# A Medium- and Long-Term Orderly Charging Load Planning Method for Electric Vehicles in Residential Areas

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## Abstract

**:**

## 1. Introduction

- (1)
- To propose a forecasting mathematical model of the charging load for RAs;
- (2)
- To develop a hierarchical load optimization method for analyzing the impact of orderly charging on the overall load level of the residential distribution network;
- (3)
- To present a new typical analysis method for the daily load characteristics of urban RAs.

## 2. Architecture of Orderly Charging Load Planning in RAs

## 3. Forecasting EV Charging Load in RAs

#### 3.1. The Ownership of EVs

#### 3.2. Charging Probability Model

- I.
- Travel Characteristics

_{wd-w}= 1.747, μ

_{wd-w}= 17.3.

_{1}= 0.3841, σ

_{wd-s1}= 2.32, μ

_{wd-s1}= 12; b

_{1}= 0.59, σ

_{wd-s2}= 2.575, μ

_{wd-s2}= 18.2.

_{2}= 0.302, σ

_{we-s1}= 2, μ

_{we-s1}= 11.6, b

_{2}= 0.6395, σ

_{we-s2}= 3.2, μ

_{we-s2}= 17.

_{s}is the expectation value of ln l; σ

_{s}is the standard deviation of ln l [2]. In this paper, the average travel distance of a single trip on weekdays is 11.4 km with a standard deviation of 4.88 km; the average mileage of a single trip on weekends is 13.2 km with a standard deviation of 5.23 km [24].

_{0}represents the starting SOC of EV; d

_{j}represents the mileage of the j-th trip; D represents the maximum mileage of the EV.

- II.
- Charging Time

_{c}is the charging time of the EV in h; P

_{c}is the charging power in kW; E is the battery capacity of the EV in kW·h.

#### 3.3. Forecasting of Charging Load

- (1)
- The maximum market potential, innovation coefficient p, and imitation coefficient q of EVs are selected, and the Bass model is used to iterate the medium- and long-term ownership of EVs in RAs;
- (2)
- According to the established mathematical model of EV travel characteristics, a large number of samples are randomly selected;
- (3)
- Using Equations (7) and (8), the charging start SOC and charging time of each random sample is calculated;
- (4)
- Determine whether each random sample is in the charging state at each moment;
- (5)
- According to the results of step (4), the daily charging probability curve of EVs in RAs is obtained;
- (6)
- Cycle the above steps (2) to (5) 100 times to obtain the average value curve of the daily charging probability of EVs;
- (7)
- Multiply the number of medium- and long-term EVs obtained in step (1) with the EV charging probability obtained in step (6), to obtain the number of charging EVs at each moment;
- (8)
- The number of charging EVs at each moment in step (7) is multiplied by the charging power to obtain the EV charging load power in RAs.

## 4. Orderly Charging Strategy for EVs in RAs

#### 4.1. Orderly Charging Optimization of Distribution Network

- I.
- Objective Function

_{EV}(i) is the EV charging load power at the i-th hour; P

_{norm}(i) is the conventional daily load power of the RA at the i-th hour; P is the average value of the overall load power of the RA.

- II.
- Constraints

_{ww-open}is the start time of orderly charging of EVs for work travel during workdays, and obeys the probability distribution at the end time of work travel during workdays, that is, Equation (3); t

_{ww-end}is the end time of orderly charging of EVs for work travels, and the value in this paper is 7:00.

_{ss1-open}is the start time of orderly charging of EVs for shopping–social travel on weekdays, and obeys the probability distribution of the end time of shopping-social travel on weekdays, that is, Equation (4); t

_{ss1-end}is the end time of orderly charging of EVs for shopping–social travel, and the value in this paper is 10:00.

_{ss2-open}is the start time of orderly charging of EVs for shopping–social travel on weekends, and obeys the probability distribution of the end time of shopping–social travel on weekdays, that is, Equation (5); t

_{ss2-end}is the end time of orderly charging of EVs for shopping–social travel, and the value in this paper is 10:00.

