# Research on Charging-Discharging Operation Strategy for Electric Vehicles Based on Different Trip Patterns for Various City Types in China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Time and Space Distribution Model of Electric Vehicles

#### 2.1. Electric Vehicle Travel Chain

#### 2.2. Distribution Network Function Division

#### 2.3. Distribution of Electric Vehicles in Each Functional Area at Each Time Period

- Type 1 (black line in Figure 2) refers to the working trip, including the H–W trip of the simple work chain A, the first H–W trip of the complex work chain B, and the H–W trip of the work–entertainment chain C.
- Type 2 (red line in Figure 2) mainly includes home or entertainment trips, including the W–H trip of the simple work chain A, both W–H trips of the complex work chain B, and the W–E trip of the work–entertainment chain C.
- Type 3 (blue line in Figure 2) includes the second H–W trip of the complex work chain B and the E–H trip of the work–entertainment chain C.

#### 2.3.1. Type 1 Trips

_{2}is the standard deviation of the standard normal distribution.

_{ij,t}indicates the travel time of the electric vehicle for a trip from region i to region j, arriving at time t. v indicates the speed of the electric vehicle, and ${t}_{i,j}^{\mathrm{arr}}$ indicates the arrival time for the journey from region i to region j.

#### 2.3.2. Type 2 Trips

_{2}and σ

_{3}are the mean and standard deviation, respectively, of the normal distribution.

#### 2.3.3. Type 3 Trips

_{min}, Δt

_{max}). I this equation, Δt

_{min}is the shortest residence time and Δt

_{max}is the longest residence time. The probability density function for the H–W departure time is given by Formula (8), and the cumulative distribution function is given by Formula (9):

_{min}and Δt

_{max}for different trips are shown in Appendix C.

#### 2.3.4. EV Departure, Arrival, and Distribution Probability in Each Region

_{A}, β

_{B}, and β

_{C}are the proportions of EVs using travel chains A, B, and C, respectively, and ${f}_{12}^{\mathrm{lv}\_\mathrm{A}}$(t), ${f}_{12}^{\mathrm{lv}\_\mathrm{B}}$(t), and ${f}_{12}^{\mathrm{lv}\_\mathrm{C}}$(t) are the moment-by-moment probabilities of a user leaving area 1 for the trip from area 1 (residential area) to area 2 (working area) under travel chains A, B and C, respectively.

_{i,t}.

## 3. Model for the Charging and Discharging of Electric Vehicles

#### 3.1. Energy Consumption Model

#### 3.1.1. EV Energy Consumption Model at the Workspace Node

_{all}indicates the possession of EVs. N

_{i}is the number of nodes with EV charging stations in region i, and [] is the round-up function.

#### 3.1.2. EV Energy Consumption Model at the Commercial Node

#### 3.1.3. EV Energy Consumption Model at the Residential Node

#### 3.2. Charging and Discharging Model of Cluster Electric Vehicles

#### 3.2.1. Charging and Discharging Constraints

_{k,t}is the charging and discharging power of node k at time t. By convention, charging is positive and discharging is negative.

#### 3.2.2. Capacity Constraint

_{k,t}of node k at time t to equal or exceed the SOC value required by the EVs leaving at time below and the sum of the minimum SOC values required by the remaining EVs, as shown in Formula (17). Conversely, Q

_{k,t}could not exceed the maximum allowable SOC value of the node, as shown in Formula (18).

^{dw}indicates the minimum SOC requirement for each EV, ${\gamma}_{i}^{\mathrm{lv}}$ indicates the SOC required for each EV leaving area i, and C is the battery capacity of each EV.

#### 3.2.3. Continuity Constraints on SOC

_{min}indicates the minimum time unit, which we set at 15 minutes for this study. Note that the last three terms of Formula (19) account for the quantity of electricity added by newly arriving EVs and the quantity of electricity taken away by newly departing EVs.

## 4. Electric Vehicle Scheduling Model, Accounting for Distribution Network Security Constraints

_{t}indicates the electricity price at time t and P

_{0t}indicates the injected power of the root node of the distribution network at time t. The purpose of the objective function is the minimization of the power purchase cost at the root node.

