## 3 Deliberate Attacks on IECPS
### Cyberattacks
#### 3.1.3 False Data Injection Attacks  
FDIA is a new type of data attack, which is becoming increasingly harmful as energy systems and cyber systems become more and more coupled. The principle of FDIA is shown in Figure 5, in which the attacker carefully designs erroneous data that can bypass the undesirable data detection mechanism, and then replaces the erroneous data with the measurement data on the physical side or the estimation of the state of the control center to mislead the control center to make wrong decisions or cause wrong actions of the actuators on the physical side, thus leading to an unsafe operation of the system. Figure 4: Schematic diagram of the MITM. With the continuous development of FDIA, FDIA can be roughly divided into general FDIA, load redistribution attack, and false topology attack. We conducted a literature survey based on the above three typical FDIAs and formed the FDIA cases for energy systems shown in Table 2.  
* **General FDIA model** The key to successfully launching a FDIA lies in bypassing the system's bad data detection mechanism. Most current research has identified the residual detection method as the detection method to be avoided in FDIA. Therefore, the attack vector \(a\) needs to satisfy the following constraints: \[z+a=H(x+x_{a})+e\] (4) \[r=z-h(\hat{x})\] (5) \[\left\|r\right\|_{2}\leq\varepsilon,\] (6) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Target** & **Ref.** \\ \hline \multirow{4}{*}{General FDIA} & State estimator & [23] \\  & Energy market & [24] \\  & RTU & [25] \\  & AGC & [26; 27; 28; 29; 30; 31; 32; 33] \\ \hline \multirow{2}{*}{Load redistribution attack} & Power system & [34; 35; 36] \\  & Weather forecast system & [37; 38] \\  & Integrated energy system & [39] \\ \hline \multirow{2}{*}{False topology attack} & DC power flow model & [40; 41; 42] \\  & AC power flow model & [43; 44] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FDIA cases for energy systems. Figure 5: Diagram of FDIA mode of action. where \(z\) is the system measurement data; \(x\) and \(x_{a}\) are the state estimation bias caused by the system state quantity and false measurements, respectively; \(H\) is the matrix describing the relationship between the measurement value and the state quantity; \(e\) is the measurement error; \(r\) is the state estimation residual; \(\hat{x}\) is the state estimation value; \(h(\cdot)\) is the nonlinear function describing the relationship between the measurement value and the state quantity; and \(\varepsilon\) is the threshold value for residual detection. Constraints (6)-(8) are the basic conditions followed in constructing the FDIA, and in the actual construction of the FDIA model, it is necessary to determine the target data to be modified and the modification range of the target data, so as to establish a specific FDIA model. * **Load redistribution attackmodel*
* As a specific form of FDIA, the LR attack requires the attacker to circumvent both the state estimator and bad data detection mechanisms during its construction, thus necessitating the preservation of the system's total load [39]. \[\sum_{i=1}^{N_{d}}\Delta D_{i}=0\] (7) \[\Delta F_{L}=-S_{F}K_{D}\Delta D,\] (8) where \(\Delta D_{i}\) is the load modification amount of load node \(i\); \(\Delta F_{L}\) is the line current attack vector; \(S_{F}\) is the transfer factor matrix; \(K_{D}\) is the node-load association matrix; \(\Delta D\) is the load modification vector; \(N_{d}\) is the number of load nodes. To avoid injected false load data being detected by the scheduler, the amount of load modification should be set within a reasonable range: \[-\xi\mathbf{D}\leq\Delta\mathbf{D}\leq\xi\mathbf{D},\] (9) where \(\xi\) is the range of modified quantities of the load; \(\mathbf{D}\) is the vector of measured values of the load node. Furthermore, the number of measurement devices under attack, including load and current measurement instruments, must be constrained: \[\eta_{D,i}=\left\{ \begin{array}{ll}0&\Delta D_{i}=0\\ 1&\Delta D_{i}\
eq 0\end{array}