*2.2. Traditional PV-VSG Technology*

In this paper, the two-stage grid-connected PV system is taken as the research object, as shown in Appendix A. Because the control objectives of DC/DC and DC/AC converters are di fferent, as shown in Table 1, the control method shown in Figure 1 cannot be applied to the two-stage grid-connected PV system. In addition, if the PV system operates in MPPT mode, the output of the PV system cannot be controlled, and the premise of VSG implementation is that the system must maintain a reserve power, then it cannot achieve autonomous frequency and voltage regulation.


**Table 1.** Comparison of the control functions of the converter in the two-stage grid-connected photovoltaic virtual (PV) system.

Figure 2 shows that for the control e ffect diagram of above method in reference [13], when the grid frequency changes suddenly, PV output power remains unchanged, and ESSs regulates output power to participate in grid FR. It is noteworthy that the active support provided by PV-ESSs is constrained by the allocation of a capacity cap and support time during the whole frequency decline stage. In addition, the addition of ESSs will greatly increase the construction cost of PV-PPs. The operation of PV-PRC can effectively reduce the above problems.

**Figure 2.** PV-energy storage systems (ESSs)-VSG output wave.

Therefore, in order to apply VSG control technology to the two-stage grid-connected PV system, it is necessary to solve the active standby problem and improve the control algorithm. External ESSs can e ffectively solve the above problems. The ESSs mainly undertake the reserve capacity required by FR. After adding ESSs, the Equation (1) is converted to:

$$\begin{cases} P\_{\rm m} = P\_{\rm mpp} + P\_{\rm ESS} \\ P\_{\rm ESS} = D\_{\rm P}(\omega\_{\rm n} - \omega) \end{cases} \tag{2}$$

#### **3. PV-PRC Principle and Voltage Operating Point Analysis**

#### *3.1. Analysis of PV Generator Output Characteristics*

The output P–V characteristic curve of the PV module is as shown in Figure 3a. In Figure 3a, there is a unique maximum power value *<sup>P</sup>*mpp; *P*deload is the output power value of the PV system in PRC mode; in PRC mode, the PV system maintains a part of the real-time active power up-regulation capability, as shown in Equation (3), Δ *P* is called the reserve active power of the PV system.

$$P\_{\rm mpp} = P\_{\rm deload} + \Delta P \tag{3}$$

(**a**) PV module P-V curve (**b**) PV output power curve at reserve 10%*<sup>P</sup>*mpp

**Figure 3.** PV-PRC voltage operating point diagram.

As shown in Figure 2a, the output power of the PV system corresponds to two voltage operating points *V*1 and *V*2 in the non-MPP. The relationship between *V*1, *V*2 and *<sup>V</sup>*mpp is shown in Equation (4). As shown in Equation (4), the same active reserve is implemented in PRC mode. Since the curve corresponding to the *V*2 side has a steeper gradient, the voltage regulation range on the *V*2 side is much smaller than that on the *V*1 side (i.e., Δ*V*2 < Δ*V*1), which will bring the faster response speed.

$$\begin{cases} \left| \begin{array}{c} V\_1 < V\_{\rm mpp} < V\_2 \\ \left| V\_{\rm mpp} - V\_2 \right| = \Delta V\_2 < \Delta V\_1 \end{array} \right| = \left| V\_{\rm mpp} - V\_1 \right| \tag{4} \tag{4}$$

where *V*in is the lowest PV output voltage that can make the inverter work normally; *V*out is the maximum input voltage that the inverter can withstand; *P*deload1 is the PV output power when PRC mode is operating on the *V*1 side; *<sup>P</sup>*mpp is the PV output power in MPPT mode; and *P*deload2 is the PV output power when PRC mode is operating on the *V*2 side.

In addition, whether operating in MPPT mode or PRC mode, ensuring the safe and reliable operation of the inverter is the necessary prerequisite for realizing grid-connected PV power generation. As shown in Figure 3b, the PV output voltage in the [*<sup>V</sup>*in, *<sup>V</sup>*out] region can make the inverter work normally. If the output voltage of the PV generator is not in this area, the inverter will go into shutdown or standby state. If PRC mode runs on the *V*1 side, when the irradiance changes from 600 to 300 <sup>W</sup>/m2, the PV output voltage will not be in the workspace of the inverter. However, when running on the *V*2 side, the voltage output is always in the operation area of the inverter.

Therefore, considering the response speed of PRC operation and the adjustable reserve capacity and ensuring the safe and efficient operation of the system, the ideal working area is expected to work on the right side of *<sup>V</sup>*mpp, namely the *V*2 side.
