# Reliability Assessment of Cyber-Physical Distribution Systems Considering Cyber Disturbances
## 1 Introduction
Additionally, Petri net is a graphical and formal modeling tool, with the benefits of expansibility and portability, which has been widely used in the reliability modeling of distributed systems, cyber systems, and discrete systems [16]. Moreover, Petri nets can be easily transformed from fault trees, with a strong logical description capability. Reference [17] establishes a Petri net representation of various complex fault tree relationships and verifies that Petri nets are more efficient than fault trees by using an example of a fault tree with five layers and seven bottom events. In terms of reliability indices adopted in the reliability assessment, there are currently three main categories: traditional distribution network reliability indices, reliability indices that consider the impact of cyber failures on control, and power supply reliability indices that consider the impact of cyber failures [18]. Traditional distribution network reliability indices mainly quantify the impact of cyber or physical systems on the reliability of the load, including two main aspects: load point reliability indices and reliability indices for systems [19]. With in-depth research on the impact of cyber-physical interactions, it is impossible to comprehensively, quantitatively, and in detail evaluate the operational characteristics of distribution network CPSs and the impact of cyber failures, especially cyber disturbances, on the system state by using the traditional distribution network reliability indices. Hence, the traditional index evaluation scope needs to be extended. Direct load outages, system control failures, and even certain reliability threats will all be brought by a cyber component failure. For example, a set of reliability assessment indices are defined in [20] to quantitatively describe the impact of component failures leading to control function failures on system reliability. Compared with the traditional distribution network reliability indices, these indices take into account the impact of component failures in cyber systems on system control. However, some of the parameters calculated by these indices come from the simulation method sampling; thus, they are only applicable to the simulation method. These indices have some limitations without considering the influence of cyber disturbances on the system reliability. Reference [21] proposes a reliability state model for different types of cyber disturbances and analyzes the impact of different types of cyber disturbances on network availability. In [22], a network reliability model that considers both cyber device failures and cyberattacks is provided, in which the cyber system status is integrated into the malfunction probability modeling of switches for the reliability assessment. Although research on cyber disturbances has steadily advanced, most studies still follow the traditional distribution network reliability assessment methods, which do not account for the impact of cyber disturbances on system reliability in the indices [13; 23; 24; 25]. As seen in the summary of the literature review of the CPS reliability assessment, few studies have defined new indices for a reliability assessment in the area of assessment indices; only a few studies have considered the impact of physical system failures, information component failures, and cyberattacks on system reliability when performing a reliability assessment of the system simultaneously. Consequently, the relevant research still has the following shortcomings: on the one hand, the research on the cyber-physical interaction has been deepened and the consequences generated by cyber failures have been refined, which require the impact of the cyber disturbance on the system state to be reflected in the indices, thus reflecting the impact on the system reliability. On the other hand, reliability indices that can make comprehensive quantitative assessments of CPS reliability are lacking and unable to scientifically measure the impact of cyber disturbances on the system.