## 1 Introduction
Literature [6] proposed a multidimensional network model that used the fault location, isolation, and supply restoration (FLISR) processes as an interface between PDS and DIS. The study constructed a path search method based on the transfer matrix by defining the composite multi-node attributes and the system transfer matrix. Literature [7] considered the impact of sensing terminal faults in information systems on distribution networks. The study proposed a reliability evaluation method for multi-voltage level distribution networks that took into account the effects of sensing terminal faults. The sequential Monte Carlo simulation method was used for reliability evaluation. The above literature has preliminarily explored the impact of cyber systems on physical systems in active distribution networks, but the analysis of the impact of information systems on physical systems is still not sufficiently in-depth. The focus of research in recent years has shifted to indirect impacts. Literature [8] proposed a reliability evaluation method based on region-based DFA (Distributed Feedline Automation) analysis. This method had high computational efficiency in large-scale CPDSs. The article analyzed the impact of network system anomalies on reliability in DFA mode and constructed a network reliability model by considering two factors: network device failures and network attacks. Literature [9] analyzed the impact of information system failures on the reliability of distribution networks under the DFA mode. It also proposed a fast reliability assessment method for CPDSs. However, compared to the research on direct impacts, indirect impacts still require further exploration and in-depth study. It is often difficult for a system to adapt to the complexity of the actual distribution network in real distribution network scenarios. Moreover, most of the existing reliability models for CPDSs are based on some simplified assumptions, which cannot accurately assess the reliability of complex situations in real engineering applications. Literature [10] categorized the factors that affect the reliability of the smart microgrid (SMG) for information systems into network failures and information transmission failures. By modeling the interdependence and information transmission failures between information systems and physical systems, a reliability assessment of the SMG was conducted. Literature [11] proposed a CPDN (cyber-physical distribution network) reliability assessment method that considered the interdependence between physical and cyber systems throughout the fault-handling process. The study established a sequential fault handling reliability model and corresponding results based on a fault tree that considered the influence of the network and proposed two metrics for assessing the network's impact on DG (distributed generation) scheduling capability. Literature [12] established reliability models for components and two systems and summarized the mapping relationship between various network system faults and physical fault-handling. It transformed them into several laws and proposed a reliability assessment procedure in the framework of the Monte Carlo method. Literature [13] proposed a new information flow modeling and computation method, which established an information flow matrix by defining the network operating parameters as the flow accumulation function, information flow rate, and time delay. Literature [14] established a reliability model for distribution network components based on cyber-physical systems (CPSs) and proposed a multi-state model for intelligent electronic devices (IEDs). Literature [15] simultaneously considered information uncertainty and multi-energy coupling characteristics to establish the basic architecture of an active CPDS, a reliability model of information domain components, and a model for analyzing the effectiveness of information transmission. Literature [16] proposed a sequential multi-stage cooperative recovery strategy for CPS failures caused by natural disasters.