## 3 False Data Injection Attacks in Smart Grids  
A group of malicious data attacks that target crucial infrastructures under the management of cyber-physical information systems is called false data injection. FDIA tactics entail the attacker interfering with sensor readings, which causes erroneous data to be inserted in calculations and variables that define the system state without being noticed [9; 10]. In an FDI attack, the attacker introduces erroneous measurements or data into the power grid's sensors or communication lines. By manipulating the data, the attacker can deceive the control systems into believing that the grid is in a different state than it is. As control systems rely on precise and timely information to make crucial decisions, like changing power generation, load balancing, or managing system problems, this could have catastrophic repercussions. false data injection (FDI) attacks are common in power system models for numerous reasons [9; 10; 11; 12; 13]:  
* High impact: Industries, businesses, and families depend on power systems. Power grid disruptions can cause economic losses, societal discomfort, and security risks. FDI attacks can cause significant harm or interruptions with little effort. * Interconnectedness: Power grids span broad geographic areas and involve many power production units, transmission lines, and distribution networks. Power systems are interconnected, allowing attackers to exploit vulnerabilities in one grid sector and cause widespread disruptions or blackouts. FDI attacks can disable a system by targeting individual components or nodes. * Power system operation depends on accurate and timely data: Control systems monitor the grid and make decisions and act using sensor measurements, communication routes, and data processing algorithms. Attackers can mislead control systems and cause disruptions by inserting misleading data. Data-dependent power system models are vulnerable to FDI attacks. * FDI attacks can adversely affect the equipment: Data and control signal manipulation can cause equipment overheating, voltage instability, and failure. Power systems are tempting targets for cyberattackers looking to cause physical damage. In an electrical power system, \"state estimation\" refers to estimating the grid system's status using data from the meters on each bus. \"The bus voltage, bus active power, and bus reactive power are monitored; bus voltage and phase angle are state variables; and this system's alternating current (AC) power flow model. \[a=m(b)+i \tag{1}\]  
where b \(\epsilon\) EF is the state variable of the power system, which is the node voltage and phase angle variable, a \(\epsilon\) EL is the measurement vector, which is the measurement data of the sensor, i \(\epsilon\) EL is the measurement noise, \(m(b)\) is the nonlinear relationship between the measurement value and the state variable [9]. The direct current flow model can be obtained by applying Taylor expansion on the AC model, which can be approximated linearly near the operating point. This is based on the assumption that the noise follows a Gaussian distribution with a mean value of 0 and a covariance matrix of \(\Lambda\) and that the system's state does not change quickly over time. \[a=Mb+i \tag{2}\]  
where M \(\epsilon\) EL is the Jacobian matrix, and the state vector estimation can be calculated by the weighted least square estimation as follows:  
\[\hat{b}=\left(M^{T}\wedge M\right)^{-1}M^{T}\wedge a \tag{3}\]  
In the case of FDI attacks, the attacker aims to tamper/alter the measurement data in the terminal to make the devices generate vague state estimation, eventually resulting in the wrong output. The measurement carried out using Equation (2) is modified when the terminal is attacked. \[\widetilde{a}=Mb+C+i \tag{4}\]  
where N a \(\in\) R is the attack vector; bad data detection (BDD) is one of the most commonly used detection methods for the attack vector.