## 4 Output Power Modelling for the Switching Process of the DFVSPS Unit
### Generating Mode
#### 4.1.2 On-Grid Operation Stage  
According to the control method of DFVSPS unit and the mathematical models of each part, the control block diagram of the power priority control strategy can be obtained as shown in Figure 16.  
By observing the control block diagram, the following conclusions can be drawn:  
1. The stator side power control closed loop is an independent control loop, and its control effect is affected by the PI regulator parameters \(k_{p1}\), \(k_{i1}\), PWM converter switching frequency, and electromagnetic parameters of the DFIM, etc. 2. The speed control closed loop is mainly used to control the guide vane control system of pump turbine. The regulation of the speed closed loop is affected by the stator side power control closed loop, as well as by parameters such as water inertia time constant of pump turbine, pump turbine governor parameters \(k_{p2}\), \(k_{i2}\), and mechanical parameters of DFIM, etc. Through the above conclusions, the adjustment of the stator side power control closed loop is not affected by the speed control closed loop. The power control closed loop is an electrical adjustment process, so it can quickly track the reference value. The response time of the speed control closed loop is longer due to the existence of the significant inertia, but since it does not affect the power control closed loop (without considering the capacity of the converter), it does not affect the speed of power regulation. Thus, the waveforms in Figures 11 and 14 can be explained. The focus of this paper is on the modelling and application of the output power of the unit. It seems to be independent from the speed control closed loop. In fact, the circulating power of the  
Figure 16: Control block diagram of the power priority control strategy in generating mode. Figure 15: Control diagram of start-up in generating mode. converter is the slip power, which is affected by the speed control closed loop. Due to the limitation of the converter capacity, it will affect the power adjustment range and adjustment speed; the analysis is as follows. In the load ramping stage and the load rejection stage, the trial-and-error method is used to determine the PI parameters in the aforementioned simulation, and the power step control is adopted to increase or decrease 30 MW every 5 s. At this stage, in order to simplify the simulation model, a straight line with a certain slope is used to replace this part of the model, as shown in Equations (17) and (18):  
\[p_{SG}=p_{g0}\cdot\frac{t-\tau_{1}}{N_{SG}},\ \tau_{1}\leq t<\tau_{1}+N_{SG}, \tag{17}\]  
\[p_{GS}=p_{g1}\cdot\left(1-\frac{t-\tau_{2}}{N_{GS}}\right),\ \tau_{2}\leq t<\tau_{2}+N_{GS}, \tag{18}\]  
where \(P_{g0}\) is the power increased during the load ramping stage, \(P_{g1}\) is the power reduced during the load rejection stage, \(\tau_{2}\) is the start time of the load rejection stage, \(N_{SG}\) and \(N_{GS}\) are the time used in the load ramping stage and load rejection stage, and Equation (17) is the load ramping stage. Equation (18) indicates the load rejection stage. The values of \(P_{g0}\), \(P_{g1}\), \(N_{SG}\), and \(N_{GS}\) characterize the rate of power change during the load ramping stage and load rejection stage. The values are related to the limits of the converter capacity, stator current and rotor current. The analysis is as follows. Firstly, the power control closed loop is analyzed. For the power model, different PI parameters will lead to different power rise time, and different segments will also affect the time of the whole load rise and fall stage.