# Fourier Singular Values-Based False Data Injection Attack Detection in AC Smart-Grids
## 4 Case Studies
### Simulation Results of Assumed Case Studies
Response time of the expressed scheme at the time of FDI attack is exposed in Figure 6. As shown, the speed of the presented scheme is allowable and can detect the attack less than 10 ms from the time which the FDIA has occurred. Figure 5: Instability stems from manipulating the voltage reference signal’s amplitude to simulate the FDIA: (**a**) ISMG’s voltage; (**b**) Loads current; (**c**) FSVs of signals; (**d**) Time response of FSVs scheme (FDIA is initiated at t = 0.5 s and is omitted at t = 1 s). Figure 6: _Cont_. **Case study III: Instability stems from manipulating the voltage reference signal according to shift in the signal**  
In this case, the efficiency of the FSVs in FDIA detection is considered by manipulating the voltage reference signal according to shift the signal to simulate the FDIA. Figure 6: Instability stems from getting started on the attack via manipulating the voltage reference waveform’s frequency: (**a**) ISMG’s voltage; (**b**) Loads current; (**c**) FSVs of signals; (**d**) Time response of FSV’s scheme (FDIA is initiated at t = 0.5 s and is omitted at t = 1 s). At t = 0.5 s, FDIA began and at t = 1 s, FDIA eliminated. To simulate the attack, the ISMG output voltage is shifted in the reference signal in the controller by the cyber-attack. The simulation outcomes of the mentioned case are explicated in Figure 7. In this case, Figure 7 displays the output voltage of the ISMG. Loads current is exposed in Figure 4:0 Figure 7 shows FSVs of signal in the mentioned mood and via choosing a threshold as 40, it is able to observe that the declared mechanism is able to successfully identify the attack. Response time of the expressed scheme at the time of FDI attack is shown in Figure 4:1 As shown, the speed of the proposed scheme is allowable and can detect the attack less than 10 ms from the time which the FDIA has occurred. **Case study IV: Instability stems from manipulating the voltage reference signal through plus noise to the main signal**  
In this case, the efficiency of the FSVs in FDIA detection is considered by manipulating the voltage reference signal through plus noise to the main signal to simulate the FDIA. At t = 0.5 s, FDI attack began and at t = 1 s, FDI attack eliminated. To simulate the FDIA, a white noise combined to the ISMG output voltage in the control unit by the cyber-attack. The simulation outcomes of the mentioned case are indicated in Figure 4:2  
Figure 8a displays the ISMG output voltage. Loads current is exposed in Figure 8b. Additionally, Figure 8c shows FSVs of signal in the proposed case and via choosing a threshold as 40, it is able to observe that the declared mechanism is able to successfully identify the cyber-attack. Response time of the expressed scheme at the time of FDI attack is depicted in Figure 8d. As shown, the speed of the proposed scheme is allowable and can detect the attack less than 10 ms from the time which the FDIA has occurred. Figure 4:3 _Cont._  
Figure 4:4 Instability stems from manipulating the voltage reference signal according to shift the signal: (**a**) ISMG’s voltage; (**b**) Loads current; (**c**) FSVs of signals; (**d**) Time response of FSV’s scheme (FDIA is initiated at t = 0.5 s and is omitted at t = 1 s). Figure 4:5 Instability stems from manipulating the voltage reference signal through plus noise to the main signal: (**a**) ISMG’s voltage; (**b**) Loads current; (**c**) FSVs of signals; (**d**) Time response of FSV’s scheme (FDIA is initiated at t = 0.5 s and is omitted at t = 1 s). **Case study V: Instability stems from manipulating the voltage sensor**  
In this case, the efficiency of the FSVs in the FDI attack detection is considered by injecting an attack on the measured voltage via smart metering. At t = 0.5 s, FDI attack began and at t = 1 s, FDI attack eliminated. To simulate the cyber-attack, the measured voltage of the ISMG, which is measured by sensor, changed in sensor by the cyber-attack, and the amount of voltage is shown less/more of the real value.