# Analysis of Charging Load Acceptance Capacity of Electric Vehicles in the Residential Distribution Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Residential Area Distribution Network Charging Load Acceptance Capacity

## 3. Analysis of Charging Load Characteristics of EVs in Residential Areas

#### 3.1. Probability of EVs Charging in Residential Areas

#### 3.1.1. Charging Start Time

#### 3.1.2. SOC at Start of Charge

_{0}is the starting SOC of EV charging in residential areas; h is the number of trips available before charging after the EV user is anxious; d

_{f}is the mileage of the f-th trip, in km; d

_{max}is the maximum travelable mileage, in km.

#### 3.1.3. Charging Duration

_{c}is the charging duration required to charge the SOC of the EV to 1, in hours; E is the battery capacity of the EV, in kWh; P

_{c}is the EV charging power provided by the residential area, in kW.

#### 3.2. Forecasting of EV Ownership in Residential Areas

## 4. Mathematical Model for Analysis of Charging Load Acceptance Capacity

#### 4.1. Load Carrying Capacity Objective Function

_{E}is the EV charging load that can be accepted by the residential distribution network, in kW; C

_{E}(i) is the EV charging load that the residential distribution network can accept at the time i, in kW; r is the power supply area of the residential distribution network; n

_{k}is the total number of nodes in the k-th power supply area of the residential distribution network; P

_{j}

^{k}(i) is the EV charging load that the j-th node of the k-th power supply area can accept at time i, in kW.

#### 4.2. Restrictions

#### 4.2.1. Residential Area Distribution Network System Capacity Constraints

_{norm}(i) is the conventional electricity load of the residential area at the i-th moment, in kW; C

_{max}is the upper limit of the capacity of the distribution network system in the residential area, in kW.

#### 4.2.2. Station Capacity Constraints

^{k}

_{norm_j}(i) is the conventional electricity load of the j-th node in the k-th power supply area at time i, in kW; C

^{k}

_{max_j}is the upper limit of the capacity of the j-th node in the k-th power supply area, in kW.

#### 4.2.3. Voltage Constraints at Each Node of the Distribution Network

_{n}is the node voltage of the n-th node of the distribution network, in V; U

_{n}

^{min}is the lower limit of the node voltage of the n-th node of the distribution network, in V; U

_{n}

^{max}is the node voltage of the n-th node of the distribution network upper limit, in V.

#### 4.2.4. Power Flow Balance Constraint

_{α}is the active power of the α-th node of the distribution network, in kW; Q

_{α}is the reactive power of the α-th node of the distribution network, in kVA; U

_{α}is the node voltage of the α-th node of the distribution network, in kW; U

_{β}is the node of the β-th node of the distribution network voltage, in kW; G

_{αβ}and B

_{αβ}represent the real part and imaginary part of the node admittance matrix of the distribution network system, respectively; δ

_{αβ}= δ

_{α}− δ

_{β}is the phase-angle difference between α and β.

#### 4.3. Calculation of the Acceptance Capacity of EVs

_{ev}is the number of EVs that can be accommodated by the distribution network in the residential area; E

_{day}is the maximum daily charging power provided by the distribution network under the condition that the load acceptance capacity of the distribution network, in kW; t

_{c}

^{a}is met and the charging load characteristics are kept constant, in an hour; P

_{c}is the average charging time of electric vehicles in residential areas, in kW; λ is the proportion of EVs that need to be charged every day.

#### 4.4. Particle Swarm Optimization Algorithm

_{1}and c

_{2}are the learning factors of the algorithm, i.e., c

_{1}is the individual learning factor of the particle and c

_{2}is the social learning factor of the particle (this paper generally takes c

_{1}= c

_{2}∈ [0, 4] and c

_{1}= c

_{2}= 1.5); rand() is a random number between 0 and 1; v

_{i}is the moving speed of particle i; x

_{i}is the current position of particle i; pbest

_{i}is the individual extremum of particle i; gbest is the global extremum of the particle population.

