# Two-Stage Multi-Period Coordinated Load Restoration Strategy for Distribution Network Based on Intelligent Route Recommendation of Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. The Configuration

## 3. The Mathematical Modelling

#### 3.1. Multi-Period Coordinated Load Restoration Model

#### 3.1.1. Objective Function

#### 3.1.2. Constraints

_{m}and V

_{n}are the voltage of the m-bus and the n-bus; P

_{mn}and Q

_{mn}are the active power and reactive power at the m-bus side; z

_{mn}, r

_{mn}and x

_{mn}are the impedance, resistance and reactance of the branch mn; I

_{mn}is the current of the branch mn; P

_{in,m}and Q

_{in,m}are the inject active power and reactive power of m-bus, respectively; P

_{in,n}and Q

_{in,n}are the inject active power and reactive power of n-bus, respectively.

- The Radial Topology Constraints of the Distribution Network

_{1}is the set of all buses without bus 1 and E is the set of all branches. ${\alpha}_{ij}$ is the connection state of branch(i,j) which is a 0–1 variable. ${\alpha}_{ij}=1$ means the branch(i,j) is connected and ${\alpha}_{ij}=0$ means the branch(i,j) is not connected. ${\beta}_{ij}$ and ${\beta}_{ji}$ are 0–1 variables which demonstrate the parent or child relationship between bus i and j. If bus i is the parent bus of bus j, ${\beta}_{ji}=1$ and ${\beta}_{ij}=0$. If bus i is the child bus of bus j, ${\beta}_{ij}=1$ and ${\beta}_{ji}=0$. If bus i and bus j are not connected, ${\beta}_{ij}={\beta}_{ji}={\alpha}_{ij}=0$.

- The Operation Constraints of the Distribution Network

_{i,t}is the square of the voltage magnitude of i-bus at time t. P

_{ij,t}and Q

_{ij,t}are the active power and reactive power of branch(i,j) at time t. r

_{ij}and x

_{ij}are the resistance and reactance of branch(i,j). i

_{ij,t}is the square of the current magnitude of the branch(i,j) at time t. S

_{ij,t}and s

_{i,t}are the complex power of branch(i,j) and the injected complex power of bus i at time t, respectively. j:i$\to $j represents the set of all buses j which are downstream of bus i. z

_{hi}is the impedance of branch(h,i) and M is a large positive value. ${s}_{i,t}^{g}$ and ${s}_{i,t}^{L}$ are the complex power supplied by the power sources in bus i and the complex load demand of bus i, respectively, at time t.

_{original}is the feasible region of the non-convex constraint before transformation, which is Equation (11). C

_{SOC}is the convex feasible region after relaxation, which is Equation (13). If the relaxation process is accurate, Equation (11) is equivalent to Equation (13). The specific proof process is shown in paper [29] and the error analysis of SOCR is shown in Section 4.1.

_{ij}

_{,max}is the allowed maximum current of branch(i,j). V

_{i}

_{,max}and V

_{i}

_{,min}are the allowed maximum and minimum voltage of bus i. G and CS are the sets of buses, which have distributed generators and EV charging stations, respectively. ${P}_{i,\mathrm{max}}^{g}$ and ${Q}_{i,\mathrm{max}}^{g}$ are the maximum active power and maximum reactive power which could be supplied by the distributed generators in bus i, respectively. P

_{dismax}and P

_{chamax}are the maximum discharging and charging power of each EV. Num

_{i}is the number of EVs in the charging station in bus i.

- The Energy Limit Constraints of Power Supply Sources

_{i}

_{,total}is the total energy of the distributed generator in bus i. E

_{car}is the total battery capacity of each EV. $\Delta $SOC is the interval length of state of charge (SOC), which could be used to restore the critical load and it is 0.6 (0.8–0.2) in this paper.

- The Constraints of the Switching Number of Load States

_{1}is the set of time period except the first time period.

#### 3.2. The Intelligent Recommendation Model of The Shortest Duration Route of EVs

_{v}

_{,route}is the driving time for the v-t EV to reach the designated charging station and V is the total number of EVs. ${f}_{\mathrm{first}}^{*}$ is the optimal value of the objective function in the first stage model.

## 4. Case Study

#### 4.1. Analysis of Critical Load Restoration

^{−6}, which meets the application needs of practical engineering, verifies the accuracy of the model constructed and confirms the reliability of the simulation results in this paper.

#### 4.2. Analysis of Optimal Route Recommendation of EVs

## 5. Conclusions

- Idle EVs are a large number of usable power generation resources, and reasonable use of these resources during a blackout is very significant. This paper realizes the optimal space assignment of EV power supply resources and verifies that it is helpful to the load restoration of the distribution network.
- By comparing the multi-period coordinated load restoration strategy and the single-time section load restoration strategy, this paper verifies that the multi-period coordinated load restoration model used in the proposed strategy can better allocate the limited energy on time scale to extend the weighted power supply time of the critical loads.
- The strategy proposed in this paper is more advantageous than the other two strategies in reducing the total network loss of the system, increasing the minimum voltage magnitude, increasing average voltage, and reducing the standard deviation of voltage, which indicates the proposed strategy also has a good effect in improving the economy and safety of the distribution network during load restoration.
- Based on the error analysis of the model after SOCR, it can be seen that the error index can meet the application requirements of actual engineering, which further verifies the accuracy of the proposed strategy.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Transportation Network Node | Distribution Network Bus | Transportation Network Node | Distribution Network Bus | Transportation Network Node | Distribution Network Bus |
---|---|---|---|---|---|

