Cascaded H-bridge energy storage system can achieve energy transfer and smooth the fluctuation of renewable energy generation, which is the preferred solution to improve the large-scale utilisation of renewable energy, but it is difficult to adapt to the complex grid environment such as grid distortion and weak grid. To address this limitation, a model-free adaptive control method for cascaded H-bridge energy storage converters is proposed to improve the capability of adapting to complex power grids. First, an enhanced second-order generalized integrator is designed in the power control loop to accurately extract the fundamental component of grid voltage, effectively mitigating harmonic interference. Second, a current data-driven model based on dynamic linearization theory is developed in the current control loop to reduce dependence on model parameters and improve the robustness and dynamics of the converter when the model is mismatched. Finally, a 10 kV/3 MW high-voltage, high-capacity energy storage system simulation model and a hardware-in-the-loop experimental platform are established to validate the effectiveness and feasibility of the proposed method.