## 5. Case Analysis

#### 5.1. Residential Area Parameters

#### 5.2. EV Access Node Prioritization

#### 5.3. Simulation Conditions

#### 5.4. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Node Number | Node Injected Active Load/kW | Node Injected Reactive Load/kVar | Node Capacity/kVA | Power Factor |
---|---|---|---|---|

1 | 0 | 0 | - | |

2 | 0 | 0 | 0 | |

3 | 0 | 0 | 0 | |

4 | 100 | 30 | 200 | 0.958 |

5 | 350 | 60 | 800 | 0.986 |

6 | 250 | 60 | 630 | 0.972 |

7 | 300 | 75 | 800 | 0.970 |

8 | 300 | 75 | 800 | 0.970 |

9 | 0 | 0 | 0 | |

10 | 300 | 75 | 800 | 0.970 |

11 | 300 | 75 | 800 | 0.970 |

12 | 0 | 0 | 0 | |

13 | 300 | 75 | 800 | 0.970 |

14 | 300 | 75 | 800 | 0.970 |

15 | 300 | 75 | 800 | 0.970 |

16 | 300 | 75 | 800 | 0.970 |

17 | 300 | 75 | 800 | 0.970 |

18 | 300 | 75 | 800 | 0.970 |

19 | 0 | 0 | 0 | |

20 | 350 | 85 | 800 | 0.972 |

21 | 0 | 0 | 0 | |

22 | 250 | 60 | 630 | 0.972 |

23 | 300 | 75 | 800 | 0.970 |

24 | 200 | 50 | 500 | 0.970 |

25 | 0 | 0 | 0 | |

26 | 250 | 60 | 630 | 0.972 |

27 | 300 | 75 | 800 | 0.970 |

28 | 300 | 75 | 630 | 0.970 |

29 | 300 | 75 | 800 | 0.970 |

30 | 350 | 85 | 630 | 0.972 |

31 | 300 | 75 | 800 | 0.970 |

32 | 250 | 60 | 630 | 0.972 |

33 | 0 | 0 | 0 | |

34 | 200 | 50 | 500 | 0.970 |

35 | 400 | 100 | 1000 | 0.970 |

36 | 350 | 85 | 800 | 0.972 |

37 | 300 | 75 | 800 | 0.970 |

38 | 200 | 50 | 500 | 0.970 |

Starting Node | End Node | Resistance/Ω | Reactance/Ω | Distance/km |
---|---|---|---|---|

1 | 2 | 0.0264 | 0.0714 | 0.2 |

2 | 3 | 0.264 | 0.714 | 2 |

3 | 4 | 0.27 | 0.335 | 1 |

3 | 5 | 0.27 | 0.335 | 1 |

5 | 6 | 0.27 | 0.335 | 1 |

5 | 7 | 0.27 | 0.335 | 1 |

5 | 8 | 0.27 | 0.335 | 1 |

2 | 9 | 0.264 | 0.714 | 2 |

9 | 10 | 0.27 | 0.335 | 1 |

9 | 11 | 0.27 | 0.335 | 1 |

9 | 12 | 0.27 | 0.335 | 1 |

12 | 13 | 0.27 | 0.335 | 1 |

12 | 14 | 0.27 | 0.335 | 1 |

12 | 15 | 0.27 | 0.335 | 1 |

12 | 16 | 0.27 | 0.335 | 1 |

12 | 17 | 0.27 | 0.335 | 1 |

12 | 18 | 0.27 | 0.335 | 1 |

2 | 19 | 0.066 | 0.1785 | 0.5 |

19 | 20 | 0.27 | 0.335 | 1 |

19 | 21 | 0.132 | 0.357 | 1 |

21 | 22 | 0.27 | 0.335 | 1 |

21 | 23 | 0.27 | 0.335 | 1 |

21 | 24 | 0.27 | 0.335 | 1 |

21 | 25 | 0.27 | 0.335 | 1 |

25 | 26 | 0.27 | 0.335 | 1 |

25 | 27 | 0.27 | 0.335 | 1 |

21 | 28 | 0.27 | 0.335 | 1 |

28 | 29 | 0.27 | 0.335 | 1 |

29 | 30 | 0.27 | 0.335 | 1 |

30 | 31 | 0.27 | 0.335 | 1 |

31 | 32 | 0.27 | 0.335 | 1 |

2 | 33 | 0.33 | 0.8925 | 2.5 |

33 | 34 | 0.54 | 0.67 | 2 |

33 | 35 | 0.27 | 0.335 | 1 |

33 | 36 | 0.27 | 0.335 | 1 |

33 | 37 | 0.27 | 0.335 | 1 |

33 | 38 | 0.27 | 0.335 | 1 |

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**Figure 2.**Distribution of end times of trip on weekdays. (

