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• Eigenvalue stability analysis of SSTI applying accurate MMC state space model. • Significant risk of SSTI between MMC HVDC and nuclear plant generators. • Conclusions contrary to previous studies on MMC and two level VSC. • Comprehensive analysis of operating conditions and controller parameters. • Different impact of PLL gains on rectifier and inverter. This paper presents a comprehensive analytical eigenvalue stability study of subsynchronous torsional interactions between the 1 GW Eleclink MMC HVDC and the 1.12 GW Gravelines turbine-generator in north France. It revalidates the conclusions of previous studies on VSC-based HVDC systems by showing that the risk of SSTI may be of significance when the HVDC is based on the MMC and not the two level VSC technology. The study demonstrates that in the case of the weak French grid and the rated HVDC power flow from France to England, the HVDC can destabilize the dominant low frequency, 6.3 Hz, torsional mode. The analysis also expands the work of previous studies on MMC and reveals that the case of the HVDC power flow from the English to the French grid may also introduce the risk of destabilizing the lower frequency mode. Furthermore, it also reveals a noticeable impact of the PLL and that increasing the gains has an opposite effect on the two HVDC power flow directions. Moreover, participation factors are analyzed for the 6.3 Hz mode indicating that the main cause of the torsional interactions is the HVDC power control loop. The main findings are verified on the detailed EMTP model. [ABSTRACT FROM AUTHOR]