An equivalent model for sub-synchronous oscillation analysis in direct-drive wind farms with VSC-HVDC systems

•An equivalent model is proposed to study the inside-wind-farm and wind-farm-grid SSO.•The adequacy of the traditional equivalent model for the SSO analysis is evaluated.•Matrix’ similar transformation is used in equivalent modeling. Field experiences have shown that sub-synchronous oscillation (SSO) can occur in direct-drive wind farms with VSC-HVDC systems. Due to the complexity of the detailed wind farm model, a dynamic equivalent model, with a reasonable order reduction of the detailed model and still reflecting inside-wind-farm and wind-farm-grid SSO characteristics is essential. In this paper, based on the principle that similar matrices have identical eigenvalues, the SSO analysis of an N-machine wind farm with VSC-HVDC system is conducted by simplifying it into two single-machine systems. The modeling method of the two single-machine systems is presented. Four case studies are presented to verify the effectiveness of the proposed model when compared with the detailed model in various scenarios. The proposed model is also benchmarked with the output multiplication-based equivalent model (OMM). Comparison results show that although the system order is reduced significantly, the proposed simplified equivalent model can still reflect inside-wind-farm and wind-farm-grid SSO modes in various scenarios. Meanwhile, the rationality of the OMM in terms of the wind-farm-grid SSO analysis is verified theoretically.