# Fourier Singular Values-Based False Data Injection Attack Detection in AC Smart-Grids
## 4 Case Studies
### Simulation Results of Assumed Case Studies  
The proposed attack detection approach is examined on a cyber-physical AC-ISMG that can be seen in Figure 4b by \(\mathrm{V_{ref}}=110\sin(2*\mathrm{pi*60*t})\). ISMG, including three units of similar capacities that are connected together through resistive lines is shown in Figure 4a. It has to be mentioned that each unit comprises of a battery coupled via DC/AC converters, respectively. To examine the efficiency of the suggested attack detection approach for an AC-ISMG, various FDIAs has been investigated (such as attacks in different smart meters, which commonly have not been discovered by the distributed monitors), and also communication links are used to identify the affected node so that security measures can be taken. So, the main objective of this study is to detect FDI attacks considering the system configuration and controller design. It should be mentioned that any events in the explained case studies is segregated via a specific time interval to make an obvious realization. The information of the local controllers, sensors, communication links and central control agents could be accessed by the attacker in the FDIAs; therefore, for simulating the FDIAs, it can be considered that the information is able to be manipulated by the attackers. Thus, when the attack has occurred, the attackers manipulate the information with the aim of showing the results of attacks. Table 2 illustrates details of the system [49]. **Case study I: Instability stems from manipulating the voltage reference signal's amplitude**  
In this case, the efficiency of the FSVs in FDIA detection is considered by manipulating the voltage reference signal's amplitude to simulate the FDIA. At t = 0.5 s, FDIA began and at t = 1 s, FDIA omitted. To simulate the cyber-attack, in this section, 10% of amplitude of voltage is decreased in reference signal in the controller by the cyber-attack. The simulation results are defined in Figure 5.  
In this section, Figure 5a displays the ISMG output voltage. Loads current is explained in Figure 5b. Figure 5c illustrates FSVs of signal in the proposed expression and via \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Quantity** & **Amount** \\ \hline V\({}_{\mathrm{dc}}\) & DC link input & 800 \\ \hline f\({}_{\mathrm{r}}\) & The frequency of the voltage & 60 \\ \hline L & Inductive filter & 250 \(\mathrm{\SIUnitSymbolMicro H}\) \\ \hline C & Capacitor filter & 100 \(\mathrm{\SIUnitSymbolMicro F}\) \\ \hline f\({}_{\mathrm{s}}\) & Switching frequency & 15 \(\mathrm{\SIUnitSymbolMicro HZ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DG units’ details. Figure 4: Studied system: (**a**) Unit sample; (**b**) Cyber-physical AC-ISMG with 3 units. 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 exposed in Figure 5d. As it is obvious, 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 5: _Cont._  
**Case study II: Instability stems from manipulating the voltage reference signal's frequency**  
In this case, the efficiency of the FSVs in FDIA detection is considered by injecting an attack via manipulating the voltage reference signal's frequency to simulate the FDIA. At t = 0.5 s, FDI attack began and at t = 1 s, FDI attack is eliminated. To simulate the cyber-attack, the frequency of signal altered from 60 Hz to 50 Hz in reference signal in the controller by the cyber-attack. The simulation results are explicated in Figure 6. In this section, Figure 6 displays the ISMG output voltage. Loads current is shown in Figure 6. Figure 6 depicts FSVs of signal in the proposed state and via choosing a threshold as 40, it is able to be observed that the declared mechanism is able to successfully identify the attack.