# Dynamic Stability Analysis of Isolated Power System
## 3 Response of the Isolated EPS to a Load Change
### Response of Isolated EPS to a Load Increase  
Analysis of the dependence of a frequency drop in the system on an increase in load is accomplished by simulating a soaring change of the transmitted active power flow through the HVDC BtB from 10 to 50 MW, in 10 MW increments. During the simulation, it was considered that only one unit operated in synchronous condenser mode (case A). The simulation results are shown in Figure 6a,b. The results show that, in cases with a load jump greater than 40 MW, damped active power oscillations occur. Damped active power oscillations are caused by a voltage drop in the 330 kV section. Fluctuations in the 330 kV voltage are caused by a decrease in the active power flow, i.e., due to the response of the system to a change in power. The dependence of the frequency drop on the active power change is presented in Table 3. A drop in frequency greater than short-term tolerance, i.e., >200 mHz, is reached in the event of the load increasing by 30 MW or more [15; 16; 17; 18; 19]. Figure 5: Structure of the electromagnetic model of a blurred generator. A frequency drop to the critical, i.e., to 49.80 Hz, limit corresponds to the load increasing by 25 MW. The minus sign here (in Table 3) denotes active power export from the EPS. After estimating the maximum allowable disturbance possible in the isolated EPS (30 MW) at the existing calculated inertia, the reaction of the EPS when two units are operating in the system in SC (synchronous condenser) mode was analyzed in Figure 7.  
When two units operate in SC mode, with a disturbance of 30 MW, the frequency of the isolated EPS drops to 49.79 Hz. A frequency drop to the 49.80 Hz limit corresponds to the load increasing by 27.5 MW. The total inertia of an isolated EPS is equal to the sum of the inertias of all the generators operating in the system. All generators and units operating in pump mode and hydro-electric generators operating in SC (synchronous condenser) mode also contribute to the total inertia of an isolated EPS. Wind power plants and solar power plants do not provide additional inertia to an isolated EPS [15; 20; 21; 22; 23]. Figure 6: (**a**) Frequency change in the isolated power system caused by a load increase (case A). (**b**) Voltage fluctuations on the 330 kV side caused by a load increase (case A). Figure 7: Frequency change in the isolated power system caused by a load increase (case B). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Power Change, MW** & **Frequency, Hz** & **Power of HVDC Converter, MW** \\ \hline
10 & 49.92 & \(-\)235 \\
20 & 49.83 & \(-\)245 \\
30 & 49.77 & \(-\)255 \\
40 & 49.69 & \(-\)265 \\
50 & 49.62 & \(-\)275 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Frequency change in the isolated power system. The amount of inertia required for the stable operation of an isolated EPS is equal to 25 MWs for every 1 MW imbalance. This amount of inertia ensures that the frequency of the isolated EPS will not drop to the critical value of 49.80 Hz [15; 16; 17; 18; 19]. The following conditions must be ensured in the isolated EPS [16; 17; 18; 19; 24]:  
1. The maximum generation source in an isolated EPS shall not exceed 200 MW;
2. Emergency power control of the HVDC BtB converter is enabled (HVDC EPC). The amount of inertia required for the stable operation of an isolated EPS is equal to 5000 MWs. The inertia of an isolated EPS is 5793 + (SC1) 992 + (SC2) 992 MWs [15; 21; 22; 25; 26]. The inertia constant (H) of an isolated EPS operating with generators ranges between 2.5-6.0 [27; 28; 29; 30]. Factor \(k\) of an isolated EPS is a relative value that indicates the response of the system (primary control, MW) to frequency deviations (Hz) and is expressed as follows:  
\[k=\frac{\Delta P}{\Delta f} \tag{1}\]  
where \(\Delta P\) is active power change (MW), and \(\Delta f\) is frequency change (Hz). Factor \(k\) helps to easily determine the amount of primary control of active power, as well as active power imbalance.