Evaluation of the near fundamental frequency oscillation in the off-shore wind farms based on the elastic energy flow

• The elastic energy flows at multiple dimensional freedom are developed to describe the energy exchange and dissipation during the oscillation. • A dissipated gradient criterion is developed to identifies the security regions of the oscillatory system. • The elastic energy flows reveal distinct mechanisms between NFFOs and SSOs by evaluating the energy dissipation at different frequencies. It is known that the dynamics of inverter-based resources (IBRs) may interact at non-fundamental frequencies. This paper proposes an elastic energy flow (EEF) method to investigate the distinct mechanisms of near-fundamental frequency oscillation (NFFO)—where the oscillation frequency is within ± 10 Hz of the fundamental frequency—and conventional subsynchronous oscillation (SSO) between the permanent magnet synchronous generator (PMSG)-based wind farm and the modular multilevel converter high-voltage direct current (MMC-HVDC) station. The EEF method not only identifies the security regions of the oscillatory system during SSO and NFFO by establishing a dissipated gradient criterion but also provides a parameter adjustment scheme for mitigating oscillations at different frequencies. As a representative case study, the EEF is applied to elucidate the distinct mechanisms of NFFO and conventional SSO in offshore wind farms based on PMSGs integrated with a MMC-HVDC station. Analytical and simulation results demonstrate that the EEF enables the determination of security regions and optimal control parameters required for mitigating NFFO and conventional SSO, respectively.