# Reliability Assessment of Cyber-Physical Distribution Systems Considering Cyber Disturbances
## 2 Problem Description
### The Proposed Reliability Assessment Method
#### 2.2.2 Reliability Indices  
The Generalized Distribution Network CPS Reliability Assessment Indices Considering Cyber Disturbances  
Cyberattacks are the primary external security threats in cyber disturbances, which normally exploit the security weaknesses of elements and tamper with the original data by injecting false data [33]. The internal threats are mainly information component failures. Since the failure rate of the information component is the inherent nature of the component that does not change with external factors, \(\lambda\) is used to represent the failure rate of the information component, while the success rate of the information component cyberattack is represented by \(P_{\text{atk}}\). Since cyberattacks against IEDs have the greatest impact on the system, IED cyberattacks are used as an example for analysis and calculation, and other cyberattacks are calculated as IED cyberattacks. Based on the characteristics and impacts of the two security threats, the system state is divided into a normal operation state and a cyberattack state, while information component failures may occur at any time in both states.  
The number of switches, IEDs, and servers in the minimum set cut for a load point failure are defined as \(m\), \(n\), and \(l\), respectively, and the probability that the load point is under a cyberattack can be derived as follows:  
\[p_{i}=1-\big{[}(1-p_{atk-IED})^{n}\big{]}, \tag{1}\]  
where \(p_{atk-IED}\) is the successful probability of IED cyberattacks.  
The probability of the load point being in normal operation is \(1-p_{i}\). The number of load outages \(C_{\text{in}}\), the duration of outages \(U_{\text{in}}\), and the amount of lost load \(E_{\text{in}}\) caused by information component failures are calculated as follows:  
\[C_{\text{in},i}=n\times\lambda_{\text{IED}}+m\times\lambda_{\text{switch}}+l \times\lambda_{\text{server}}, \tag{2}\]  
\[U_{\text{in},i}=n\times U_{\text{IED}}+m\times U_{\text{switch}}+l\times U_{ \text{server}}, \tag{3}\]  
\[E_{\text{in},i}=U_{\text{in},i}\times D_{i}, \tag{4}\]  
where \(\lambda_{\text{IED}}\), \(\lambda_{switch}\), and \(\lambda_{server}\) denote the component failure rates of IEDs, switches, and servers, respectively; \(U_{\text{IED}}\), \(U_{switch}\), and \(U_{server}\) are the annual failure times of individual IED, switch, and server, respectively; and \(D_{i}\) represents the average load at the load point.  
The number of load outages \(C_{\text{ia}}\), the duration of outages \(U_{\text{ia}}\), and the amount of lost load \(E_{\text{ia}}\) caused by cyberattacks are calculated as:  
\[C_{\text{ia},i}=\left\{\begin{aligned} & 0,n_{1}=0\\ & 1,\ n_{1}\
eq 0\end{aligned}\right. \tag{5}\]  
\[U_{\text{ia},i}=\left[1-(1-P_{\text{atk}})^{n_{1}}\right]\times n_{1}\times U _{\text{IED}}+(n-n_{1})U_{\text{IED}}+m\times U_{\text{switch}}+l\times U_{ \text{server}}, \tag{6}\]\[E_{\text{ia},i}=U_{\text{ia},i}\times D_{i}, \tag{7}\]  
where \(n_{1}\) represents the number of IEDs subjected to cyberattacks.