_{EV}(i) is the total charging load power of the EV at the i-th hour; C

_{max}is the maximum capacity of the residential distribution network.

_{EV}(i) is the EV charging electricity at the i-th hour; E

_{sum}is the total charging electricity.

#### 4.2. Node Orderly Charging Optimization

- I.
- Objective Function

_{j}is the overall load variance of the node j; p

_{EV-j}is the EV charging load of the node j at the i-th hour; p

_{norm-j}is the conventional daily load of the node j at the i-th hour; p

_{j}is the load mean value of the node j in the RA.

- II.
- Constraints

_{EV-j}(i) is the EV charging electricity of the node j at the i-th hour; E

_{sum-j}is the sum of the charging electricity of the node j.

_{j-max}is the maximum capacity of the node j.

#### 4.3. Nonlinear Optimization

## 5. Case Analysis

#### 5.1. Simulation Parameters

#### 5.2. Simulation Result

## 6. Conclusions

- (1)
- For the optimization of the distribution network layer, when using orderly charging, the overall peak–valley difference and peak load of the RA does not exceed the daily peak load until the target year.
- (2)
- For the optimization of each access node, the charging load power will be shifted after the implementation of the orderly charging strategy. The total peak load of the EV access node may be bigger than the peak power of disorderly charging depending on the number of EV access nodes and the shifted charging load power. The orderly charging load of each EV access node can provide a data basis for the future planning of charging facilities in RAs.
- (3)
- Implementation of orderly charging can improve the voltage quality of the distribution network in RAs and can reduce the network loss. With the increasing proportion of EV charging electricity, distribution network planning considering orderly charging can effectively save investment and operation costs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Parameter | Description |

g | Ratio of newly added products to the largest market potential [-] |

G | Ratio of the total cumulative products to the largest market potential [-] |

p | Innovation coefficient [-] |

q | Imitation coefficient [-] |

h | Private vehicle ownership growth rate [-] |

f_{wd-w} | Probability density function at the work travel end time in the weekdays [-] |

f_{wd-s} | Probability density function at the end time of the weekday shopping and social travel [-] |

f_{we-s} | Probability density function at the end time of the weekend shopping and social travel [-] |

L | Probability density function of a single mileage [-] |

l | Mileage of the vehicle in a single travel [km] |

μ_{s} | Expectation of lnl [km] |

σ_{s} | Standard deviation of lnl [km] |

SOC_{0} | Starting SOC of the electric vehicle charging [%] |

d_{j} | Mileage of the j-th travel [km] |

D | Maximum mileage of the electric vehicle [km] |

t_{c} | Charging time of the electric vehicle [hour] |

E | Battery capacity of the electric vehicle [kW·h] |

P_{c} | Charging power [kW] |

F | Objective function of the upper level [-] |

P_{EV} | Charging load [kW] |

P_{norm} | Conventional electricity load [kW] |

P | Average value of the overall load [kW] |

t_{ww-open} | Start time of orderly charging of electric vehicles for work travels on workdays [hour] |

t_{ww-end} | End time of orderly charging of electric vehicles for work travels on workdays [hour] |

t_{ss1-open} | Start time of orderly charging of electric vehicles for shopping and social travel on weekdays [hour] |

t_{ss1-end} | End time of orderly charging of electric vehicles for shopping and social travel on weekdays [hour] |

t_{ss2-open} | Start time of orderly charging of electric vehicles for shopping and social travel on weekends [hour] |

t_{ss2-end} | End time of orderly charging of electric vehicles for shopping and social travel on weekends [hour] |

C_{max} | Maximum capacity of the residential distribution network [kVA] |

E_{EV} | Electric vehicle charging electricity in each hour [kW·h] |

E_{sum} | Total charging electricity [kW·h] |

f_{j} | Load variance of the node j [-] |

p_{EV-j} | Electric vehicle charging load of the node j [kW] |

p_{norm-j} | Conventional daily load of the node j [kW] |

P_{j} | Average value load of the node j [kW] |

E_{EV-j} | Electric vehicle charging electricity of the node j in each hour [kW·h] |