_{k,t}is the net injected power at node k at time t, and L

_{k}

_{,t}is the load of node k at time t.

_{km,t}indicates the apparent power of branch k-m, and g

_{km}and b

_{km}are the conductance and susceptance, respectively, of branch k-m. V

_{k,t}is the voltage amplitude at time t, and θ

_{km,t}is the voltage phase angle difference between nodes k and m.

_{k,t}V

_{m,t}cosθ

_{km,}

_{t}, and V

_{k,t}V

_{m,t}sinθ

_{km,t}are converted to R

_{k,t}, W

_{km,t}, and T

_{km,t}, respectively.

## 5. Algorithm Flow Chart

## 6. Results and Discussion

#### 6.1. Basic Parameters

- 1.
- The power factor of each node is 0.85, and the reactive power of the node is determined based on the active power injected into the node.
- 2.
- All nodes, except for nodes 10 and 11, are equipped with EV charging stations. The total number of EVs is 2400. Other predefined parameters include L
_{12}= 15 km, L_{23}= 12 km, L_{13}= 12 km, v = 30 km/h, and the energy consumption factor E = 0.25. The network assumes that EVs are evenly distributed in the same functional area. The specific parameters of EVs are shown in Table 2. - 3.
- Electricity prices in Jiangsu Province are divided into three rates based on time of use (peak, normal, and valley). Prices for each usage period are shown in Table 3.

#### 6.2. Comparison with Traditional Monte Carlo Sampling

_{2}) required by the traditional Monte Carlo sampling method gradually increases, as shown in Figure 5. However, the resulting distribution gradually approaches uniformity. Given the increasing number of EVs in the current city and the uniform distribution pattern of cluster EVs, we therefore derived the probability distribution formula mathematically which uses less time (t

_{2}) with the growth of the number of EVs.

#### 6.3. Distribution of Electric Vehicles in Various Cities

_{A}, β

_{B}and β

_{C}parameters are different). In this study, we compared the following three urban travel chain models:

- Small cities, where simple work chain A and complex work chain B are considered but the work–entertainment chain C is absent (β
_{A}= 30%, β_{B}= 70%, β_{C}= 0%). - Large industrial cities: simple work chain A is more common than work–entertainment chain C (β
_{A}= 70%, β_{B}= 0%, β_{C}= 30%). - Large commercial cities: simple work chain A is less common than work–entertainment chain C (β
_{A}= 30%, β_{B}= 0%, β_{C}= 70%).

#### 6.4. Charging and Discharging Scheduling Results of Electric Vehicles in Various Cities

## 7. Conclusions

- The time distribution obtained by Monte Carlo sampling is stochastic and volatile, so we derived the probability distribution formula of EVs mathematically based on different travel chain patterns of EVs in different cities.
- In our proposed scheduling strategy, the distribution pattern of EVs in each region was fully considered when coordinating charging and discharging strategies. Furthermore, scheduling results differ among different types of cities due to the different proportions of EVs in different regions at different time periods.
- The cost of the distribution network is minimized, and the profit of EVs is maximized in small cities. EVs prefer charging rather than discharging in commercial areas, limiting the efficiency of the V2G strategy for EVs in commercial areas. Therefore, EVs in commercial cities have the highest cost and the lowest profit, and the power grid economy is relatively low.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{2}is the standard deviation of the normal distribution.

α | θ | σ_{2} | |
---|---|---|---|

H–W trip of chain A | 18.63 | 28.14 | 79.36 |

The first H–W trip of chain B | 7.69 | 68.14 | 29.36 |

H–W trip of chain C | 18.63 | 28.14 | 79.36 |

## Appendix B

_{2}and σ

_{3}are the mean and standard deviation of the normal distribution.

