# Fourier Singular Values-Based False Data Injection Attack Detection in AC Smart-Grids  
[PERSON]  
1 Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz 7155713876, Iran; [EMAIL_ADDRESS] (M.D. ); [EMAIL_ADDRESS] (M.G.) [PERSON]  
1 Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz 7155713876, Iran; [EMAIL_ADDRESS] (M.D. ); [EMAIL_ADDRESS] (M.G.) [PERSON]  
1 Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz 7155713876, Iran; [EMAIL_ADDRESS] (M.D. ); [EMAIL_ADDRESS] (M.G.) [PERSON]  
2 Department of Management and Innovation Systems, University of Salerno, 84084 Salerno, Italy 23 Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg 2028, South Africa 34 School of Electrical and Electronic Engineering, University College Dublin, 4 Dublin, Ireland 45 Department of Electrical and Computer Engineering, Sultan Qaboos University  
system states might disrupt electrical power network performance, resulting in physical or economic damages on the energy system. Good examples here are References [5; 6], where comprehensive studies are based on an influx of these kinds of cyber-attacks. False Data Injection (FDI) threat can be mentioned as a prominent challenge on the system state estimation among common cyber-physical attacks in EPGs [7; 8]. The use of FFT in detecting cyber-attacks that have the ability to extract high-level features has made this approach a powerful method against new attacks or small mutations. Additionally, a combination of machine-learning-based techniques and FFT can lead to better performance of cyber-attack detection. Recently published papers [9; 10; 11] dealt with the issue of signal injection attack and FFT. Jamming in False Data Injection Attack (FDIA) is different from other physical or cyber-attacks. Successful FDIAs are able to revolve the conventional residuary-based spoiled, invalid, incorrect and bad data detection scheme [12]. Without a progressive diagnostic scheme, FDIA is able to be secretly started several times and a dramatic threat to the network is rendered. Many studies have been assigned to investigate possible approaches of constructing FDIA in SGs. Many of the existing researches on constructing FDIA are focusing on cyber or physical attacks in EPGs via DC state estimation with several cases owing to usual system systematic models [7]. For example, a universal known scenario attack is that when the other party gains access to the part of electrical infrastructure information, then the attacker is able to change a group of measured values [8; 13]. In such techniques, FDIA should be able to bypass or change conventional detection approaches successfully, and false information injects and throws in the sensors or devices of the subsystem. Nowadays, attack state estimation of FDI with the aim of evaluating AC has been gradually taken into consideration, and to construct such attacks, analytical and technical studies have been conducted. In References [14; 15], in order to execute FDI attack in AC power system state estimation with some or entire system information, viable techniques have been presented. Generally, both AC and DC state estimations can be under FDI attacks. Potential FDI attack detection techniques have been explored in prior studies over vulnerable points of EPGs system [16; 17]. Besides, negative effects and possible defense strategies have also been examined [14; 15; 18]. Additionally, many commentators are of the view that basically two categories according to AC or DC models have been considered and studied separately [19]. Several methods have been employed to detect FDIA in DC power systems, including statistical techniques [20], sparse optimization [21], state forecasting methods [22], network theory approaches [23], and also schemes based on machine learning [24; 25]. All of them displayed acceptable detection efficiency and incorrect signal rates versus FDIA in DC model.