## 1 Introduction  
Power balance is the foundation of stable operation of a power system, and the frequency and voltage of a power system must be maintained within a certain range to maintain the balance of active power and reactive power. However, with the increase in the proportion of a large-capacity rigid power supply such as nuclear power, and the large-scale development of renewable energy generation, the power balance of a power system is confronted with great challenges [1,2]. The power balance of a power system can be realized through the power absorption and emission of an energy storage system, which is an important way to keep the system running smoothly [3]. A pumped storage power station is an important method of energy storage. It has functions such as peak load shifting, frequency modulation and accident standby [4]. Compared with traditional fixed-speed pumped storage unit, the variable-speed pumped storage unit can adjust the speed according to the change of the head under generating mode, which can improve its operating efficiency and can adjust its power under pump mode, which has a wider range of adjustment, faster adjustment speed and better adjustment effect [5,6]. Therefore, research on switching process and the dynamic response  
of these studies is to improve the operating performance of units during tough conditions. As shown in Ref. [7], transient characteristics during the closure of guide vanes in a pump-turbine in pump mode were studied. In Refs. [8; 9], the S-shaped region of pump turbine was analyzed. Flow characteristics of the transient power interruption process of a prototype pump-turbine at pump mode were studied in Ref. [10], and flow analysis of pump turbine in load rejection was mentioned in Ref. [11]. However, these studies are only focused on the unit itself and do not take into account the requirements of the power system on the unit's operational performance. For the application research of the DFVSPS unit in the power system, the current research is mainly on the combined operation of pumped storage system and photovoltaic, wind power, etc., to reduce the fluctuation of wind power and photovoltaic output. There is also literature on the power output characteristics of DFVSPS units in the stable operation stage. In Ref. [12], the coordinated control of wind turbine and pumped storage unit were studied, and pumped storage unit and photovoltaic power generation system in Refs. [13; 14; 15] carried out modelling and static analysis on the stable operation stage of DFVSPS unit. Ref. [16] reviewed the converters used in DFVSPS units. However, the above literature only shows that the DFVSPS units have the compensation ability for power fluctuations, but the compensation range and compensation speed are not studied. Therefore, it is of great significance for DFVSPS units to exert their advantages, suppress the fluctuation of output and enhance the reliability of the power system to research the influence of the DFVSPS units on the power system in the transition process, study the compensation range and compensation speed of the DFVSPS units for power fluctuation, and established a power output model based on unit parameters and control parameters of DFVSPS units. In the second part of the paper, the mathematical model of each part of the DFVSPS unit is established. The control methods of start-up stage, load ramping stage, stable operation stage, load rejection stage and shutdown on generating mode and pump mode of DFVSPS unit are analyzed in the third part of the paper, and each stage is simulated in MATLAB/Simulink; the converter switching frequency is up to 2-10 kHz, and there will be problems such as slow simulation speed and large amount of data. Therefore, in the fourth section of this paper, the power output model of the DFVSPS unit to the grid is simplified, and the simulation effect and simulation time are compared with the electromagnetic transient model. Finally, the simplified power model is applied to a three-machine system to verify the correctness of the conclusion.