# Optimized Power Distribution Technology for Fast Frequency Response in Photovoltaic Power Stations

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## Abstract

**:**

## 1. Introduction

## 2. Problems with the Traditional Structure and the Average Distribution Strategy

#### 2.1. Response Time Constraint of FFR

#### 2.2. Traditional Average Distribution Strategy

#### 2.3. Distribution Effect Analysis of Traditional Average Strategy

## 3. Proportional Distribution Strategy Based on Subarray PMPC Value

#### 3.1. Methods to Evaluate the PMPC Value

#### 3.2. Proportional Distribution Algorithm

_{si}at a specific time t. Then, the average natural maximum power of the s reference inverters in the subarray is $\overline{{P}_{\mathrm{s}i}}$, as shown in Equation (7).

#### 3.3. Distribution Effect Analysis of the Proportional Strategy

## 4. Comparison and Analysis of the Two Distribution Strategies

#### 4.1. Relationship between the Two Strategies

#### 4.2. Error Performance Comparison between the Two Strategies

- When Pstation_tgt satisfies the relation Pstation_tgt ≤ N × Pi_min,

- 2.
- When Pstation_tgt increases and satisfies the relationN × Pi min ≤ Pstation_tgt ≤ Pmax,$$\left\{\begin{array}{l}Avg:\alpha \%=\frac{{\displaystyle \sum _{i=1}^{k}\left|({P}_{\mathrm{station}\_\mathrm{tgt}}/N)-{P}_{i}\right|}}{{P}_{\mathrm{station}\_\mathrm{tgt}}}\times 100\%,k<n\\ \mathrm{Pr}\mathrm{op}:\beta \%=0,\begin{array}{c}\mathrm{when}\text{}\mathrm{N}\times {P}_{i\_min}\le {P}_{\mathrm{station}\_tgt}\le {P}_{\mathrm{max}}\end{array}\end{array}\right.$$

- 3.
- When Pstation_tgt satisfies the relation Pstation_tgt > Pmax,

_{i}is the real-time power output of the ith subarray. The deviation of the average strategy is extended to all subarrays beyond this point (see Equation (19)).

- 4.
- When Pstation_tgt satisfies the relation Pstation_tgt ≥ N × Pi-max,

## 5. Application Test and Analysis

- ①
- Subarray target power issued by the station system (blue)
- ②
- Subarray real power output value (red)
- ③
- Subarray real-time PMPC curve (green)
- ④
- Subarray three-day average PMPC curve (black)

#### 5.1. Calculation of Subarray PMPC Value

#### 5.2. Response Performance Comparison of FFR Based on Different Strategies

#### 5.3. Analysis of Typical FFR Response Based on the Two Strategies

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FFR | fast frequency response |

RES | renewable energy source |

PV | photovoltaic |

PMPC | potential maximum power capability |

AGC | automatic generation control |

AVC | automatic voltage control |

PPC | power plant controller |

POC | point of connection |

MPPT | maximum power point tracking |

SCADA | supervisory control and data acquisition |

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**Figure 1.**Two- or three-layer fast frequency response (FFR) control system structure in photovoltaic (PV) power station.

**Figure 4.**Deviation error curves of the average and proportional distribution strategies and the probability of error occurrence.

**Figure 5.**Power curves for the potential maximum power capability (PMPC) and the real power output in a PV subarray.

Subarray Name | Power Value Type | PMPC Calculation and Actual Output Power Value (kW) | |||||
---|---|---|---|---|---|---|---|

Time T0 | 5 s Later | 5 min Later | 15 min Later | 30 min Later | 1 h Later | ||

A1 | Evaluated PMPC | 778 | 774 | 759 | 770 | 749 | 779 |

Actual Output | 770 | 778 | 772 | 763 | 754 | 768 | |

A2 | Evaluated PMPC | 829 | 828 | 805 | 816 | 801 | 817 |

Actual Output | 820 | 820 | 818 | 810 | 806 | 806 | |

A3 | Evaluated PMPC | 754 | 760 | 761 | 767 | 769 | 761 |

Actual Output | 769 | 765 | 763 | 762 | 763 | 767 | |

A4 | Evaluated PMPC | 751 | 759 | 768 | 778 | 783 | 772 |

Actual Output | 759 | 755 | 763 | 768 | 770 | 778 | |

A5 | Evaluated PMPC | 843 | 844 | 845 | 840 | 841 | 852 |

Actual Output | 831 | 832 | 834 | 836 | 837 | 838 |

No | Theory Power Ability (MW) | Stratage Type | Freq Disturb Type | Freq Step Target (f/Hz) | Response Time (s) | Power Before Step (MW) | Power After Step (MW) | Error (%) | Qaualified (Y/N) |
---|---|---|---|---|---|---|---|---|---|

