prof. Lennart Harnefors, ABB Corporate Research, Västerås, and KTH, Stockholm.


Georgios Stamatiou

Chalmers, Energi och miljö, Elkraftteknik


Elektroteknik och elektronik




Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4206


Chalmers tekniska högskola

EA, Hörsalsvägen 11, Chalmers University of Technology.

Opponent: Prof. Lennart Harnefors, ABB Corporate Research, Västerås, and KTH, Stockholm.