E_{sum-j} | Charging electricity of the node j [kW·h] |

C_{j-max} | Maximum capacity of the node j [kVA] |

## Appendix A

Node Number | Node Injected Active Power (kW) | Node Injected Reactive Power (kVar) | Node Capacity(kVA) |
---|---|---|---|

1 | - | - | - |

2 | 100 | 30 | 400 |

3 | 90 | 25 | 400 |

4 | 120 | 35 | 400 |

5 | 60 | 15 | 400 |

6 | 60 | 15 | 400 |

7 | 200 | 60 | 400 |

8 | 200 | 60 | 400 |

9 | 60 | 15 | 400 |

10 | 60 | 15 | 400 |

11 | 45 | 10 | 400 |

12 | 60 | 15 | 400 |

13 | 60 | 15 | 400 |

14 | 120 | 35 | 400 |

15 | 60 | 10 | 400 |

16 | 60 | 15 | 400 |

17 | 60 | 15 | 400 |

18 | 90 | 25 | 400 |

19 | 90 | 25 | 400 |

20 | 90 | 25 | 400 |

21 | 90 | 25 | 400 |

22 | 90 | 25 | 400 |

23 | 90 | 25 | 400 |

24 | 420 | 100 | 630 |

25 | 420 | 100 | 630 |

26 | 60 | 15 | 400 |

27 | 60 | 15 | 400 |

28 | 60 | 10 | 400 |

29 | 120 | 35 | 400 |

30 | 200 | 60 | 400 |

31 | 150 | 45 | 400 |

32 | 210 | 60 | 400 |

33 | 60 | 15 | 400 |

Starting Node | End Node | Resistance (Ω) | Reactance (Ω) |
---|---|---|---|

1 | 2 | 0.0922 | 0.047 |

2 | 3 | 0.493 | 0.2511 |

3 | 4 | 0.366 | 0.1864 |

4 | 5 | 0.3811 | 0.1941 |

5 | 6 | 0.819 | 0.707 |

6 | 7 | 0.1872 | 0.6188 |

7 | 8 | 0.7114 | 0.2351 |

8 | 9 | 1.03 | 0.74 |

9 | 10 | 1.044 | 0.74 |

10 | 11 | 0.1966 | 0.065 |

11 | 12 | 0.3744 | 0.1238 |

12 | 13 | 1.468 | 1.155 |

13 | 14 | 0.5416 | 0.7129 |

14 | 15 | 0.591 | 0.526 |

15 | 16 | 0.7463 | 0.545 |

16 | 17 | 1.289 | 1.721 |

17 | 18 | 0.732 | 0.574 |

2 | 19 | 0.164 | 0.1565 |

19 | 20 | 1.5042 | 1.3554 |

20 | 21 | 0.4095 | 0.4784 |

21 | 22 | 0.7089 | 0.9373 |

3 | 23 | 0.4512 | 0.3083 |

23 | 24 | 0.898 | 0.7091 |

24 | 25 | 0.896 | 0.7011 |

6 | 26 | 0.203 | 0.1034 |

26 | 27 | 0.2842 | 0.1447 |

27 | 28 | 1.059 | 0.9337 |

28 | 29 | 0.8042 | 0.7006 |

29 | 30 | 0.5075 | 0.2585 |

30 | 31 | 0.9744 | 0.963 |

31 | 32 | 0.3105 | 0.3619 |

32 | 33 | 0.341 | 0.5302 |

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**Figure 4.**Orderly charging planning results: (

