###### Abstract  
In this paper, the load frequency control (LFC) of multi-area power systems incorporating photovoltaic (PV) and energy storage systems (ESSs) is studied. First, the model of the LFC system encompassing PV and ESS is established. Then, a novel LFC scheme based on adaptive global fast terminal sliding mode control (AGFTSMC) is proposed. To make the system robust globally, an adaptive sliding mode control law and a new type of global fast terminal sliding mode surface containing a nonlinear time-varying function are designed. Moreover, by utilizing the improved Lyapunov function, the stability of the system is analyzed. Finally, two simulation experiments incorporating the two-area LFC system and IEEE 39-bus test power system are presented to validate the effectiveness of the proposed method. The simulation results show that adopting the AGFTSMC can significantly reduce steady-state error and stabilization time  
dynamic regulation capabilities. Compared to traditional frequency regulation methods, energy storage systems (ESSs) exhibit superior advantages. Notably, with the escalating environmental challenges posed by conventional energy sources [7], the penetration of renewable energy generation in power systems is continuously increasing. Consequently, this paper develops a coordinated LFC control framework incorporating photovoltaic (PV) and ESS, aiming to address the frequency regulation capacity gap in high-penetration renewable energy grids through PV-ESS dynamic complementarity mechanisms. As the core safeguard for stable system operation, this architecture effectively suppresses frequency exceedance while significantly reducing frequency regulation costs and carbon emission intensity, thereby providing a low-carbon stability solution for modern power systems [8]. However, relying solely on PV-ESS for frequency regulation often necessitates large-capacity storage devices, substantially increasing construction costs. Thus, PV-ESS should operate synergistically with other control strategies. Over past decades, numerous control methods have been proposed for frequency regulation. PID controllers were applied to a five-area interconnected power system to minimize area control error to zero [9]. Simulation results indicate that the PID controller exhibits sluggish response speeds, with excessive response time under load transients or frequency deviations. A hybrid optimization technique combining bacterial foraging optimization (BFO) [10; 11] and particle swarm optimization (PSO) [12; 13; 14] was proposed to suppress frequency and tie-line power deviations [15]. And a rat swarm optimization method [16] and reinforcement learning [17] were proposed to improve the dynamic response of the system. Nevertheless, as renewable penetration rates increase, the design of PID controller gains to achieve desired LFC performance becomes increasingly challenging. Consequently, advanced control strategies have emerged. [PERSON] and [PERSON] proposed a decentralized LFC for two-area regulated power systems using H-infinity loop shaping, but its applicability to non-regulated power systems remains unverified [18]. A fuzzy logic controller for electric vehicles (EV) and PV integrated frequency regulation was developed [19], yet its performance under uncertainty and nonlinear dynamics requires further validation. Distributed model predictive control (MPC) [20] was implemented to enhance coordinated control with reduced computational burdens inherent to centralized schemes, but linearized models were employed. [PERSON] introduced an L1 adaptive controller to robustly balance generation-load demand with rapid convergence to zero steady-state error [21], yet only validated on single-input-single-output (SISO) isolated systems with fixed non-reheat turbine parameters, omitting multi-input-multi-output (MIMO) scenarios and parameter adaptability analysis. A novel PID controller based on the honey badger algorithm (HBA) was designed to reduce frequency deviations significantly [22].