**a**) Distribution of end times of works trips, (

**b**) Distribution of end times of social shopping trips.

**Figure 10.**Temporal and spatial distribution of EV acceptance capacity in residential areas in the target year. (

**a**) Weekdays, (

**b**) Weekends.

**Figure 11.**The maximum charging load that can be connected to each partition of the distribution network. (

**a**) Weekdays, (

**b**) Weekends.

**Figure 12.**Node voltage at the maximum output power of node 1 of the distribution network. (

**a**) Weekdays, (

**b**) Weekends.

**Figure 13.**Comparison of acceptance ability and charging load of 5 nodes in the target year. (

**a**) Weekdays, (

**b**) Weekends.

EVs as a Proportion of Private Vehicles/% | Battery Capacity/kWh | Recharge Mileage/km | Charging Power/kW |
---|---|---|---|

2.05 | 40.62 | 305 | 7 |

Year | Private Vehicle Quantity/Thousands | Private Vehicle Growth Rate/% |
---|---|---|

2011 | 1033 | 32.8 |

2012 | 1277 | 23.6 |

2013 | 1572 | 23.1 |

2014 | 1933 | 23.0 |

2015 | 2241 | 15.9 |

2016 | 2564 | 14.4 |

2017 | 2853 | 15.0 |

2018 | 3158 | 10.7 |

2019 | 3499 | 10.8 |

Power Distribution Area | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Level 6 | Level 7 | Level 8 | Level 9 | Level 10 | Level 11 |
---|---|---|---|---|---|---|---|---|---|---|---|

Area I | 5 | 7 | 8 | 6 | 4 | - | - | - | - | - | - |

Area II | 13 | 18 | 17 | 14 | 15 | 16 | 10 | 11 | - | - | - |

Area III | 20 | 28 | 29 | 30 | 27 | 23 | 26 | 22 | 31 | 32 | 24 |

Area IV | 35 | 36 | 37 | 34 | 38 | - | - | - | - | - | - |

Type of Trip | Work Trips on Weekdays | Social Shopping Trips on Weekdays | Social Shopping Trips on Weekends |
---|---|---|---|

Average charging time/hours | 2.36 | 2.38 | 2.38 |

Node | 5 | 13 | 20 | 35 |
---|---|---|---|---|

All-day charging capacity (weekdays)/kWh | 1339 | 1421 | 1339 | 1736 |

The number of charging EVs throughout the day (weekdays)/vehicles | 202 | 215 | 202 | 262 |

Number of EVs that can be accommodated (weekdays)/vehicles | 538 | 573 | 538 | 698 |

All-day charging capacity (weekends)/kWh | 2355 | 2557 | 2355 | 3095 |

The number of charging EVs throughout the day (weekends)/vehicles | 353 | 383 | 353 | 464 |

Number of EVs that can be accommodated (weekdays)/vehicles | 1009 | 1095 | 1009 | 1326 |

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**MDPI and ACS Style**

Hua, Y.-P.; Wang, S.-Q.; Han, D.; Bai, H.-K.; Wang, Y.-Y.; Li, Q.-Y.
Analysis of Charging Load Acceptance Capacity of Electric Vehicles in the Residential Distribution Network. *World Electr. Veh. J.* **2022**, *13*, 214.
https://doi.org/10.3390/wevj13110214

**AMA Style**

Hua Y-P, Wang S-Q, Han D, Bai H-K, Wang Y-Y, Li Q-Y.
Analysis of Charging Load Acceptance Capacity of Electric Vehicles in the Residential Distribution Network. *World Electric Vehicle Journal*. 2022; 13(11):214.
https://doi.org/10.3390/wevj13110214

**Chicago/Turabian Style**

Hua, Yuan-Peng, Shi-Qian Wang, Ding Han, Hong-Kun Bai, Yuan-Yuan Wang, and Qiu-Yan Li.
2022. "Analysis of Charging Load Acceptance Capacity of Electric Vehicles in the Residential Distribution Network" *World Electric Vehicle Journal* 13, no. 11: 214.
https://doi.org/10.3390/wevj13110214