Existing sub-/super-synchronous oscillation stability control methods are primarily focused on specific operating conditions at discrete frequencies, limiting their adaptation to varying oscillation ​scenarios in the power system connected with direct-drive permanent magnet synchronous generator (PMSG)-based wind farms. Based on supplementary dissipation compensation, this paper proposes an oscillation stability control method incorporating equipment-level and farm-level cooperative optimization ​to enhance the system-level stability. First, the effects of dynamic self-dissipation and dynamic coupled dissipation on system stability are analyzed, ​establishing the foundational principle of supplementary dissipation compensation. Subsequently, the optimal locations for supplementary dissipation compensation are identified based on critical control designed to enhance the dynamic self-dissipation effect and suppress the dynamic coupled dissipation effect. Furthermore, by considering energy requirements under the combined wind farm-grid interaction and inter-PMSG interactions and balancing the wind farm-grid interaction dissipation energy with inter-PMSG interaction dissipation energy distribution, an equipment-level control parameter optimization algorithm and a farm-level power cooperative optimization algorithm are established. Finally, the simulation results demonstrate that dynamic coupled dissipation constitutes the ​root cause of oscillation inception and progression. Through equipment-level and farm-level cooperative optimization, the proposed method can reliably compensate dynamic dissipation energy, while adapting to the variation of oscillation frequency and the oscillation scenario. It can maximize the energy dissipation effect of the interconnected system, achieving rapid suppression of sub-/super-synchronous oscillations.