1 | 20 | 8 | 12 | 15 | 7 |

2 | 22 | 9 | 3 | 16 | 29 |

3 | 10 | 10 | 4 | 17 | 17 |

4 | 1 | 11 | 15 | 18 | 33 |

5 | 2 | 12 | 16 | 19 | 27 |

6 | 23 | 13 | 17 | 20 | 31 |

7 | 9 | 14 | 5 | 21 | 18 |

Strategy | Reasonably Allocate EVs to Charging Stations | Multi-Period Coordinated Load Restoration |
---|---|---|

1 | × | × |

2 | × | √ |

3 | √ | √ |

Time Period | DG Output (kW) In Different Strategy | CS1 Output (kW) In Different Strategy | CS2 Output (kW) In Different Strategy | CS3 Output (kW) In Different Strategy | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |

1 | 420.8 | 210.8 | 126.2 | 321.1 | 69.9 | 266.4 | 378.9 | 168.5 | 0 | 198.4 | 154.3 | 168.2 |

2 | 420.8 | 210.8 | 126.2 | 321.1 | 69.9 | 267.7 | 378.9 | 168.5 | −1.3 | 198.4 | 154.3 | 168.2 |

3 | 420.8 | 210.8 | 126.2 | 321.1 | 69.9 | 266.4 | 378.9 | 168.5 | 0 | 198.4 | 154.3 | 168.2 |

4 | 128.3 | 210.7 | 187.9 | 320.9 | 196.2 | 266.4 | 378.9 | 168.5 | 0 | 196.6 | 154.2 | 106.6 |

5 | 11.7 | 210.7 | 294.4 | −68.1 | 196.2 | 266.4 | −25.5 | 168.5 | 168.4 | 82.1 | 154.2 | 168.2 |

6 | 11.7 | 210.7 | 294.4 | −68.1 | 196.2 | 266.4 | −25.5 | 168.5 | 168.4 | 82.1 | 154.2 | 168.2 |

7 | 11.7 | 209.5 | 294.4 | −68.1 | 281.5 | 350.6 | −25.5 | 379.5 | 168.4 | 82.1 | 154.3 | 168.2 |

Remaining Energy(kWh) | Network Loss(kW) | Total Weighted Number of Restored Load | ||||
---|---|---|---|---|---|---|

DG | CS1 | CS2 | CS3 | |||

Strategy 1 | 74.0 | 0.3 | 0.8 | 42.0 | 12.833 | 1312.2 |

Strategy 2 | 26.1 | 0 | 49.3 | 0 | 12.477 | 2210.4 |

Strategy 3 | 50.3 | 29.9 | 0 | 0 | 8.041 | 2230.2 |

(p.u.) | Minimum Voltage Magnitude | Average Voltage | Standard Deviation of Voltage |
---|---|---|---|

Strategy 1 | 0.9876 | 0.9969 | 0.0031 |

Strategy 2 | 0.9881 | 0.9962 | 0.0030 |

Strategy 3 | 0.9910 | 0.9972 | 0.0021 |

Transportation Network Node | Strategy 1 | Strategy 2 | Strategy 3 | ||||||
---|---|---|---|---|---|---|---|---|---|

7 | 14 | 21 | 7 | 14 | 21 | 7 | 14 | 21 | |

1 | 0 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 |

3 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 0 |

5 | 0 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 |

8 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 0 |

9 | 0 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 |

11 | 10 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 0 |

13 | 0 | 0 | 10 | 0 | 0 | 10 | 9 | 0 | 1 |

16 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 8 | 2 |

17 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 0 | 10 |

18 | 0 | 0 | 10 | 0 | 0 | 10 | 0 | 0 | 10 |

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## Share and Cite

**MDPI and ACS Style**

Su, S.; Wei, C.; Li, Z.; Xia, D.
Two-Stage Multi-Period Coordinated Load Restoration Strategy for Distribution Network Based on Intelligent Route Recommendation of Electric Vehicles. *World Electr. Veh. J.* **2021**, *12*, 121.
https://doi.org/10.3390/wevj12030121

**AMA Style**

Su S, Wei C, Li Z, Xia D.
Two-Stage Multi-Period Coordinated Load Restoration Strategy for Distribution Network Based on Intelligent Route Recommendation of Electric Vehicles. *World Electric Vehicle Journal*. 2021; 12(3):121.
https://doi.org/10.3390/wevj12030121

**Chicago/Turabian Style**

Su, Su, Cunhao Wei, Zening Li, and Dong Xia.
2021. "Two-Stage Multi-Period Coordinated Load Restoration Strategy for Distribution Network Based on Intelligent Route Recommendation of Electric Vehicles" *World Electric Vehicle Journal* 12, no. 3: 121.
https://doi.org/10.3390/wevj12030121