1 | 4.10 | AVG | Freq Upward | 50.21 | 3.08 | 2.50 | 1.47 | 0.30 | Y |

2 | 4.20 | AVG | 50.21 | 3.20 | 2.50 | 1.48 | 0.20 | Y | |

3 | 8.47 | AVG | 50.21 | 4.06 | 7.74 | 6.73 | 0.10 | Y | |

4 | 9.01 | AVG | 50.21 | 4.28 | 7.59 | 6.60 | 0.10 | Y | |

5 | 4.52 | AVG | 50.21 | 3.06 | 4.52 | 3.50 | 0.20 | Y | |

6 | 4.21 | AVG | 50.21 | 6.42 | 4.21 | 3.18 | 0.30 | Y | |

7 | 4.08 | PROP | Freq Upward | 50.21 | 3.10 | 2.50 | 1.48 | 0.20 | Y |

8 | 4.23 | PROP | 50.21 | 3.17 | 2.50 | 1.49 | 0.10 | Y | |

9 | 4.38 | PROP | 50.21 | 3.12 | 4.38 | 3.35 | 0.30 | Y | |

10 | 4.10 | PROP | 50.21 | 3.14 | 4.10 | 3.08 | 0.20 | Y | |

11 | 8.65 | PROP | 50.21 | 3.56 | 7.73 | 6.76 | 0.30 | Y | |

12 | 8.93 | PROP | 50.21 | 3.75 | 7.34 | 6.35 | 0.10 | Y | |

13 | 4.25 | AVG | Freq Down ward | 49.79 | 1.94 | 2.47 | 3.47 | 0.00 | Y |

14 | 4.50 | AVG | 49.79 | 1.86 | 2.50 | 3.52 | 0.20 | Y | |

15 | 4.61 | AVG | 49.79 | / | 3.50 | 4.25 | 2.50 | N | |

16 | 4.42 | AVG | 49.79 | / | 3.50 | 4.21 | 2.90 | N | |

17 | 8.56 | AVG | 49.79 | 2.98 | 6.00 | 6.95 | 0.50 | Y | |

18 | 8.48 | AVG | 49.79 | 3.10 | 6.00 | 6.96 | 0.40 | Y | |

19 | 7.05 | AVG | 49.79 | / | 5.95 | 6.67 | 2.80 | N | |

20 | 8.32 | AVG | 49.79 | / | 7.30 | 8.04 | 2.60 | N | |

21 | 4.27 | PROP | Freq Down ward | 49.79 | 1.96 | 2.47 | 3.48 | 0.10 | Y |

22 | 4.38 | PROP | 49.79 | 1.92 | 2.50 | 3.48 | 0.20 | Y | |

23 | 7.90 | PROP | 49.79 | 3.34 | 6.79 | 7.81 | 0.20 | Y | |

24 | 8.20 | PROP | 49.79 | 2.87 | 6.85 | 7.85 | 0.00 | Y | |

25 | 7.10 | PROP | 49.79 | 2.98 | 5.99 | 6.95 | 0.40 | Y | |

26 | 7.21 | PROP | 49.79 | 3.10 | 5.80 | 6.82 | 0.20 | Y | |

27 | 8.34 | PROP | 49.79 | 3.34 | 7.20 | 8.17 | 0.30 | Y | |

28 | 8.47 | PROP | 49.79 | 3.42 | 7.30 | 8.32 | 0.20 | Y |

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**MDPI and ACS Style**

Wang, S.; Duan, S.; Mi, G.; Lu, Y. Optimized Power Distribution Technology for Fast Frequency Response in Photovoltaic Power Stations. *Energies* **2022**, *15*, 8923.
https://doi.org/10.3390/en15238923

**AMA Style**

Wang S, Duan S, Mi G, Lu Y. Optimized Power Distribution Technology for Fast Frequency Response in Photovoltaic Power Stations. *Energies*. 2022; 15(23):8923.
https://doi.org/10.3390/en15238923

**Chicago/Turabian Style**

Wang, Shuchao, Shenpeng Duan, Gaoxiang Mi, and Yuping Lu. 2022. "Optimized Power Distribution Technology for Fast Frequency Response in Photovoltaic Power Stations" *Energies* 15, no. 23: 8923.
https://doi.org/10.3390/en15238923