# Dynamic Stability Analysis of Isolated Power System
## 5 Impact of the Isolated System's Response on Settings of HVDC BtB Converter
### Response of Isolated EPS to SC Start-Up  
The initial conditions for the digital simulation were as follows:  
1. One unit starts operating in synchronous condenser mode;
2. The HVDC BtB converter frequency control gain \(K\) is 250 MW/Hz and corresponds to 4% droop;
3. The HVDC BtB converter active power ramp speed is 100 MW/s;
4. The HVDC BtB converter dead-band limit of frequency change of the isolated system is 10 mHz. The simulation results are shown in Figures 20 and 21. After synchronizing the unit operating in SC mode with the isolated EPS, at the initial point in time, the SC generates electricity to the isolated EPS at about 3 MW (duration 1 s); due to the additional functions required to prepare the unit to operate in SC, demand starts to grow linearly until it reaches a load of (\(-50\) MW), and the length of the process is 10 s. When a load of (\(-50\) MW) is reached, demand spasmodically decreases to (\(-10\) MW) and stabilizes, and the unit can operate indefinitely with a constant demand of (\(-10\) MW). A graphic representation of this process is given in Figure 20a [20; 22; 35; 36; 37; 38; 20; 39; 33; 34; 35; 36; 37; 38]. The process of preparing the unit to operate in SC mode causes fluctuations in the frequency of the isolated EPS; if the frequency control function of the HVDC BtB converter is enabled, the frequency of the isolated EPS does not drop below 49.9 Hz. When the frequency control function of the HVDC BtB converter is switched off, the frequency of the isolated EPS drops to 49.78 Hz. The isolated EPS frequency response is shown Figure 20b. The HVDC BtB converter's response to a disturbance is shown in Figure 21 [15; 21; 22; 32]. Response of the Isolated System to a Load Change When HVDC BtB Converter's Frequency Control Function Is On  
In this section, frequency changes in the islanded system caused by a load increase or decrease while the frequency control capability of the HVDC BtB converter is applied are analyzed. The response of the system is presented when the converter's dead-band setting range is 0 to 200 mHz. Response of Isolated EPS to System's Insufficient Frequency, When HVDC BtB Converter's Frequency Control Function Is Enabled  
Based on the obtained results, it is assumed in this simulation that the load change soars over 30 MW. The HVDC BtB converter's frequency control gain is \(K=1250\) MW/Hz, and its active power ramp speed is 100 MW/s. The numerical simulation is performed using different dead-bands: 0 mHz, 50 mHz, 100 mHz, 150 mHz, and 200 mHz. The simulation results are shown in Figures 22 and 23. Frequency drops using different dead-bands are shown in Table 5. The results obtained show that the frequency control of the HVDC BtB converter reduces the frequency drop. The frequency drop directly depends on the set dead-band. In order to evaluate the frequency control capabilities of the HVDC BtB converter, the use of a 0 mHz dead-band is not recommended during the operation of an isolated EPS [15; 21; 22; 32]. Figure 22: (**a**) Frequency change when the HVDC BtB converter has a different frequency insensitivity range. (**b**) Response of the active power of the HVDC BtB converter to insufficient frequency. The smallest frequency drop occurs when using the HVDC BtB converter dead-bands of 0-50 mHz. If possible, use a 0 mHz HVDC BtB converter dead-band. Response of Isolated EPS to Load Reduction, When HVDC BtB Converter Frequency Control Function Is Enabled  
In the numerical simulation, it is assumed that the load change soars over 30 MW. The frequency control gain \(K\) of the HVDC BtB converter is 1250 MW/Hz. The active power ramp speed is 100 MW/s. The digital simulation is performed by setting different HVDC BtB converter frequency dead-bands: 0 mHz, 50 mHz, 100 mHz, 150 mHz, and 200 mHz. The simulation results are shown in Figures 24 and 25. Figure 23: Voltage fluctuations on the 330 kV side.