# On the robust stability analysis of VSC-HVDC systems Doctoral thesis, 2016

This thesis focuses on small signal stability analysis of VSC-HVDC systems, emphasizing the system stability robustness with regard to the connected AC-grid and the distributed parameter DC-grid model respectively. In addition, for strong AC-grid connected systems, analytical eigenvalue expressions are provided to investigate the impact of physical or control parameters on the system stability for both two-terminal and multi-terminal VSC-HVDC systems. The VSC-HVDC system with a distributed parameter DC-cable model can be described by two cascaded blocks. The first block is a transfer function that will be different, due to which input and output variables that are considered. The second block is a feedback loop, where the forward path is a rational function and the return path is a dissipative infinite dimensional function, that remains the same in all cases. The stability is then analyzed using the Nyquist criterion in a straight forward manner. Examples with different operating points P20 and different SCRs of the connected AC-grids have been studied, showing that the VSC-HVDC system with a single Pi-section cable model is sufficient to evaluate system stability, independently of the DC-cable length and impedance density. Based on the mixed small gain and passivity theorem, this thesis provides a theoretical method to evaluate a sufficient stability condition for a two terminal VSC-HVDC system with respect to the connected AC-grid. The result is that, for the frequency band where the converter admittance matrix is not passive, the negative closed loop system is stable if the loop gain is strictly less than one. On the basis of such a theorem, the sufficient stability conditions are provided, showing that at the DC-voltage controlled converter side, the system robustness can be increased by designing iref = Pref/E0 instead of iref = Pref/E. In addition, the active power controlled converter can be designed to have passive converter admittance for all frequencies and thus the system is stable under all kinds of connected AC-grid.

passivity theorem

VSC-HVDC system

Nyquist stability analysis

distributed parameter cable model

symbolic eigenvalue expressions

small gain theorem

AC-grid interaction

KB-salen, Kemigården 4, Chalmers
Opponent: Lennart Harnefors, Adjunct professor, Royal institute of technology and ABB, Sweden

## Author

#### Yujiao Song

Chalmers, Signals and Systems

Chalmers, Signals and Systems, Systems and control, Automatic Control

#### Nyquist stability analysis of a VSC-HVDC system using a distributed parameter DC-cable model

19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, Cape Town, South Africa, 24-29 August 2014,; Vol. 19(2014)p. 8202-8209

Paper in proceedings

#### Analytical investigation of poorly damped conditions in VSC-HVDC systems

2016 IEEE 55th Conference on Decision and Control, CDC 2016,; (2016)p. Art no 7798762, Pages 3279-3285

Paper in proceedings

Energy

#### Subject Categories

Control Engineering

Other Electrical Engineering, Electronic Engineering, Information Engineering

#### ISBN

978-91-7597-511-5

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4192

#### Publisher

Chalmers University of Technology

KB-salen, Kemigården 4, Chalmers

Opponent: Lennart Harnefors, Adjunct professor, Royal institute of technology and ABB, Sweden