## 4 EPS Response to Different Values of the \(k\) Factor  
Calculations of the \(k\) factor are required when:  
1. The frequency of the EPS starts to fluctuate within a range of 0.2-0.25 Hz;
2. The insensitivity limits of the generators operating in the EPS are higher than 10 mHz;
3. Power plants operating within the EPS have a large active power reserve;
4. EPS is in a quasi-static state and its frequency varies within the range of 0.2-0.3 Hz. The calculation of the \(k\) factor shall only be carried out when the operation of the EPS is already steady and stable. The dependence of frequency and active power of the EPS is then presented in Figure 4.  
The \(k\) factor helps to determine the amount of FCR required and the active power imbalance. The value of the \(k\) factor is determined from the sum of \(P_{\mathrm{nom}}\) values of all the generators with FCR enabled operating in the isolated EPS. The \(k\) factor of an isolated EPS is a relative value that indicates the response of the system (primary regulation, MW) to frequency deviations (Hz) [1; 21; 22; 23; 24; 25]. To study the response of the EPS and the effect on the system frequency with different values of the \(k\) factor, three generators with 100 MW of active power generation are switched on successively in digital simulations. For all three generators (G1, G2, and G3) the FCR function is enabled. EPS has an additional load of 10 MW connected. The response of EPS to different \(k\) factor values is presented in Figure 5:  
1. One generator (G1) with the FCR function enabled is switched on;
2. Three generators (G1, G2 and G3) with FCR function enabled are switched on. The results show that the more generators in the system can contribute to the primary frequency regulation and slow down the frequency drop of the EPS before it reaches the emergency limit, the lower frequency variation in the EPS. This study has shown that the more generators are operating with the FCR function enabled, the lower frequency deviation and the more accurate and lower frequency difference (\(\Delta f\)) from the 50 Hz value during the reset. Figure 4: Frequency dependence on active power. According to the European Commission Regulation (EU) 2017/2196 establishing a network code on electricity emergency and restoration, the EPS with the highest real-time estimated \(k\) factor will be appointed as the frequency leader, unless the EPSs of the synchronized region, or the synchronous area, agree to appoint another EPS as the frequency leader [28]. Each generator connected to the EPS is unique and therefore has different operating limits, \(k\) factor value, frequency insensitivity limit \(\Delta f\), and inertia constant \(H\). Depending on these different characteristics of the generator, the \(k\) factor of the EPS is generally determined as follows (see Figure 6):  
Figure 5: Frequency change of power system when changing the \(k\) factor. Figure 6: The \(k\) factor and frequency characteristic of EPS. The frequency response of the system depends on the combined frequency response of the generators connected to the EPS. For each generator connected to the EPS, it is mathematically described as follows:  
\[k_{\text{PP}}=\frac{P_{\text{nom}}}{\delta\cdot f_{\text{nom}}}, \tag{7}\]  
where: \(\delta\) is droop relative value (%), \(f_{\text{nom}}\) is nominal frequency (50 Hz), \(P_{\text{nom}}\) is nominal value of the active power of generator [1]. Generator turbine controller can be configured/set for the following:  
1. Active power control, in which case the setpoint \(P_{\text{set}}\) is set and the power control/variation takes place up to its setpoint \(P_{\text{act}}\);
2. Frequency control, in which case a setpoint\(f_{\text{set}}\) is set and the frequency control/variation takes place up to the setpoint \(f_{\text{act}}\). The variation takes place in cycles per minute. 3. Primary frequency control, in which case the active power value is set to setpoint \(P_{\text{set}}\) and frequency control/variation takes place up to setpoint \(f_{\text{act}}\).