**a**) 2021 (weekday), (

**b**) 2022 (weekday), (

**c**) 2023 (weekday), (

**d**) 2025 (weekday), (

**e**) 2021 (weekend), (

**f**) 2022 (weekend), (

**g**) 2023 (weekend), (

**h**) 2025 (weekend).

**Figure 6.**EV access node load power: (

**a**) Node 2 (weekday), (

**b**) Node 3 (weekday), (

**c**) Node 7 (weekday), (

**d**) Node 26 (weekday), (

**e**) Node 2 (weekend), (

**f**) Node 3 (weekend), (

**g**) Node 7 (weekend), (

**h**) Node 26 (weekend).

**Figure 7.**The voltage of the EV access nodes. (

**a**) Node 2 (weekday), (

**b**) Node 3 (weekday), (

**c**) Node 7 (weekday), (

**d**) Node 26 (weekday), (

**e**) Node 2 (weekend), (

**f**) Node 3 (weekend), (

**g**) Node 7 (weekend), (

**h**) Node 26 (weekend).

**Figure 8.**Voltage of nodes 18, 22, 25, and 33: (

**a**) Node 18 (weekday), (

**b**) Node 22 (weekday), (

**c**) Node 25 (weekday), (

**d**) Node 33 (weekday), (

**e**) Node 18 (weekend), (

**f**) Node 22 (weekend), (

**g**) Node 25 (weekend), (

**h**) Node 33 (weekend).

Number of Households | Charging Power of a Single Charging Post | Number of Residents | Capacity of Distributed Network |
---|---|---|---|

2000 | 7 kW | 6000 | 5000 kVA |

Years | 2021 | 2022 | 2023 | 2025 |
---|---|---|---|---|

EV ownership | 168 | 260 | 373 | 654 |

Private vehicles | 2303 | 2409 | 2495 | 2618 |

Years | Peak-to-Valley Difference/kW | |||
---|---|---|---|---|

Disorderly Charging (Weekday) | Orderly Charging (Weekday) | Disorderly Charging (Weekend) | Orderly Charging (Weekend) | |

2021 | 2208.1 | 1949.1 | 1971.8 | 1506.7 |

2022 | 2285.3 | 1970.3 | 2025.9 | 1403.8 |

2023 | 2375.5 | 1928.8 | 2080.2 | 1277.6 |

2025 | 2579.9 | 1937.3 | 2238.3 | 1035.6 |

Typical Day | Node 2 Overall Electricity (kWh) | Node 2 Charging Electricity (kWh) | Node 3 Overall Electricity (kWh) | Node 3 Charging Electricity (kWh) | Node 7 Overall Electricity (kWh) | Node 7 Charging Electricity (kWh) | Node 26 Overall Electricity (kWh) | Node 26 Charging Electricity (kWh) |
---|---|---|---|---|---|---|---|---|

Weekday | 2218 | 637 | 3271 | 1848 | 4716 | 1554 | 2285 | 1337 |

Weekend | 2433 | 574 | 3395 | 1722 | 5181 | 1463 | 2368 | 1253 |

Typical Day | Daily Electricity (kWh) | EVs Charging Electricity (kWh) | Network Loss of Disorderly Charging (kWh) | Network Loss of Orderly Charging (kWh) |
---|---|---|---|---|

Weekday | 58,725.7 | 5376 | 2658 | 2545 |

Weekend | 69,066.8 | 5012 | 3499 | 3388 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, Z.; Zhou, Y.; Cao, J.; Xu, R.
A Medium- and Long-Term Orderly Charging Load Planning Method for Electric Vehicles in Residential Areas. *World Electr. Veh. J.* **2021**, *12*, 216.
https://doi.org/10.3390/wevj12040216

**AMA Style**

Xiao Z, Zhou Y, Cao J, Xu R.
A Medium- and Long-Term Orderly Charging Load Planning Method for Electric Vehicles in Residential Areas. *World Electric Vehicle Journal*. 2021; 12(4):216.
https://doi.org/10.3390/wevj12040216

**Chicago/Turabian Style**

Xiao, Zhaoxia, Yi Zhou, Jianing Cao, and Rui Xu.
2021. "A Medium- and Long-Term Orderly Charging Load Planning Method for Electric Vehicles in Residential Areas" *World Electric Vehicle Journal* 12, no. 4: 216.
https://doi.org/10.3390/wevj12040216