Variations in wind-turbine rotor speed and converter power margin under different operating conditions constrain the frequency-support power output of wind turbines, thereby affecting the controllability and stability of the frequency-support response. To address this problem, this paper proposes a dual virtual synchronous generator (VSG) coordinated control method for energy-storage doubly fed induction generator wind turbines based on frequency-support power-response equivalence. First, frequency-support power-response models are established for the VSGs implemented at the rotor-side converter and the grid-side converter to describe the active-power dynamic characteristics of the two frequency-support channels. Second, using the target inertial-support power response as the reference, the dual-VSG parameter configuration is transformed into a power-response consistency optimization problem. Furthermore, considering rotor speed, state of charge (SOC), and the grid-side converter upward power margin, the inertia-support and primary frequency regulation power contributions are assigned between the stator and grid-side converter channels. Hardware-in-the-loop validation results show that the proposed method coordinates the dual-channel frequency-support power output under four typical operating conditions with high/low wind speeds and high/low SOC levels, maintains a consistent frequency-support power response, and achieves controllable and stable frequency support over a wide operating range.

Under weak-grid conditions, grid-following (GFL) control of doubly fed induction generators (DFIGs) suffers from reduced stability margins, deteriorated dynamic performance, and intensified oscillations near the stability boundary. To address these issues, a pre-synchronized switching strategy between GFL and grid-forming (GFM) modes, triggered by locally measured operating variables, is proposed. Based on the GFL control model, the evolution of system dynamics with decreasing short-circuit ratio is analyzed, thereby elucidating how reduced grid strength progressively weakens robustness and disturbance rejection and eventually leads to instability. To characterize this deterioration, a set of normalized indices is constructed to quantify the oscillation levels of active power, phase-locked loop frequency, and point of common coupling voltage, enabling reliable identification of control-performance deterioration. A pre-synchronization scheme based on a virtual power closed loop is then developed, allowing the target mode to converge to the current operating point prior to takeover and enabling smooth bidirectional switching between GFL and GFM modes. Hardware-in-the-loop results demonstrate that the proposed strategy accurately detects GFL performance deterioration and effectively suppresses boundary oscillations while mitigating switching transients, thereby enhancing the adaptability of DFIGs to variations in grid strength.