## 3 Materials and Methods  
All synchronous generators connected to the electrical power system rotate at the same synchronous speed while maintaining a constant frequency. In the event of a disturbance or other abnormal event in the electrical power system that causes an imbalance between generation and load, a deviation from the normal 50 Hz frequency is observed. When enough rotating conventional generators are connected to the electrical power system, their KE prevents a sudden change in the frequency of the power system. The KE of synchronous generators is proportional to their inertia, and the term \"conventional system inertia\" is used to define the inertia of all rotating units (generators, turbines, motors, and all other rotating units that are not connected to the grid through power converters) connected to the electrical power system, and it describes how the frequency will change as the power balance in the power system changes. CSI can be expressed as follows:  
\[H=\frac{\textit{stored energy at rated speed in MW}\times s}{\textit{MVA rating}}, \tag{2}\]  
\[H=\frac{1}{2}\frac{\textit{J}\omega_{0m}^{2}\times 10^{-6}}{\textit{MVA rating}}. \tag{3}\]  
The basic parameters affected by the CSI are RoCoF, frequency nadir, and steady-state frequency. In the event of insufficient quantities, the CSI, which is mainly generated by high-mass conventional generation sources, helps to reduce the RoCoF before the electrical power system begins to change the power output signal by activating initial frequency damping. Thus, in the event of a disturbance in the conventional electricity system and a change in the power balance, the CSI reduces the frequency nadir, and only after a certain delay takes place does the primary frequency control stabilize the frequency of the electrical power system. The secondary frequency control returns the frequency to the nominal value. Using a large real-network mathematical model and the PSS/E, data are required for the calculation and validation of the parameters of the SI algorithm. Here, a mathematical model consisting of more than 3500 buses was used for the calculations. The simulation was performed by evaluating the high-power loss in the electrical power system with the aim to cause a change in frequency and to capture changes in frequency, active power, generator terminals, and system angles and voltage. A dynamic model was created using standard PSS/E models. Generators were modeled using the round rotor generator model (GENROU) and salient pole generator model (GENSAL). To model turbines, the hydro turbine governor model (HYGOV), modified IEEE type 1 turbine governor model with boiler controls (TGOV5), and IEEE type 1 speed-governing model with speed deadband (IEEEG1 SDU) were used. Excitation systems were modeled using IEEE type ST4B potential or a compounded source-controlled rectifier (ESST4B) and a 1992 IEEE type ST1A excitation system model (ESST1A). To model the power stabilizer, a 1992 IEEE type PSS2A dual-input signal stabilizer model (PSS2A) [33] was used. Objectives of the methodology development and determination of its effectiveness:  
1. Using the results of the generator mathematical model in the presence of power imbalance in the power system, develop efficient methodology to generate an SI algorithm. 2. Develop an efficient SI algorithm suitable for integration into the controllers of power sources connected to the power system via power electronics converters. 3. Evaluate the efficiency of the developed SI algorithm in ensuring the frequency stability of the electrical power system in the presence of power imbalance. A general linear (GL) model (Figure 1), which provides flexibility for system dynamics and stochastic dynamics, can be used for parametric identification. However, nonlinear optimization techniques are required to develop a general linear model. These methods require complex mathematical calculations, and it is unclear whether stable results can be obtained. Therefore, in this paper, we chose to use a simplified output-error (OE) model.