k | λ | μ_{2} | σ_{3} | |
---|---|---|---|---|

W–H trip of chain A | 8.63 | 1061.4 | 156.45 | 91.17 |

The first W–H trip of chain B | 10.63 | 750 | 68.45 | 26.17 |

The second W–H trip of chain B | 10.63 | 1061 | 68.45 | 26.17 |

W–E trip of chain C | 8.63 | 1061.4 | 0 | 79.36 |

## Appendix C

Time | Δt_{min} (min) | Δt_{max} (min) |
---|---|---|

The second H–W trip of chain B | 30 | 90 |

E–H trip of chain C | 0 | 120 |

## References

- Mukherjee, J.C.; Gupta, A. A Review of Charge Scheduling of Electric Vehicles in Smart Grid. IEEE Syst. J.
**2015**, 9, 1541–1553. [Google Scholar] [CrossRef] - Nimalsiri, N.I.; Mediwaththe, C.P.; Ratnam, E.L.; Shaw, M.; Smith, D.B.; Halgamuge, S.K. A Survey of Algorithms for Distributed Charging Control of Electric Vehicles in Smart Grid. IEEE Trans. Intell. Transp. Syst.
**2020**, 21, 4497–4515. [Google Scholar] [CrossRef] [Green Version] - Cao, Y.; Wang, T.; Kaiwartya, O.; Min, G.; Ahmad, N.; Abdullah, A.H. An EV Charging Management System Concerning Drivers’ Trip Duration and Mobility Uncertainty. IEEE Trans. Syst. Man Cybern. Syst.
**2018**, 48, 596–607. [Google Scholar] [CrossRef] [Green Version] - Chaudhari, K.; Ukil, A.; Kumar, K.N.; Manandhar, U.; Kollimalla, S.K. Hybrid Optimization for Economic Deployment of ESS in PV-Integrated EV Charging Stations. IEEE Trans. Ind. Inform.
**2018**, 14, 106–116. [Google Scholar] [CrossRef] - Franco, J.F.; Rider, M.J.; Romero, R. A Mixed-Integer Linear Programming Model for the Electric Vehicle Charging Coordination Problem in Unbalanced Electrical Distribution Systems. IEEE Trans. Smart Grid
**2015**, 6, 2200–2210. [Google Scholar] [CrossRef] - Xu, S.; Feng, D.; Yan, Z.; Zhang, L.; Li, N.; Jing, L.; Wang, J. Ant-Based Swarm Algorithm for Charging Coordination of Electric Vehicles. Int. J. Distrib. Sens. Netw.
**2013**, 9, 268942. [Google Scholar] [CrossRef] - Qi, W.; Xu, Z.; Shen, Z.-J.M.; Hu, Z.; Song, Y. Hierarchical Coordinated Control of Plug-in Electric Vehicles Charging in Multifamily Dwellings. IEEE Trans. Smart Grid
**2014**, 5, 1465–1474. [Google Scholar] [CrossRef] - Zhou, J.; Jiang, H.; Zhang, X.; Li, Z.; Pang, J. Electric Vehicle Travel Chain Model and Case Analysis Based on Time and Space Characteristics. In Proceedings of the 2019 IEEE Sustainable Power and Energy Conference (iSPEC), Beijing, China, 21–23 November 2019; pp. 1535–1539. [Google Scholar]
- Moghaddass, R.; Mohammed, O.A.; Skordilis, E.; Asfour, S. Smart Control of Fleets of Electric Vehicles in Smart and Connected Communities. IEEE Trans. Smart Grid
**2019**, 10, 6883–6897. [Google Scholar] [CrossRef] - He, Y.; Venkatesh, B.; Guan, L. Optimal Scheduling for Charging and Discharging of Electric Vehicles. IEEE Trans. Smart Grid
**2012**, 3, 1095–1105. [Google Scholar] [CrossRef] - Tang, Y.; Zhong, J.; Bollen, M. Aggregated optimal charging and vehicle-to-grid control for electric vehicles under large electric vehicle population. IET Gener. Transm. Distrib.
**2016**, 10, 2012–2018. [Google Scholar] [CrossRef] - Yuan, Z.; Yu, L.; Xu, Q.; Zou, C.; Qv, K.; Xu, S.; Yin, S. Optimization of Orderly Charge and Discharge Scheduling of Electric Vehicles and Photovoltaic in Industrial Par. In Proceedings of the 2020 Asia Energy and Electrical Engineering Symposium (AEEES), Chengdu, China, 29–31 May 2020; pp. 226–229. [Google Scholar]
- Liang, H.; Lee, Z.; Li, G. A Calculation Model of Charge and Discharge Capacity of Electric Vehicle Cluster Based on Trip Chain. IEEE Access
**2020**, 8, 142026–142042. [Google Scholar] [CrossRef] - U.S. Department of Transportation, Federal Highway Administration. 2017 National Household Travel Survey [EB/OL]. Available online: http://nhts.ornl.gov (accessed on 28 October 2021).
- UK Department for Transport. National Travel Survey: 2016. [EB/OL]. Available online: html://https://www.gov.uk/government/statistics/national-travel-survey-2016 (accessed on 28 October 2021).
- Xu, W. Understanding the Intra-urban Residents’ Trip Characteristics Based on GPS. In Proceedings of the 2019 IEEE 19th International Conference on Communication Technology (ICCT), Xi’an, China, 16–19 October 2019; pp. 1555–1559. [Google Scholar]
- Zhenru, L.; Xuemei, L.I. Review of trip-chain-based travel activity study of residents. In Proceedings of the 2010 International Conference on Logistics Systems and Intelligent Management (ICLSIM), Harbin, China, 9–10 January 2010; pp. 1527–1531. [Google Scholar]
- Xue, M. Cangnan Inhabitant Trips Characteristics Study. Traffic Transp.
**2009**, 12, 7–10. [Google Scholar] - Chen, Z.; Zhang, Z.; Zhao, J.; Wu, B.; Huang, X. An Analysis of the Charging Characteristics of Electric Vehicles Based on Measured Data and Its Application. IEEE Access
**2018**, 6, 24475–24487. [Google Scholar] [CrossRef] - Neumanenn, F. Optimal Scheduling of EV Charging in Distribution Networks. Master’s Thesis, The University of Edinburgh, Edinburgh, Scotland, 2017. [Google Scholar]

