# Two-Stage Grid-Connected Frequency Regulation Control Strategy Based on Photovoltaic Power Prediction

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## Abstract

**:**

## 1. Introduction

## 2. System Topology and General Control Strategy

#### 2.1. Photovoltaic Array Structure

_{p}columns with N

_{s}PV panels per column, and V

_{PV}and I

_{PV}are the DC voltage and current for the PV array, respectively.

_{PV}and output power P

_{PV}versus output voltage V

_{PV}are as follows [24]:

_{sc}and U

_{OC}are the short-circuit current and open-circuit voltage for the PV panel, and C

_{1}and C

_{2}are coefficients to be determined.

#### 2.2. Two-Stage Photovoltaic Power System Structure

_{dc1}and C

_{dc2}are the filter capacitors, and U

_{t}and U

_{g}are the parallel network voltage and grid voltage, respectively. Compared with the single-stage PV system, the two-stage system adds a Boost converter on top of it, reducing the PV output power’s volatility and randomness, stabilising the high-voltage-side DC voltage, and, finally, connecting the AC output to the grid through the grid-side inverter.

#### 2.3. Conventional Control for Boost Converter

_{PVref}, and the error signal is output by the PI controller with the duty cycle d, which drives the normal operation of the Boost converter.

## 3. Dynamic Characteristics of Grid Frequencies under PV Penetration

_{HP}is the proportion of work performed by the high-pressure cylinder of the prime mover, H is the inertia time constant of the synchronous generator set, and D is the damping factor.

_{L}to the frequency perturbation Δf

_{g}is:

_{n}is the undamped oscillation frequency, G

_{0}is the scaling factor, and z

_{0}is the inverse of the reheat time constant of the prime mover.

_{r_pu}(s) is the grid frequency reference, f

_{ref_pu}(s) is 1/s, G(s)/s is the frequency disturbance value and ω

_{d}is the natural damping frequency. The grid frequency in the time domain is obtained after the pull-type inverse transformation of Equation (4) as:

_{d}is the damped oscillation frequency.

## 4. Analysis of Frequency Regulation Control Strategy for PV and Its Mechanism

#### 4.1. FR Control to the Left for the MPP

_{0}is the rated electrical rotor angular velocity, ω is the rotor electrical angular velocity, and H

_{SG}is the rotor inertia time constant.

_{dc}is the virtual inertia time constant, U

_{dc0}is the initial value of the grid-side DC capacitor voltage, and f

_{0}is the nominal system frequency of 50 Hz. Linearisation of Equation (11) yields:

_{dc}are important influencing parameters of the control strategy proposed in this paper, and it can be seen that the regulation factor k and the virtual inertia time constant H

_{dc}are proportional to the incremental DC voltage ΔU

_{dc}on the grid-connected side of the inverter. When the regulation factor k and the virtual inertia time constant H

_{dc}increase, ΔU

_{dc}then increases and the more support power the PV plant can provide to the system, which can weaken the volatility in the dynamic process of the system frequency. Therefore, we can improve the grid-side inverter control strategy, as shown in Figure 7.

_{PV}= k

_{f}U

_{dc}, the corrected grid-side DC voltage will be transmitted to the low-voltage-side DC voltage, and the fluctuation of the low-voltage-side voltage will increase the output power of the PV array. The control of each converter thus achieves the purpose of frequency regulation.

_{1}(s) from the load perturbation ΔP

_{L}to the frequency perturbation Δf

_{g}is as follows:

_{f}k.

_{peak}of grid frequency and the inertial time constant H

_{dc}is shown in Figure 9. From Figure 9, it can be seen that the change of control coefficient k has no effect on the initial value of grid frequency change rate; as the time constant H

_{dc}increases, the lowest frequency drop increases.

#### 4.2. FR Control to the Right for the MPP

_{dc}= 2H + kC

_{dc2}U

_{dc0}+ 2H

_{PV}.

