## 4 Output Power Modelling for the Switching Process of the DFVSPS Unit
### Generating Mode
#### 4.1.2 On-Grid Operation Stage
For example, under the parameters \(k_{p1}\) = 0.00005, \(k_{i1}\) = 0.0005, it takes only about 7 s to upload 270 MW, but the forward power \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(k_{p1}\) & **0.000005** & **0.000007** & **0.000009** & **0.000015** & **0.00003** & **0.00005** \\ \hline \(k_{i1}\) & 0.00005 & 0.00007 & 0.00009 & 0.00015 & 0.0003 & 0.0005 \\ response time & 5.0 & 3.5 & 2.8 & 1.8 & 1.1 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Response time of step signal under different PI parameters. Figure 18: Effect of power control closed loop. (**a**) different response times; (**b**) different number of segments. of the converter is 54 MW, the reverse power is about 4 MW, so the capacity of the converter needs to be 58 MW; Figure 19b shows the fluctuation of converter power when the response time is the same, but the number of segments is different. The fewer the number of segments, the shorter the response time of load ramping stage will be, and also the converter power will greatly increase. For example, when uploading all 270 MW power at a time, the time required for the load ramping stage is only 5 s, but the forward power of the converter is about 80 MW, the reverse power is about 20 MW, and the capacity of the converter needs to be 100 MW. Figure 19 shows the power change of the converter only considering the load ramping stage. Considering the load rejection stage and the pump mode, the converter power flow direction will be opposite to that of the load ramping stage, so the capacity requirement of converter is higher. For the equivalent of the power model in the load ramping stage and load rejection stage, the parameters of \(P_{g0}\), \(P_{g1}\), \(N_{SG}\), and \(N_{GS}\) can be selected according to the parameters of the power control closed loop and the related limits of the rotor side voltage, current, capacity of converter and other parameters. The overall conclusion is the higher the power change and the shorter the response time, the higher the corresponding converter capacity. Therefore, the parameters of the load ramping stage and load rejection stage can be selected in terms of achievability, economy, and the like. The parameter selected in the simulation is: \(k_{p1}\) = 0.000005, \(k_{i1}\) = 0.00005, so the response time of each segment is 5 s, each segment is superimposed 30 MW, superimposed seven times to reach 240 MW. This choice requires small capacity, easy implementation, and high economy. According to the selected parameters, \(P_{g0}\) = 210 MW, \(P_{g1}\) = 210 MW, \(N_{SG}\) = 35 s, \(N_{GS}\) = 35 s, the comparison of the waveforms before and after the equivalent of the load ramping stage and load rejection stage is shown in Figure 20. The red line in the figure is unit active power of simplified model obtained by Equations (17) and (18). In addition, the black line is the unit active power simulation waveform obtained by the electromagnetic transient simulation model. When the unit is operating near the stable operation point, the power regulation is still completed by the power control closed loop but unlike the wide range of power changes that occur during the load ramping stage and load rejection stage. Therefore, it can be expressed by the transfer function of power control closed loop, as shown in the following equation:  
\[p_{G}=G_{1}(s)P_{ref},\ \tau_{1}+N_{SG}\leq t<\tau_{2}, \tag{22}\]  
where \(G_{1}\)(s) is the transfer function of power control closed loop, shown in Formula (19). Figure 19: Change diagram of converter power. (**a**) different response times; (**b**) different number of segments. The equivalent effect of the stable operation stage is shown in Figure 21. The red line in the figure is unit active power of simplified model obtained by Equation (22) and the black line is the unit active power simulation waveform obtained by the electromagnetic transient simulation model. \(\tau_{2}\) is the end time of the stable operation stage.