*4.4. Fixed Dummy Value Model (Results)*

The proposed model of a fixed dummy value was implemented for the AC power flow network of the IEEE 14-bus system. The meters sent the actual value and the fixed dummy value to the control room in the form of a measurement vector. Table 1 shows the actual values and the fixed dummy values at the first instant for the first five buses and first five transmission lines. In the control room, the difference, i.e., the residue of two dummy values, was calculated. One dummy value was obtained from the measurement vector and the other was already present in the control room. As the dummy value was fixed in this case, it should not change at any instance. Therefore, for a secure system, the value of the residue should be zero.

**Figure 4.** Categorization of safe measurements, simple attacks, and stealth attacks based on the threshold in an AC SE.

**Figure 5.** The results of an AC SE for simple and stealth attacks in the form of a bar graph.


**Table 1.** Active and reactive powers injected into the first 5 buses and the active and reactive powers flowing through the first 5 transmission lines in the forward and backward directions.

The results are shown in Figure 6. The bar graph shows the results for safe measurements, simple-attacked measurements, and stealth-attacked measurements. Safe measurements are labeled as 1, simple-attacked measurements as 0, and stealth-attacked measurements as −1. The residue was calculated for each measurement and plotted along the vertical axis. For safe measurements, the value of the residue was zero, as shown in the bar graph. In the case of simple-attacked measurements and stealth-attacked measurements, the residue was not zero, as the dummy value was changed. Therefore, our proposed model could detect all kinds of attacks, such as simple attacks and stealth attacks. Stealth FDI attacks remained undetected by the DC and AC state estimation, but they could be detected by using our proposed approach.

**Figure 6.** Detection results of the fixed dummy value model for simple and stealth attacks based on dummies.
