## 5 SI Algorithm Verification Based on the Simple Theoretical Model of a Power System  
In this paper, we present the results of the comparison of the efficiency of the SI algorithm to ensure the frequency stability of the system when the frequency change is modeled in a simple theoretical model with and without the integrated SI algorithm. A simple theoretical model (Figure 10) with 1090 MW of generating sources was modeled, of which 240 MW was generating sources connected to the electricity system via power converters with an integrated SI algorithm developed according to the methodology presented in this paper. The remaining generating sources were traditional generators. Calculations were performed to investigate the efficiency of the developed SI algorithm in ensuring the frequency stability of the power system in the presence of power imbalance. For this purpose, two sets of calculations were performed: first--when generating sources were connected to 1212 busbar in the research model via power converters with the integrated SI algorithm; second--without the SI algorithm. Dynamic calculations were performed in both cases when the three-phase short circuit in 1215 busbar was simulated, and the relay protection was disconnected after 140 ms.  
As can be seen from the results of the calculations in Figure 11, when 240 MW generating sources have an integrated SI algorithm with H = 5 s, a change of 525 mHz frequency is observed after a three-phase short circuit and the loss of 85 MW generation, and without the SI algorithm, when H = 0.5 s-650 mHz. Thus, when 22% (of the total power of the generators, including generating sources connected via converters) of generating sources connected via converters with the integrated SI algorithm with H = 5 s are integrated into the power system; the frequency drop is reduced by 19.2% compared to the variant when the SI algorithm is not used. The amount of inertia can be chosen by each owner when applying to participate in the SI market or by asking the TSO to issue the terms and conditions of connection by concluding a bilateral SI service agreement with the TSO. The choice of the amount of SI depends on the type of generation source planned to be installed, the power, and the market price of the SI service. This is not addressed in this paper, as it would require a cost-benefit analysis (CBA) to be performed and the establishment of a market for SI services with service prices. It is recommended that the SI algorithm should be divided into several options, with H = 3 s and H = 5 s, which would lead to a more flexible and competitive market for SI services. Not only can generation sources with an SI algorithm participate in such a market, but traditional generators and consumers that have synchronous motors can also participate. These users could give the energy system even more flexibility. Considering that an increasing amount of attention is being paid to smart grid (SG) systems [35,36], the SI algorithm presented in the article can be integrated not only into transmission system HVDC and battery energy storage systems but also into small HVDC systems producing consumers (Figure 12), thereby contributing to the increase in the inertia of the electric energy system. This service can be provided by any user participating in the SI market. A comparison of the SI algorithm output with the simulated synchronous generator output proved that the obtained SI algorithm identically reproduces the behavior of a traditional generator in the event of sudden disturbances in the electric power system. Thus far, all of the previous articles have provided a comparison of the obtained SI performance results with other SI system results. This does not show how well SI performs in comparison with real units that provide inertia to the electrical power system. The SI algorithm presented in this paper can be adapted to various inertia coeffici  
Figure 11: Frequency nadir in power system during 3 ph short circuit following 85 MW disconnection.