*3.2. PV-PRC Implementation Analysis*

Equation (3) shows that the premise of introducing active reserve is that the current maximum output power value *<sup>P</sup>*mpp is a known amount. Therefore, the maximum power point estimation (MPPE) link is necessary for the PV-PRC operation, and the active power can be introduced when the MPPE link is found to be *<sup>P</sup>*mpp. For the sake of simplicity, the MPPE method in the reference [17] is used, as shown by the red dashed box in Figure 4, taking two sets of PV modules or arrays of the same model and quantity as an example. When operating under the same operating conditions, PV1 operation in MPPT mode, its output power can be used as the available power value of PV2 (*P*mpp<sup>1</sup> = *<sup>P</sup>*mpp2). However, in [17], the PV output power is controlled by controlling the output voltage. The calculation of the voltage command in the process leads to a cumbersome control process. In view of this, this paper improves it by using direct power control to control the output power. In addition, in this kind of control mode, through the lowest voltage limit, the PRC runs with the *V*2 side, and the control block diagram is shown in Figure 4.

**Figure 4.** PV-PRC block diagram.

#### **4. PV-PRC-VSG Control Strategy and Reserve Ratio Analysis**

In PRC operation mode, a part of the power up-regulation capability is maintained in the PV system, so that the output of the PV system can be adjusted within a certain range, and the regulation of the reserve power has the same effect as the charging and discharging of the energy storage system, and the active output can be adjusted. With the VSG technology, the inertial response and the participating power system primary frequency response can be realized. In this mode, the output power of the virtual prime mover is as shown in Equation (5).

$$\begin{cases} J\omega \frac{d\omega}{dt} = P\_{\rm m} - P\_{\rm e} \\ P\_{\rm m} = P\_{\rm deload} + D\_{\rm P}(\omega\_{\rm n} - \omega) \end{cases} \tag{5}$$

Equation (5) can be reduced to:

$$P\_\mathbf{e} = P\_\text{deload} - J\omega \frac{\mathbf{d}\omega}{\mathbf{d}t} + D\_\mathbf{p} (\omega\_\mathbf{n} - \omega) \tag{6}$$

where from left to right are PV output power, inertial response process demand power and primary frequency modulation demand power.

Define *Pf* = <sup>−</sup>*J*ωd<sup>ω</sup>d*t*+ *<sup>D</sup>*p(<sup>ω</sup>n − <sup>ω</sup>), where *Pf* is the required power for frequency response.

Assuming that the PV system operates in PRC mode initially and maintains a certain active reserve Δ*P*, when the frequency change of the grid is detected to exceed the dead zone (±0.03 Hz), the required power *Pf* for the PV system to participate in frequency regulation is calculated through the VSG control link. Then, by release or increasing the reserve power, it can participate in the frequency regulation of the power grid to provide power support for the power grid. The control block diagram of the whole system is shown in Figure 5.

**Figure 5.** Principle of PRC-VSG implementation.

The PRC operation mode of the PV system essentially abandons part of the PV resources, which is in contradiction with the efficient use of energy and relevant national network codes. However, considering that the realization of PV-PRC-VSG technology can improve the stability of the power system, enhance the acceptance of the power grid to PV energy, and save the investment of ESSs, it is necessary to keep the power reduction within a certain range, and the proportion of the power reserve in the actual operation process is mainly constrained by the following factors:


To sum up, considering the limitation of abandoning PV energies and the requirement of the VSG for primary frequency modulation, it is more appropriate to reduce power by 10%*P*mpp. During the operation of the power system, when the system frequency increases, the active output of the PV

system further reduces the frequency change of the response system by increasing the value of Δ*P*. When the system frequency decreases, the value of Δ*P* of the PV system needs to be reduced to release the reserve active power. It is noteworthy that when *Pf* > Δ*P*, there is no active power up-regulation ability in the PV system. In addition, Δ*P* is still limited by the upper limit. When Δ*P* increases to 30%*P*mpp, it cannot be increased any more. As shown in Equation (7), because of the limitation of active reserve capacity, the ability of PV-PRC-VSG to participate in primary frequency regulation is limited.

$$
\Delta P' = \begin{cases}
30\%P\_{\rm mpp} & , P\_f < -20\%P\_{\rm mpp} \\
\Delta P - P\_f & , -20\%P\_{\rm mpp} \le P\_f < \Delta P \\
0 & , P\_f \ge \Delta P
\end{cases}
\tag{7}
$$

where Δ*P* is a reference value of reserve power during primary frequency response.

## **5. Simulation of Proposed Method**

To verify the effectiveness of the proposed control strategy, the corresponding simulation model was built in MATLAB/Simulink. The model topology adopts the grid-connected structure of the PV system in Figure 2. The corresponding experimental verification was made for a DC/DC inverter working in PRC mode and DC/DC and DC/AC inverter coordinated control participating in power system frequency response.

## *5.1. PV-PRC Simulation and Analysis*

Firstly, the PRC operation control strategy of the DC/DC side proposed in the second section is simulated and analyzed. Taking the parameters of a single 240-W PV module (JLS60P240W) as an example, the parameters of PV modules are shown in Table 2. The maximum power value of the PV module is calculated in the MPPE process, and then the active reserve is introduced. For the convenience of calculation, the reserve ratio (*R*) is introduced. The value of *R* can be calculated by Equation (8). In the operation process control, *R* is the direct control object.

$$R = \Delta P / P\_{\rm mpg} \times 100\% \tag{8}$$

where: *<sup>V</sup>*oc(*V*)-Open circuit voltage; *<sup>I</sup>*sc(A)-short-circuit current; *<sup>V</sup>*mpp(V)-Maximum Power Voltage; *<sup>I</sup>*mpp(A)-Maximum Power Current; β*<sup>V</sup>*oc(%/◦C)-temperature coefficient of open circuit voltage; <sup>α</sup>*I*sc(%/◦C)-temperature coefficient of short circuit current.


**Table 2.** PV module parameter data sheet.

The primary task of PRC operation is to calculate the value of *<sup>P</sup>*mpp at each moment; that is, the MPPE process. MPPE plays a vital role in the whole PRC operation process, which directly affects the accuracy of the power reserve. In Figure 6a, the red dotted line is the maximum output power (actual *<sup>P</sup>*mpp value) of the PV system in MPPT mode, and the black dotted line is the *<sup>P</sup>*mpp value calculated by MPPE, which deviates little from the actual value, thus laying a foundation for subsequent experiments.

(**a**) Output power contrast diagram (**b**) Reserve ratio contrast diagram

(**c**) Output power contrast diagram 

**Figure 6.** PV-PRC mode simulation waveform.

As shown in Figure 6b, there is no active reserve in the PV system before 0.4 s, and the PV system works in MPPT mode; between 0.4–2 s, the PV system maintains the active reserve in PRC mode. In Figure 5b, the solid line is the given value of the reserve rate, and the dotted line is the actual reserve rate value in the simulation operation. It has good tracking accuracy in the whole operation process. The output power is shown by the blue solid line in Figure 6a. It is noteworthy that the direct power reduction method used in this paper can work in MPPT and PRC modes in a time-sharing manner according to the actual needs, and there is no need to switch control modes, which provides greater convenience for engineering implementation.

Figure 6c is a comparison of output voltage of MPPT mode and PRC mode. It was found that the output voltage in PRC mode is always greater than that in MPPT mode. It is proved that in PRC mode, the output voltage always works on the right side of the P–V curve, which is the same as the expected result in Section 3. It is interesting to find that the DC voltage ripple in PRC mode is much smaller than that in MPPT mode.
