A modeling approach is presented in this paper in order to investigate instabilities originated from dc-network resonances in Voltage-Source Converter HVDC (VSC-HVDC) systems. Through frequency domain modeling, it is shown that the VSC-HVDC system can be represented as a feedback interconnection of two subsystems. These subsystems are defined in this paper as a dc-network impedance connected to a VSC dc-side power dependent admittance. The conditions in which this admittance has a negative conductance are investigated since they can amplify dc-network resonances. It is found that, when the VSC that controls the direct-voltage injects power into the dc network, the mentioned conductance becomes negative above certain frequencies. In addition, the impact of weak ac grids, control system delays, and other direct-voltage controllers on the studied conductance are investigated. The theoretical findings are verified through time-domain simulations.

In this paper, an analysis of the dc dynamics of multiterminal VSC-HVDC systems using the small signal modeling method is presented. Usually, the VSC controllers are designed under the consideration that they operate independently of each other. However, the possible interactions among them and the dc grid should be studied, especially in multi-terminal topologies. In this paper, three VSC-HVDC systems are modeled and, after linearization, the eigenvalues of the system are calculated for different loading conditions. The results from this analysis are compared to those obtained from more detailed models using PSCAD. It is shown that the operating point, the gains of the direct-voltage controller and the cable dynamics have an impact on the system performance.

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Instabilities related to dc-side resonances can occur in Voltage Source Converters based HVDC (VSC-HVDC) systems due to undesirable interactions between its dc-transmission link and the VSC dynamics. Previous works have shown that this instability takes place when dc-side resonances coincide with non-passive behavior of one of the VSCs within the VSC-HVDC system, typically, the VSC that controls the direct-voltage. Through Nyquist stability criterion, it is shown in this paper that also the resonance peak of the dc-side resonance has also a negative impact on the instability, i.e. the higher the resonance peak, the greater the risk of instability. Based on the analysis presented in this paper, it is proposed that, around the dcside resonance frequency, the magnitude of the VSC subsystem transfer function is limited to the inverse of the resonance peak at highest. Finally, time domain simulations show that the proposed measure stabilizes the system.

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