# Research on Load State Sensing and Early Warning Method of Distribution Network under High Penetration Distributed Generation Access

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Model of Distribution Network Based on Graph Theory

## 3. Distribution Network Operation Risk Index

#### 3.1. Out-of-Limit Probability Index

#### 3.2. Risk of Voltage Overrun

#### 3.3. Risk of Power Overrun

## 4. Random Power Flow Analysis Based on the Monte Carlo Method

## 5. Dynamic Optimization Strategy for Load State Aware Operation Risk of Distribution Networks

#### 5.1. Dynamic Optimization of Reactive Power Compensation Equipment

#### 5.2. Dynamic Optimization of the Distributed Power Factor

#### 5.3. Optimal Reduction of Active Power Output of Distributed Power Supply

## 6. Simulation Analysis

^{2}. The main network is set as a balanced node and the load is set as a PQ node. The simulation platform is based on the seventh generation CPU of i7 and Matlab2021a on a computer with 16G memory, and it is solved by Gurobi solver. The loads of some nodes within 24 h are shown in Figure 2.

## 7. Discussion

## 8. Conclusions

- (1)
- In this paper, the dynamic model of distribution networks based on complex network theory is established, and the operation risk index of distribution networks is put forward. The uncertainty caused by high penetration distributed generation access is analyzed, and the degree of expected risk is quantified.
- (2)
- In this paper, the Monte Carlo method is used to sample and analyze the power flow of distribution networks, and a dynamic evaluation system of key nodes of distribution networks under different time scales is proposed. At the same time, this paper determines the access mode of high penetration distributed generation, and establishes the state awareness method system of distribution networks.
- (3)
- In this paper, four access modes under different penetration rates of distributed power supply are proposed and simulated. Through the analysis of a node voltage deviation index and a branch load overload index, it is proven that this method can effectively improve the stability margin of distribution networks.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${C}_{t}({L}_{{p}_{i}{p}_{j}})$ | electrical betweenness |

${P}_{i}$,${P}_{j}$ | corresponding node pair |

${S}_{{p}_{i}}$ | weight of nodes ${v}_{i}$ |

${S}_{{p}_{j}}$ | weight of nodes ${v}_{j}$, |

${I}_{{p}_{i}{p}_{j}}$ | current generated between the node pairs |

${P}_{t}$ | node input power |

${D}_{{v}_{i}}$ | average connectivity index |

$N$ | number of nodes |

${C}_{i}$ | reciprocal of the sum of the electrical distances |

${W}_{ij}$ | electrical distance |

${\overline{D}}_{{v}_{i}}$ | strength of the stability of the distribution network structure |

${P}_{\mathrm{vi}}$ | out-of-limit probability index |

${N}_{\mathrm{vi}}$ | sampling times of out-of-limit behavior |

$N$ | total sampling times |

${C}_{\mathrm{Vvi},i}$ | exceeding index |

${P}_{\mathrm{Vvi},i}$ | exceeding probability |

$\Delta {V}_{\mathrm{ave},i}$ | average value of the exceeding index level |

$\Delta {V}_{\mathrm{max},i}$ | upper limit of the exceeding index limit level |

${N}_{\mathrm{Vvi},i}$ | number of overruns drawn |

${V}_{i,k}$ | node voltage value |

${V}_{\mathrm{lim},i}$ | maximum value of voltage |

${C}_{\mathrm{Svi},j}$ | out-of-limit indicator |

${P}_{\mathrm{Svi},j}$ | probability of exceeding the limit of branch j |

$\Delta {S}_{\mathrm{ave},j}$ | average power over-limit level of branch j |

${C}_{\mathrm{Svi},s}$ | out-of-limit indicator |

${N}_{\mathrm{br}}$ | number of branches |

${N}_{\mathrm{Svi},j}$ | number of overruns |

${S}_{\mathrm{max},j}$ | rated capacity |

$v$ | speed |

${\kappa}_{\mathrm{u}}$ | upper limit of air clarity coefficient |

${\overline{P}}_{\mathrm{L}}$ | average load value |

$\sigma $ | variance |

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Node | Connectivity Index | Voltage Risk Indicators | Branch Load Risk Indicators | Risk Indicators of Branch Line Loss | Weighted Average Path |
---|---|---|---|---|---|

2 | 7.76 | 50.178 | 45.564 | 36.786 | 0.189 |

3 | 0.033 | 17.303 | 32.163 | 19.043 | 0.083 |

4 | 15.029 | 45.789 | 35.123 | 15.478 | 0.187 |

9 | 0.027 | 14.813 | 27.770 | 20.188 | 0.059 |

17 | 10.232 | 54.378 | 16.379 | 25.967 | 0.089 |

20 | 11.078 | 46.658 | 20.453 | 16.373 | 0.111 |

22 | 0.001 | 10.822 | 19.686 | 13.688 | 0.037 |

24 | 13.054 | 61.172 | 83.673 | 50.107 | 0.168 |

29 | 6.321 | 50.439 | 69.910 | 46.327 | 0.166 |

32 | 0.009 | 12.009 | 18.089 | 12.196 | 0.011 |

Scenario | The method Proposed in the Ref. [18] | Proposed Method | ||
---|---|---|---|---|

Node Voltage Offset Index | Branch Load Overload Index | Node Voltage Offset Index | Branch Load Overload Index | |

Scenario 1 | 0.823 | 0.779 | 0.716 | 0.732 |

Scenario 2 | 0.587 | 0.432 | 0.565 | 0.405 |

Scenario 3 | 0.326 | 0.373 | 0.247 | 0.310 |

Scenario 4 | 0.198 | 0.156 | 0.133 | 0.121 |

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**MDPI and ACS Style**

Gu, C.; Wang, Y.; Wang, W.; Gao, Y. Research on Load State Sensing and Early Warning Method of Distribution Network under High Penetration Distributed Generation Access. *Energies* **2023**, *16*, 3093.
https://doi.org/10.3390/en16073093

**AMA Style**

Gu C, Wang Y, Wang W, Gao Y. Research on Load State Sensing and Early Warning Method of Distribution Network under High Penetration Distributed Generation Access. *Energies*. 2023; 16(7):3093.
https://doi.org/10.3390/en16073093

**Chicago/Turabian Style**

Gu, Cailian, Yibo Wang, Weisheng Wang, and Yang Gao. 2023. "Research on Load State Sensing and Early Warning Method of Distribution Network under High Penetration Distributed Generation Access" *Energies* 16, no. 7: 3093.
https://doi.org/10.3390/en16073093