## 1 Introduction  
Wind energy is currently the fastest growing and most commercially promising clean renewable energy source globally. With its mature technology and low-cost advantage, wind power generation has been developed and utilized on a large scale, demonstrating high environmental, economic, and social benefits [1, 2]. Due to the long-distance, high-capacity transmission capabilities far exceeding those of AC transmission, along with flexible control and lower loss, DC transmission has become the primary method for the large-scale transmission of wind power. However, due to the weak AC grid infrastructure and the singular power structure in wind power regions, it is necessary to integrate a certain capacity of hydropower or thermal power units to meet the power fluctuations of wind power. In [3], a cost-effective off-grid power system for clean energy generation consisting of wind energy, pumped storage and open wells was proposed. Reference [4] established a simulation model of a water-wind complementary operation system and investigated the dynamic response characteristics of this system under active power control. According to the different converters of the transmission line, there exist two types of DC wind power transmission: LCC-HVDC and VSC-HVDC. In comparison with traditional DC transmission technologies, the flexible DC transmission based on VSC has no reactive power compensation problem and no commutation faults [5; 6; 7]. Flexible DC transmission has become a hot topic of research, and several studies have explored ways to further enhance the performance of VSC-HVDC systems. Reference [8] constructed a hybrid AC-DC system including a VSC-MTDC system, onshore grids, and offshore wind farms. An adaptive droop control strategy was proposed. It mentioned that converter stations can autonomously adjust their DC voltage reference based on grid frequency deviation, allowing for the redistribution of power. The performance of the ADC strategy was verified, which can enhance the system's response to frequency fluctuations. This provides a new approach for efficient control of power systems. Wind power, with its intermittent and highly stochastic characteristics, can lead to large fluctuations in output power when integrated into the system on a large scale, significantly impacting the frequency based on the active power balance [9]. Reference [10] investigates the frequency stability concerns arising from the integration of large-scale wind power into the system. The findings suggested that conventional power system frequency control methods are no longer adequate to meet the heightened demands posed by the frequent and substantial fluctuations in wind power output for maintaining power system frequency stability. Moreover, in the case of large-scale wind power grid integration, the uncertainty of wind power significantly increases the adjustment pressure on AGC units, which makes the regulation performance of AGC on system power and frequency fluctuations worse [11]. PI control is a traditional method widely used in AGC systems. In the field of industrial control, various techniques have been applied to tune the parameters of PID controllers. Traditional PI control often faces challenges in selecting parameters that yield optimal performance. To address this, recent studies have incorporated artificial intelligence (AI) techniques for PID controller tuning to achieve better performance. The three main branches of AI are neural networks, fuzzy control, and genetic algorithms, which can be integrated with the PID controller, respectively [12]. Reference [13] focused on an air rudder servo system and proposed a PI control method optimized by a genetic algorithm. The genetic algorithm optimized the initial parameters of the PI controller, and the deep deterministic policy gradient algorithm controller performs real-time tuning. However, this type of controller is often used for offline parameter tuning and has poor real-time performance.