# Data-Driven Voltage Control in Isolated AC Microgrids Subject to Sensor Saturation
## 1 Introduction  
AC microgrids, which are compact power systems, combine renewable energy sources and various types of distributed generation to improve the reliability and efficiency of the energy supply [1, 2]. AC microgrids have the capability to function either interconnected with, or independently from, the main grid. When connected to the grid, the primary regulation of AC microgrids is managed by the main grid [3, 4, 5]; whereas in independent mode (isolated operation), effective control strategies are required to maintain power balance and ensure voltage stability [6]. This paper primarily investigates the control strategies for AC microgrids operating in isolated mode. In isolated mode, the AC microgrid generally employs a hierarchical control system consisting of primary, secondary, and tertiary levels of control [7, 8]. Primary control is mainly based on droop control techniques, aimed at achieving real-time balance between generation and load [9]. However, droop control cannot completely eliminate deviations in voltage and frequency, thus necessitating adjustments through secondary control [10]. Tertiary control concentrates on optimizing power and addressing economic dispatch concerns [11]. In terms of secondary control, centralized [12], decentralized [13], and distributed control strategies can be adopted. Among these, distributed control is widely used due to its excellent scalability and stability characteristics [14, 15]. Voltage qualityis a key factor affecting the reliability and safety of AC microgrid operations [16]. Maintaining stable voltage not only enhances user experience but also boosts the performance of equipment. This paper investigates distributed secondary voltage control strategies in AC microgrids. Control methods based on models are extensively employed in the secondary control of microgrids. In [17; 18; 19], a multi-agent distributed cooperative control strategy utilizing feedback linearization is introduced to manage the nonlinear challenges in AC microgrids and to accomplish voltage control. An extended observer method aimed at addressing the challenges posed by the numerous parameters in the modeling process of AC microgrids is proposed in [20]. Finite-time control techniques that enhance the convergence speed of secondary control in AC microgrids, thereby quickly restoring voltage to its rated value, are employed in [21; 22]. However, all these control strategies rely on precise system models and require comprehensive knowledge of all parameters and states in the microgrid, as well as the interferences during signal transmission. While this is feasible in experimental simulation environments, it proves challenging in practical applications, especially when faced with the diversity of new energy devices, making it difficult to obtain the necessary system parameters and states. These model-based control strategies are only effective under ideal conditions; once the actual operational conditions deviate from the nominal states, the stability of the system cannot be guaranteed. Therefore, exploring adaptive control strategies based on real-time measurement data to design microgrid secondary controllers with online learning capabilities has become a new direction in research. Researchers have begun to focus on data-driven, model-free control methods to address the shortcomings in model-based secondary control strategies for microgrids. In [5; 23], Model Predictive Control (MPC) was utilized for distributed secondary voltage and frequency control, demonstrating effective control performance. A robust sliding mode control approach was employed in [24], effectively enhancing the system's convergence speed. The use of a Proportional-Integral (PI) control method was reported in [25], which is simple yet effective. In [26; 27], researchers utilized neural networks and deep reinforcement learning techniques, conducting offline training with data collected from microgrid operations to design secondary controllers.