Owing to the challenges of unstable generation and random load disturbance in new energy power system, this paper integrates the battery energy storage model into the traditional load frequency control (LFC) framework, and proposes a LFC scheme based on adaptive global sliding mode control to stabilize the frequency of power systems amid unpredictable load frequency deviation. First of all, the nonlinear time-varying function is added to the sliding mode surface to make the system globally robust. Then, an adaptive sliding mode control law is crafted to dynamically adjust the frequency variations caused by random load disturbance. Moreover, by utilizing the improved Lyapunov function and Bessel-Legendre inequality, the stabilization criteria of multi-area interconnected power system are built. Finally, the efficacy of the proposed method is demonstrated through single and double area LFC simulation experiments with the common system parameters.