Time | Morning Peak 7:00–9:00 | Evening Peak 17:00–19:00 | Other Time 0:00–7:00, 9:00–17:00, 19:00–24:00 |
---|---|---|---|

Congestion coefficient | 1.5 | 1.5 | 1 |

EV Battery Capacity (kWh) | Maximum SOC | Minimum SOC | Max Charging Power (kW) | Max Discharging Power (kW) | Demand SOC |
---|---|---|---|---|---|

24 | 0.95 | 0.2 | 15 | 15 | Residential 0.9 Working 0.85 Commercial 0.85 |

Time | Peak (8:00–12:00; 17:00–21:00) | Normal (12:00–17:00; 21:00–24:00) | Valley (0:00–8:00) |
---|---|---|---|

Price (USD) | 169.12 | 101.47 | 49.52 |

**Table 4.**Costs of the distribution network and benefits of electric vehicles in different functional areas.

Network Cost (USD) | EV Benefit (USD) | Benefit in Residential Areas (USD) | Benefit in Working Areas (USD) | Benefit in Commercial Areas (USD) | |
---|---|---|---|---|---|

Small cities | 72,090 | 6781 | 4576 | 2197 | 0 |

Large industrial cities | 74,538 | 4432 | 3527 | 1449 | −226 |

Large commercial cities | 74,688 | 4270 | 3517 | 1332 | −579 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Qi, S.; Lin, Z.; Song, J.; Lin, X.; Liu, Y.; Ni, M.; Wang, B.
Research on Charging-Discharging Operation Strategy for Electric Vehicles Based on Different Trip Patterns for Various City Types in China. *World Electr. Veh. J.* **2022**, *13*, 7.
https://doi.org/10.3390/wevj13010007

**AMA Style**

Qi S, Lin Z, Song J, Lin X, Liu Y, Ni M, Wang B.
Research on Charging-Discharging Operation Strategy for Electric Vehicles Based on Different Trip Patterns for Various City Types in China. *World Electric Vehicle Journal*. 2022; 13(1):7.
https://doi.org/10.3390/wevj13010007

**Chicago/Turabian Style**

Qi, Sirui, Zhengchong Lin, Junwen Song, Xinwei Lin, Yan Liu, Meng Ni, and Beibei Wang.
2022. "Research on Charging-Discharging Operation Strategy for Electric Vehicles Based on Different Trip Patterns for Various City Types in China" *World Electric Vehicle Journal* 13, no. 1: 7.
https://doi.org/10.3390/wevj13010007