# Analysis of Six Active Power Control Strategies of Interconnected Grids with VSC-HVDC
## 5 Transient Stability Simulation Results with Six Different Active Power Control Schemes
### Angle Spread Evaluation with PGs
#### 5.1.2 Ramp-Rate Control  
Figure 12 shows the results regarding (c) and (d). Both control schemes are ramp-rate control strategies, and both the RRS between \(t_{1}\) and \(t_{2}\) and the active power reference are different. In (c), 1000 MW power is transferred to area 2 with a high RRS, so the angle stability of the sending side is further worsened compared to that in (d), which sends 750 MW. In area 1, (c) experiences a sudden large power change at \(t_{1}\), and shows a more unstable result. Concerning the receiving side in area 2, the angle deviation \(x_{0}\) is explicitly different between the two methods. The results show that the generators of area 2 could not cover the severe frequency drop, and there is a possibility of loss of synchronisms at time = 1.45 s. Therefore, applying method (c) is more stable in terms of the angle stability of area 2. However, a tradeoff was observed as method (d) is more suitable for area 1, where the SCR is low.  
Figure 11: Angle spread results of each area according to (a) and (b) in Table 1.  
Figure 12: Angle spread results of each area according to (c) and (d) in Table 1.  
Figure 13 shows the results regarding (e) and (f). Both control schemes are ramp-rate control strategies, and the only difference is the RPS between \(t_{2}\) and \(t_{3}\). The power change references are all the same as 1000 MW; thus, the \(|\Delta P_{\mathit{vsc}}(k)|\) is also the same. By adjusting time \(t_{3}\), the two control methods were set to have a twofold slope difference. Scheme (f), which has a low RRS, shows slightly greater angle stability results in area 1. From the result of area 2, scheme (e) shows a greater angle stability result that the first encountered peak time and its recovery characteristic is faster than that in (f). Thus, it is concluded that active power control with a certain RRS is more suitable for both areas. However, using an overly low RRS will limit the stability improvement of area 2.  
Figure 14 shows the results regarding (c) and (e). Both control schemes are ramp-rate control strategies with the same RRS, and the only difference is the power sending time. In (c), the power is transmitted immediately following the contingency event (=\(t_{1}\)) while the power is increased during the frequency recovery stage (=\(t_{2}\)) in (e). As shown in the result of area 2, if the grid operator uses both ramp-rate control schemes, sending power during the frequency recovery stage shows more stable results in terms of the angle stability. This is because, as mentioned earlier in Section 5.1.1, the initial frequency drop will not be immediately reduced by (c). This characteristic causes the PGs of area 2 to generate less power. Therefore, at about 1.3 s the first damping angle \(x_{F}\) is more mitigated with (e); thus, sending power at \(t_{2}\) is more suitable for both TSOs.  
Figure 14: Angle spread results of each area according to (c) and (e) in Table 1.  
Figure 13: Angle spread results of each area according to (e) and (f) in Table 1.