# Nyquist Stability Analysis of a VSC-HVDC System with a Distributed Parameter DC-cable Model Licentiatavhandling, 2015

Voltage source converter based high voltage direct current (VSC-HVDC) transmission systems have now been in operation since 1997 as it is a reliable and flexible method of power transmission. This thesis focuses on small signal dynamics of such systems, emphasizing stability properties. When modeling such systems, the DC-cable is most often approximated by a single Π-section and there are questions if this is accurate enough to decide on if a certain VSC-HVDC system is stable or not. To be independent of this approximation, we propose the use of a distributed parameter cable model, based on the damped wave equation. Under assumption of strong grid AC environment, the VSC-HVDC system with 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 but is in all realistic cases stable. 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. The stability analysis of two terminal VSC-HVDC systems embedded in a weak AC-grid can be separated into two parts: the active power controlled VSC and the VSC-HVDC system while the active power controlled VSC is under steady state. The stability of the first part is analyzed by the small gain theorem. The second part is analyzed by the Nyquist criterion. Similar to the strong AC-grid case, the system can be described by two cascaded blocks. The first block is a transfer function and the second block is a feedback loop. Note that all blocks, however, will be a bit more complicated than in the strong AC-grid case. One example is given, showing that the VSC-HVDC system with a single Π-section cable model is sufficient to prove system stability, independently of the DC-cable length and impedance density.

Electric power transmission

Nyquist stability analysis

VSC-HVDC system

Distributed parameter cable model

Small gain theorem.

Weak AC-grid

Room EB, Hörsalsvägen 11, Campus Johanneberg
Opponent: Henrik Sandberg, Associate Professor, Department of Automatic Control, KTH, Stockholm

## Författare

### Yujiao Song

Chalmers, Signaler och system, System- och reglerteknik

### 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 i proceeding

Energi

### Ämneskategorier

Elektroteknik och elektronik

R - Department of Signals and Systems, Chalmers University of Technology

Room EB, Hörsalsvägen 11, Campus Johanneberg

Opponent: Henrik Sandberg, Associate Professor, Department of Automatic Control, KTH, Stockholm

2017-10-07