## 4 Results and Discussion  
Based on the methodology presented in Section 3, Materials and Methods, the low-order SI algorithm transfer function was obtained. Simulink and the PSS/E modeling software packages were used to obtain this algorithm. The input signal of this algorithm must be system frequency change (\(\Delta\)f), and the output signal is fed to a controller of a generating source that is connected to a power system through power converters. An advantage of this algorithm compared to the solutions provided by other authors is that no additional tuning is required after the SI algorithm is developed with appropriate inertia magnitude. Power system frequency and comparable generator active power output calculations were performed using the PSS/E modeling environment to obtain transfer functions in the event of disturbance of the electrical power system. For this purpose, the PSS and the turbine governor were not evaluated to obtain the most accurate possible active power change due to the characteristics of the generator. The PSS was disconnected because it is a system designed for low-frequency power fluctuation damping by transmitting control signals to the excitation system to reduce influence on the active power component, which is not related to the inertia of the generator. The turbine governor was disconnected because it undergoes thermodynamic processes that are in the order of 10 to 104 s, meaning they are irrelevant to the calculations related to the SI algorithm. Thus, after the elimination of both the PSS and turbine governor, a comparable generator was obtained, and only electromechanical processes were evaluated. Different frequency changes in the power system after disturbance were also modeled, i.e., in the case of the loss of different generating sources. In total, five different cases were modeled and calculated. To explain the principles of the methodology in this paper, we present one of the five research models developed in the Simulink (Figure 4). The data obtained were used to compare an output signal of the SI algorithm with the active power output of the comparable generator to the network in the event of a fault. The SI algorithm was obtained using the Simulink software package according to the fourth point of the methodology presented in this paper. The results were also compared using a developed model (Figure 4). This model simulates the acceleration block (gray square) to eliminate the delay of the controller, inverter semiconductor elements/bridge (e.g., IGBT transistors), and frequency measurements. Three different options were calculated: Option No. 1: H = 5 s and 4173 MW loss of generation; Option No. 2: H = 5 s and 2273 MW loss of generation; Option No. 3: H = 5 s and 1263 MW disconnected load. Using the research model given in Figure 3., all the options were compared with the output signal of the developed SI algorithm, and the results are presented in Figures 5-7. Figure 4: Research model developed in the Simulink environment (the Simulink model only presented one of five). We compared SI algorithm output with a comparable generator without turbine governor, i.e., the deadband of the turbine governor was increased so as not to affect the change in calculated frequency. This eliminates thermodynamic processes that do not affect SI. From the presented modeling results, we can see that the output signal of the SI algorithm reproduces the power of the comparable generator. In the case of different faults, the active power amplitude and power direction of the SI algorithm correspond to those of the comparable generator, i.e., in the case of excess active power, power is decreased, and in case of a deficit, power is increased. In a real system, the SI algorithm should only work at the initial moment of the fault (Figures 5b, 6b and 7b), i.e., activation is limited in time and by limiting the direction of active power change twice. Figure 5: Comparison of active power outputs of the SI algorithm and simulated power output when H = 5 s and there is 2273 MW loss of generation.