# Security-Oriented Cyber-Physical Risk Assessment for Cyberattacks on Distribution System
## 4 Security-Oriented Cyber-Physical Risk Assessment for CPPDS
### Analysis and Calculation of Physical Consequence under Cyberattack
#### 4.3.1 Physical Consequence Index  
In order to comprehensively measure the physical consequences of power loss caused by cyberattack in CPPDS, they are divided into instantaneous consequences at the time of accident and long-term consequences in a period of time. This paper proposes the following four indicators to measure the physical consequences:  
1. Instantaneous consequences (1) Loss of power load The total load loss of the \(j\)th feeder section on the \(i\)th feeder considering the consumer level factor is denoted by \[C_{f_{i},j}^{1}=\sum_{m\in\varphi(f_{i},j)}\mu_{m}\times L_{m}\] (10) where \(f_{i}\) is the \(i\)th feeder, \(\varphi(f_{i},j)\) is the set of consumer units of the \(j\)th feeder section on the \(i\)th feeder, \(\mu_{m}\) is the consumer level factor for the consumer unit \(m\), and \(L_{m}\) is the total load of the consumer unit \(m\).
2. Loss of power consumers The total consumer loss of the \(j\)th feeder section on the \(i\)th feeder considering the consumer level factor is denoted by \[C_{f_{i},j}^{2}=\sum_{m\in\varphi(f_{i},j)}\mu_{m}\times U_{m}\] (11) where \(U_{m}\) denotes all consumers contained in the consumer unit \(m\).  
* Long-term consequences (1) Loss of energy of power load The total loss of energy of the power load of the \(j\)th feeder section on the \(i\)th feeder considering the consumer level factor is denoted by \[C_{f_{i},j}^{3}=\sum_{m\in\varphi(f_{i},j)}\mu_{m}\times L_{m}\times T(f,a,b)\] (12) where \(T(f,a,b)\) is the duration of power outage. \(f\), \(a\), and \(b\) denote the feeder location, the fault location, and the type of power outage, respectively. If there is no fault, \(a=0\). Three types of \(T(f,a,b)\) related to different \(b\) are considered as follows: 1. \(b=1\), power supply restoration time caused by cyberattack (undesired tripping). 2. \(b=2\), power supply restoration time for fault areas caused by conventional physical faults. 3. \(b=3\), power supply restoration time for nonfault areas caused by conventional physical faults. (2) Loss of energy of power consumers The total loss of energy of power consumers of the \(j\)th feeder section on the \(i\)th feeder considering the consumer level factor is denoted by \[C_{f_{i},j}^{4}=\sum_{m\in\varphi(f_{i},j)}\mu_{m}\times U_{m}\times T(f,a,b)\] (13)  
When comprehensively considering the physical consequences caused by a cyberattack, different physical consequence indices have different degrees of impact. Using the benchmark values \(C_{ref}^{k}\), the four dimensionless indices are denoted by  
\[C_{f_{i},j}^{k,R}=\frac{C_{f_{i},j}^{k}}{C_{ref}^{k}}\quad,\quad k=1,2,3,4 \tag{14}\]  
The weight coefficients of the four consequence indices are determined by AHP. The total relative consequence of the \(j\)th feeder section on the \(i\)th feeder is obtained by  
\[C_{f_{i},j}^{TR}=\omega_{1}\cdot C_{f_{i},j}^{1,R}+\omega_{2}\cdot C_{f_{i},j} ^{2,R}+\omega_{3}\cdot C_{f_{i},j}^{3,R}+\omega_{4}\cdot C_{f_{i},j}^{4,R} \tag{15}\]  
where \(\omega_{1}\), \(\omega_{2}\), \(\omega_{3}\), and \(\omega_{4}\) are the weight coefficients.