**1. Introduction**

China's new-generation energy revolution advocates the development of non-fossil energy, and PV energy has become an important part of non-fossil energy due to its inexhaustible advantages. It is estimated that in 2035, photovoltaic virtual (PV) energy will account for 26% of total installed capacity and 14% of electricity generation [1].

Power system frequency is an important standard to reflect the power surplus and deficiency of a power system. Frequency response control mainly reflects the power support function of source side to grid side. The influence of large-scale PV power plants (PV-PPs) on power system frequency is mainly reflected in two aspects [2–4]:

• Reduce the equivalent moment of inertia of the power system. The PV cell is a static original, which does not have any rotating standby. After being connected to the power grid, the original equivalent inertia will be less;

• The primary frequency response capability of the system is weakened. Under the action of maximum power point tracking (MPPT), the PV output is uncontrollable and cannot provide power support for the system.

It is obvious that large-scale PV-PPs will weaken this support after they are connected to the power grid [5–7]. The proposal and promotion of virtual synchronous generator (VSG) control technology can effectively solve the above problems and, at the same time, can give the PV grid-connected system the ability to participate in the frequency and voltage regulation of the power grid independently [8–10]. However, the PV system active power output changes with the external environment (including solar irradiance and temperature) under the effect of maximum power point tracking (MPPT). Since the active output is not controllable, the traditional VSG control strategy cannot be directly used in PV systems. Existing related research in joining the ESSs to the DC or AC side of the PV system [11,12] can effectively solve the above problems. By controlling the charging and discharging of ESSs, the effect of controlling PM output can be simulated in a short time, but it will be affected by the physical constraints of the ESSs. In reference [13], a 50 kW × 30 min lithium-ion battery pack is used to connect a PV array (installed capacity of 500 kW) DC side, and active frequency response is realized by controlling the output of the ESSs. However, any benefit brought by the ESSs to the power grid is based on the economic cost of ESSs [14].

In large-scale PV-PPs such as Hexi New Energy Base in GanSu Province, China, limited by the current energy storage technology level, ESSs cannot be widely used in PV-PPs, and the charging and discharging efficiency is low. Frequent charging and discharging not only makes the energy utilization rate lower but also affects the service life of the ESSs, resulting in greater economic losses. PV-power reserve control (PRC) maintains a part of the power up/down capability by reducing the output of the PV system [15–20] and participates in the power system frequency response in combination with inertial response control and droop control, which is called fast frequency response (FFR) or active power control (APC) [2,21,22]. However, compared with the VSG control method, the VSG is a direct simulation of the internal potential phase motion and its basic inertia and damping characteristics of the SG, and it is the simplest and most effective way to realize the characteristics of the traditional SG. In addition, in the previously published works on PV-PRC, there are different views of whether the voltage operating point should be located to the left or right of the maximum power point voltage (*V*mpp) in PV-PRC mode. In addition, the PV-PRC model means that a part of the photovoltaic energy is wasted, but there is little work on how to choose the appropriate reserve ratio.

Aiming at the above problems, this paper takes the two-stage PV grid-connected system as the research object. The DC/DC and DC/AC converters implement PV-PRC/MPPT and VSG control respectively. We named this control method as the PV power reserve control type VSG (PV-PRC-VSG) control technology. In this paper, the traditional PV-PRC and PV-VSG are combined and further improved. The main contributions are as follows:


In Section 2 of the paper, the traditional PV-VSG technology is introduced in detail. The implementation strategy of PV-PRC and the position of the voltage operating point are elaborated in Section 3. The proposed PV-PRC-VSG control technology and the range of the reserve ratio in PV-PRC mode are described in Section 4. In Section 5, the validity of the proposed method is verified by simulation experiments under various operating conditions.

#### **2. Modeling and Analysis of PV-VSG**

#### *2.1. Principle and Embodiment of the VSG*

VSG control can be divided into active loop control and reactive loop control from the function and control target. Its active loop includes active frequency droop control and inertial response control, which mainly realizes the function of independent FR. The reactive loop consists of reactive power-voltage droop control and end-voltage closed-loop control, which realizes automatic voltage regulation and voltage amplitude control of the VSG [23]. The basic mathematical model of the VSG is as shown in Equation (1). The VSG control block diagram controlled by the mathematical model is shown in Figure 1.

$$\begin{cases} J\frac{d\boldsymbol{\omega}}{d\boldsymbol{\omega}} = \left(P\_{\rm m} - P\_{\rm e}\right) / \boldsymbol{\omega} \\ P\_{\rm m} = P\_{\rm ref} + D\_{\rm P}(\boldsymbol{\omega}\_{\rm R} - \boldsymbol{\omega}) \\ E\_{\rm m} = \frac{1}{K\boldsymbol{\varepsilon}} \Big(D\_{\rm q}(l\boldsymbol{I}\_{\rm ref} - l\boldsymbol{I}\_{\rm m}) + Q\_{\rm ref} - Q\_{\rm e}\Big) \end{cases} \tag{1}$$

where *J* is the moment of inertia, *P*ref and *Q*ref are the given values of active power and reactive power, *P*e and *Q*e are the actual output values of active power and reactive power, ωn and ω are the rated and actual values of electric angular velocity, *<sup>D</sup>*p and *<sup>D</sup>*q are the droop coe fficients of active and reactive loops, *U*m and *U*ref are the actual and given values of grid voltage amplitude, *E*m is the internal potential amplitude of the VSG, *K* is the integral coe fficient, and it can be replaced by PI regulator.

**Figure 1.** Principle and embodiment of the virtual synchronous generator (VSG).