_{m}comes from the generator and the virtual inertial control of the PV can affect the system equivalents H and D. Further, the Lyapunov energy function can be constructed as:

_{k}and E

_{p}are the kinetic and potential energies, respectively, of the system. Derivation of the Lyapunov energy function yields:

_{HP}∈ (0, 1), so that we have:

_{HP}< 1. In the ideal case, if F

_{HP}= 1 and there is no hysteresis in the governor, the equivalent damping of the power system is D + 1/R, which can further increase the stability of the system.

## 5. PV Power Prediction Algorithm

#### 5.1. Selection of Datasets and Correlation Coefficients

_{1}and ρ

_{2}, respectively. It has strong correlation.

#### 5.2. SOM Clustering Algorithm

_{ij}—weight between node i and node j; W

_{c}—weight of the winning node.

_{ij}:

_{c}

_{,j}(t)—domain function, which usually uses a Gaussian function, i.e.,:

_{cj}—the distance between neuron c and any activated neuron j; r—the domain radius.

#### 5.3. Quadratic Decomposition

#### 5.4. Power Prediction Algorithm Framework

## 6. Simulation Example Validation

_{1}, G

_{2}, and G

_{3}, with a capacity of 300 MW, a PV module device with a capacity of 50 MW, and three loads.

#### 6.1. Analysis of the Inertial Response of a System with Different Control Parameters

^{2}, a load consuming 70 MW of active power is put in at t = 4 s, the capacity of the PV module equipment is 50 MW, and the PV module is left with 20% of spare power, with the simulation comparison results displayed in Figure 15, Figure 16 and Figure 17.

_{2}when the regulation factor k is changed are pictured in Figure 18.

_{2}output power are displayed in Figure 19 when the virtual inertia time constant H

_{dc}is varied.

_{dc}increases sequentially, the lowest values of the system frequency drop are 49.511 Hz, 49.568 Hz, and 49.612 Hz, respectively, with it observed that the system frequency drop has slowed down and deviated less from the reference value. The PV installation output power can accurately respond to the system frequency variation, supplying effective inertia power to lift the system frequency, which is conducive to the steady system operation.

#### 6.2. Analysis of the Inertial Response of the System during Fluctuations in Light Intensity

_{2}in Figure 22 reveals that the proposed control can make the PV system respond quickly to changes in system load and release the backup energy of the PV system quickly to increase the output power. Since the inertial response is different from that of the control in the literature [27], their transient processes will also be different, and the PV output peak power under the proposed control strategy is the largest to reduce the frequency shift of the system. At steady state, the proposed control performs similarly to that of the literature [27], with the maximum steady-state power at the PV output and the minimum steady-state power at the synchronous generator output, providing a primary frequency regulation for the system and reducing the standby load shedding rate. Simulation results show that the control strategy proposed in this paper improves the frequency response performance of the system and the effect is better than that of the literature [27].

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Conventional control for Boost converter (The blue arrow represents the driver signal in the control link that is transmitted to the IGBT gate).

**Figure 13.**PV power prediction process. (

**a**) SOM clustering process. (

**b**) Secondary decomposition and power prediction.

**Figure 22.**Comparison of system response before [27] and after FR control strategy improvement.

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**MDPI and ACS Style**

Wang, S.; Zhu, H.; Zhang, S.
Two-Stage Grid-Connected Frequency Regulation Control Strategy Based on Photovoltaic Power Prediction. *Sustainability* **2023**, *15*, 8929.
https://doi.org/10.3390/su15118929

**AMA Style**

Wang S, Zhu H, Zhang S.
Two-Stage Grid-Connected Frequency Regulation Control Strategy Based on Photovoltaic Power Prediction. *Sustainability*. 2023; 15(11):8929.
https://doi.org/10.3390/su15118929

**Chicago/Turabian Style**

Wang, Shuzheng, Haiming Zhu, and Shaowen Zhang.
2023. "Two-Stage Grid-Connected Frequency Regulation Control Strategy Based on Photovoltaic Power Prediction" *Sustainability* 15, no. 11: 8929.
https://doi.org/10.3390/su15118929