# On the Analysis of DC Network Dynamics of VSC-based HVDC Systems

[Licentiatavhandling]

In this thesis, the dc network dynamics of VSC-HVDC systems is investigated through eigenvalue and frequency domain analysis. The eigenvalue analysis has been used to identify the factors that have an impact on the system stability. It has been determined that instability in the form of sustained oscillations can take place, and that the operating point, the dc side electrical characteristics, the strength of the ac system and the controller structure, are the major factors that impact the stability of the system. A frequency domain approach is proposed in this thesis in order to explain the instability that occurs in the system. A two-terminal VSC-HVDC system is modelled as a Single-Input-Single-Output feedback system, and the VSC-system and the dc grid transfer functions are defined and derived. The VSC-system transfer function has been interpreted as an admittance, whose conductance is positive or negative, depending on the direction of the power. The main characteristic of the dc grid transfer function is the resonance peak, which appear as a result of the RLC characteristic of the dc transmission line. When the resonance phenomenon takes place at a frequency in which the VSC conductance is negative, there is a risk that the resonance becomes amplified. Whether or not the system becomes unstable depends on the magnitude of the dc grid resonance peak and the magnitude of the VSC conductance. Then, the proposed procedure can provide criteria for the design of controllers which guarantee that dc side resonances do not become amplified. Finally, simulations in a four-terminal HVDC system show that instability takes places according to the conditions stated in the previous analysis. The dynamic performance of the voltage-droop and the voltage-margin control strategies have been compared as well and it has been found that the former performs better than the latter. The impact of other control loops is also studied through simulations, and it is shown that reactive power injection and the control of the alternating-voltage increases the stability limit. Furthermore, it has been shown that abrupt changes on the control modes trigger other types of phenomena which need to be studied from the large signal point of view.

**Nyckelord: **HVDC, VSC, Eigenvalue Analysis, Frequency Domain Analysis, DC Side Dynamics, DC Grid Resonance, VSC Admittance, DC Grid Impendance

Denna post skapades 2014-04-29. Senast ändrad 2014-05-05.

CPL Pubid: 197255