# Analysis of dc-network stability of VSC-based HVDC grids

[Doktorsavhandling]

This thesis presents a modelling approach for the investigation of dc-network stability in HVDC grids. It consists on dividing the system under analysis into subsystems such that their individual impact on the stability of the overall system can be studied. This principle is first applied to a point-to-point HVDC system and then to a multi-terminal HVDC system. Preliminary studies in a point-to-point HVDC system show that, under specific conditions, dc-network instabilities can occur. These are dependent on the dc-network resonance, the power flow direction and the Voltage Source Converter (VSC) control parameters. To further investigate these instabilities, the system is divided into the dc-network and the VSC subsystems. The VSC-subsystem can be interpreted as a frequency-dependent admittance whose conductance is positive or negative depending mainly on the power direction. The main characteristic of the dc-network subsystem is its resonance. Thus, if the dc-network resonance coincides with a negative conductance, there is a risk that the resonance becomes amplified, or unstable. Moreover, it has been found that decreasing the VSC ac-system strength and increasing the VSC control system delays turns the VSC conductance more negative, consequently, increasing the risk of instability. The dc-network subsystem is also studied, and it is found that high resonance peaks increase the risk of instability. A stability criterion is proposed, based on limiting the magnitude of the VSC subsystem transfer function to less than the inverse of the resonance peak around the resonance frequency. The modelling approach is also applied to a multi-terminal HVDC system, where VSC subsystems are defined together with a dc-network subsystem. The main characteristic of the dc-network subsystem is that different resonances are localized in specific terminals.For example, it has been found in a four-terminal HVDC system that one resonance can take place in terminals 1 and 2, while another resonance, with a different frequency, can take place in terminals 3 and 4. This means that, for the first resonance, the VSCs connected to terminals 1 and 2 have the strongest impact on the system stability, and analogously for the second resonance. Moreover, the resonance peak at each terminal determines the level of influence of each VSC meaning that the VSC connected to the terminal with the highest resonance peak will have the greatest impact on the system stability. On the other hand, the VSC-subsystems are, in principle, similar as the ones defined for point-to-point HVDC systems, i.e. they can be interpreted as admittances whose conductances can be negative in certain conditions. Thus, instability occurs when resonances coincides with negative conductances. Finally, simulations and tests in a real time digital simulator show the validity of the theoretical findings of this thesis.

**Nyckelord: **VSC, HVDC, Multi-terminal HVDC system, power dependent admittance, dc-network stability, resonance, passivity

Denna post skapades 2016-08-15. Senast ändrad 2016-08-25.

CPL Pubid: 240231