## 1 Introduction  
As a physical entity and operational unit, the microgrid is one of the components of virtual power plants (VPPs) [1]. Through the integration and optimization of distributed energy resources (DERs), VPPs rely on information technology and intelligent management to achieve virtual integration of dispersed resources through software and communication technologies, improving the flexibility and efficiency of their power systems. Microgrids can integrate distributed generations (DGs) through DERs for distributed power production and supply, along with loads, energy storage devices, power electronic converters, etc. For their operation and control, a hierarchical control approach is often adopted, where islanded microgrids can include a primary level covering droop control and a secondary level that corrects operational state deviations caused by droop control [2, 3]. Currently, there are many studies investigating secondary control in microgrids. Secondary control can be classified into three types based on communication connection structure: centralized, distributed, and decentralized [4; 5]. A secondary control method based on distributed model predictive control is proposed in [6] for frequency regulation in AC microgrids. A distributed control strategy is adopted in [7] and combined with a self-triggered mechanism for frequency restoration in AC microgrids. Reference [8] introduces a proportional-integral secondary control for frequency and voltage restoration in islanded microgrids. Reference [9] investigates improved secondary control strategies for dynamic boundary microgrids to enhance the resilience of distribution systems. A novel privacy-preserving average consensus algorithm is proposed in [10] to achieve distributed load sharing in microgrids. However, these methods all aim to shift the droop characteristic curve by adding compensation to eliminate deviations caused by droop control. Frequency and voltage recovery is not achieved through load power adjustment. Yet, the same secondary control effect can actually be achieved by setting the power reference value in the droop control. However, this is from the perspective of power distribution at the primary level. For example, paper [11] proposed methods to eliminate operational state deviations, but the method used in that paper is achieved through quantitative numerical relationship corrections rather than using intelligent methods. This paper draws on the same approach to correct operational state deviations, so the key is how to establish the proper numerical relationship between the power commands within the controller and the common load. Although these data sets maintain physical connectivity via power lines and impedance correlations, their numerical interdependence presents significant complexity due to the intricate control structure and circuit complexity. To better explore the relationship between the abovementioned two data sets, artificial intelligence (AI) algorithms can be the preferred method due to their highly nonlinear mapping and self-learning capabilities. These have been successfully applied in power systems applications [12; 13]. A shallow neural network (SNN) reward model is used in [14] to control grid-connected microgrids. The SNN is adopted in [15] for short-term hourly energy consumption prediction. Reference [16] explores the potential of AI-based solutions for hierarchical control layers and investigates AI-driven strategies for single and networked microgrid environments. Reference [17] utilizes deep reinforcement learning to develop a resilience-oriented microgrid formation method for distribution networks. A two-stage deep learning approach is proposed in [18] to solve the economic dispatch problem in microgrids. A summary of the above literature review is shown in Table 1. In the table, \(\checkmark\) indicates \"involved\", \(\checkmark\) indicates \"not involved\", and - indicates \"no content in this aspect\".