## 4 Output Power Modelling for the Switching Process of the DFVSPS Unit
### Generating Mode
#### 4.1.2 On-Grid Operation Stage
The response time can be calculated according to the power control closed loop, which is shown in Figure 17.  
If \(k_{2}=-3\)\(U_{s}L_{m}/2\)\(L_{s}\), then the closed loop transfer function of the power control closed loop is shown in Equation (19):  
\[G_{c}(s)=\frac{-k_{2}k_{PWM}(k_{p1}s+k_{i1})}{s(T_{s}s+1)-k_{2}k_{PWM}(k_{p1}s+k_{i1})}. \tag{19}\]  
Since the switching frequency of the PWM link is very high and the switching frequency in simulation is 2 kHz, the influence of the PWM on the power control closed loop can be ignored. According to the characteristic equation of the power control closed loop, it can be calculated that, when the \(k_{p1}\) and \(k_{i1}\) are greater than 0, the characteristic equation does not have poles in the right half plane, and the closed loop is stable. The response of the power control closed loop to the step signal is solved as follows. If \(-k_{2}k_{p1}=m\), \(-k_{2}k_{i1}=n\), the response of the power control closed loop to the step signal is:  
\[Y(s)=\frac{1}{s}\cdot\frac{ms+n}{(1+m)s+n}. \tag{20}\]  
The corresponding time-domain expression is:  
\[y(t)=1-\frac{1}{1+m}e^{\frac{-n}{1+m}t}. \tag{21}\]  
The larger the parameters \(k_{p1}\) and \(k_{i1}\), the shorter the response time of the step signal, as shown in Table 2 (The PI parameters can be arbitrarily selected within the range of \(kp1>0\), \(ki1>0\), and different parameters correspond to different response times.). Figure 17: Power control closed loop. The above table shows the response time of the power control closed loop after each stacking step instruction. For the load ramping stage and load rejection stage, in order to reduce the influence of the power adjustment on the speed, the method of segmented superimposed power command is adopted. Taking the unit parameters selected in this paper as an example, the rated power of the unit is 300 MW, and the no-load grid-connected power is 30 MW. It is necessary to superimpose a further 270 MW power from no-load power to rated power. The specific number of segments can be divided into the following types: scheme 1: each stack is 30 MW and nine times; scheme 2: each stack is 45 MW and six times; scheme 3: each stack is 67.5 MW and four times; scheme 4: each stack is 90 MW and three times; scheme 5: each stack is 135 MW and two times; scheme 6: adjust 270 MW at a time. The effect of power control closed loop with different response times and different number of segments is shown in Figure 16:0  
According to Figure 18a, it can be found that, when the number of segments is the same, the response time of the power control closed loop is different with different regulator parameters. The larger the parameter of the PI regulator, the shorter the response time, such as the parameter \(K_{p1}\) = 0.00005, \(k_{i1}\) = 0.0005, loading 270 MW power only takes about 7 s; Figure 18b is the waveform of the power control closed loop at the load ramping stage with the same response time and different number of segments. It can find that the fewer number of segments, the shorter the response time. For example, when all 270 MW power is loaded at one time, the time needed for load ramping stage is only 5 s.  
During the load ramping stage and load rejection stage, different response times and number of segments are used, and the response of the speed control closed-loop is also different. Since the power flowing through the converter is the slip power, the converter power is constantly adjusted when the speed is continuously adjusted. The following two figures show the effect on converter power with different response times and different number of segments. Figure 19a shows that, when the number of segments is the same, the fluctuation of converter power with different regulator parameters used in the power control closed-loop. It can be found that the larger the parameter of the PI regulator, the shorter the response time, but it will cause greater fluctuation on speed, and also greater power flowing through the converter.