## 3 Calculation of System Inertia and Permissible Active Power Imbalance
The results show that the lower the rate of frequency variation in the EPS, the more generators in the system can contribute to the primary frequency regulation and further slow down the frequency drop in the EPS before the frequency reaches the emergency limit. In this case, the EPS frequency deviation (\(\Delta f\)) is the same for both simulations and depends only on the available FCR reserve. Figure 2: Frequency change of the power system during load increase. The total inertia of the EPS is equal to the sum of the inertia of all generators producing electricity in the isolated EPS. All generators or units operating in pump mode, and hydroelectric units operating in SC mode also contribute to the total EPS inertia. Renewable energy sources do not provide additional inertia to EPS [21; 22; 23; 24; 25; 26; 27]. To maintain stable operating mode, the following requirements must be met:  
1. In an isolated EPS, the maximum generation source should not exceed 300 MW;
2. In an isolated EPS, the emergency power control (EPC) function of the HVDC BtB converters must be enabled. The amount of inertia required for the stable operation of an abruptly disconnected and isolated EPS is equal to 25 MWs for each 1 MW imbalance [4; 5; 6; 22; 23; 24; 25]. This amount of inertia ensures that the frequency of the isolated EPS will not drop to the critical value of 49.20 Hz (see Table 1). Table 1 below gives an overview about needed levels of inertia in a power system during isolated operation. Concisely, according to precondition that rate of change of frequency (RoCoF) in power system during isolated operation should not be bigger than 1 Hz/s. It can be calculated that for each 1 MW of imbalance 25 MWs of inertia needs to be provided to the power system. Based on the generator operating at its maximum capacity, the amount of inertia required for stable operation of an isolated EPS must be at least 15,300 MWs. The value of inertia constant for generators operating in an isolated EPS varies between 3.2 and 6. Inertia of the EPS part No.1 is shown in Table 2.  
Figure 3: Prediction of change in the EPS frequency. \begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Level of Inertia in Power System, MWs**} &
\begin{tabular}{c} **Max Allowed Level of Instant Imbalance (Due to** \\ **Trip of Generation or HVDC Link or Import from** \\ **Neighbor Countries**) \\ \end{tabular} \\ \hline
4500 & 180 \\
5400 & 216 \\
6300 & 252 \\
7200 & 288 \\
8100 & 324 \\
9000 & 360 \\
9900 & 396 \\
10,800 & 432 \\
11,700 & 468 \\
12,600 & 504 \\
13,500 & 540 \\
14,400 & 576 \\
15,300 & 612 \\
16,200 & 648 \\
17,100 & 684 \\
18,000 & 720 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inertia and imbalance of power grid. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Generator**} & **Inertia Constant H** & **Apparent Power S, MVA** & **Inertia, MWs** \\ \hline G1 & 4.2 & 253 & 1062.6 \\ G2 & 6.11 & 372 & 2272.9 \\ G3 & 4.43 & 235 & 1041.1 \\ G4 & 4.43 & 235 & 1041.1 \\ G5 & 4.43 & 235 & 1041.1 \\ G6 & 4.2 & 253 & 1062.6 \\ SUM & – & – & 7521.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inertia of the first part of power grid. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Generator**} & **Inertia Constant H** & **Apparent Power S, MVA** & **Inertia, MWs** \\ \hline G7 & 5.2 & 531 & 2761.2 \\ G8 & 3.75 & 105 & 393.8 \\ G9 & 3.75 & 105 & 393.8 \\ G10 & 3.75 & 105 & 393.8 \\ G11 & 3.2 & 150 & 480 \\ G12 & 3.2 & 150 & 480 \\ G13 & 3.2 & 75 & 240 \\ G14 & 3.2 & 75 & 240 \\ SUM & – & – & 5382.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inertia of the second part of power grid. Total inertia of the EPS is 17,078.5 MWs.