# An Optimal Domestic Electric Vehicle Charging Strategy for Reducing Network Transmission Loss While Taking Seasonal Factors into Consideration

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## Abstract

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## 1. Introduction

- (1)
- Key factors (users’ driving habits, users’ preference of charging vehicles, and ambient temperature, etc.) that can affect domestic users’ charging behavior have been fully analyzed when modelling a domestic electric vehicle charging loads model. It is worth noting that for the first time in the context of domestic electric vehicles, seasonal factors are considered to model the electrical charging loads of a single domestic electric vehicle.
- (2)
- It is the first time that the exponential distribution is used to model the domestic users’ daily travelling distance, and compared with the logarithmic normal distribution, the exponential distribution model is more suitable and accurate to reveal domestic users’ daily travelling distance.
- (3)
- The 0-1 integer programming method is proposed to regulate electric vehicle charging loads and reduce distributed power system transmission loss. By introducing binary states to domestic electric vehicle charging loads, calculation complexity can be significantly reduced, which makes the proposed strategy more real-world feasible.

## 2. Domestic Electric Vehicle Charging Loads Modelling

#### 2.1. Users’ Driving Habits and Preference of Charging Electric Vehicles

_{end}(t

_{r}) is the probability density function of daily return time from the last trip, σ

_{end}represents the standard deviation, μ

_{end}is the mathematical expectation, and t

_{r}is daily return time from the last trip. In addition, according to Figure 1b, users’ daily return time from the last trip varies greatly according to the seasons. It is shown that compared to the summer, domestic users finish their last trips much earlier in winter. Therefore, in this paper, it is the first time that seasonal factors are taken into consideration when modelling the probability density function of domestic users’ daily return time from the last trip. By implementing MATLAB (R2016b, MathWorks company, Nettie, MA, USA) Simulation, the standard deviations and mathematical expectations of users’ return time from the last trip in different seasons can be acquired. Table 1 summarizes the simulation results of these two parameters in different seasons.

_{mile}is the mathematical expectation which equals 56.22 miles.

#### 2.2. Ambient Temperature

#### 2.3. Domestic Users’ Electric Vehicle Charging Loads Modelling

_{c}is the electrical charging power of a single electric vehicle (in kW), and p

_{t}is the probability of an electric vehicle under charging condition at time t, which can be expressed as:

_{end}and f

_{tev}are the probability density functions of domestic users’ daily return time from the last trip and domestic users’ electric vehicle charging period, respectively and T

_{max}is the upper limit of charging period t

_{ev}. In Equation (4), charging period f

_{tev}can be expressed as:

## 3. Electric Vehicle Charging Loads Control Strategy and the Transmission Loss Optimization

#### 3.1. 0-1 Integer Programming for Regulating Electric Vehicle Charging Loads

_{1}is the objective function; L(j) is the total electrical demand of the power system without considering the electric vehicle charging loads at time period j, j = 1, 2, 3…m; S

_{ij}is the binary charging states of electric vehicle i at time period j; and P

_{av}is the average electrical demand of a power system. Given that the proposed model only shifts loads, P

_{av}is a constant for a given power system. Therefore, the objective function can be simplified as:

_{n}(j) is the slope of the load of the nth segment at time period j after linearization; and δ

_{n}(j) is the value of the load of the nth segment at time period j after linearization. Therefore, the linearized equivalent simplified objective function of the proposed model can be written as:

_{r}is the daily return time from the last trip and t

_{s}is the daily start time of the first trip.

_{b}and SOC

_{a}are the SOCs of the ith electric vehicle battery before and after charging, respectively; SOC

_{s}is the SOC of the ith electric vehicle battery before the trip starts; C is the capacity of the electric vehicle battery; SOC

_{Exp}and SOC

_{Full}are the expected and the fully-charged SOCs of an electric vehicle battery, respectively and Δt is the discrete time, which is inversely proportional to the number of discretized charging loads periods m.

#### 3.2. The Transmission Loss Optimization

_{loss}is the power system transmission loss, R is the resistance of the transmission line, T

_{r}is the length of a day, and i(t) is the current of a transmission line at time period t. In addition, in Equation (15), the current of a transmission line at time period t is relevant to the total daily demands, the voltage of the power system, and the difference between the current at time period t and the daily average current, therefore, i(t) can be expressed as:

_{total}is the total daily demands of the power system; U is the voltage of the power system, and Δi(t) is the difference between the current at time period t and the daily average current. By combining Equations (15) and (16), the mathematical expression of the power system transmission loss can be modified as:

## 4. Case Study

## 5. Results and Analysis

#### 5.1. Charging Electric Vehicle without Any Optimal Strategy

#### 5.2. Charging Electric Vehicle with the Proposed Optimal Strategy

#### 5.3. The Transmission Loss Optimization Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Probability distribution of domestic users’ daily return time from the last trip; (

**a**) For one year; (

**b**) For different seasons.

**Figure 2.**Probability distribution of domestic users’ daily travelling distance per vehicle (in miles); (

**a**) For one year; (

**b**) For different seasons.

**Figure 3.**Average daily load curves of 2000 electric vehicles in different seasons [20].

**Figure 5.**A flow diagram of distributed power system transmission loss optimization based on the electric vehicle 0-1 integer programming model. EV = electric vehicle.

**Figure 7.**The daily load curves of the given network in different seasons [26].

**Figure 8.**Daily load curves of the given network without considering any optimal charging strategy; (

**a**) spring, (

**b**) summer, (

**c**) autumn, (

**d**) winter.

**Figure 9.**Daily node voltage curves of the given network without considering any optimal charging strategy; (

**a**) spring, (

**b**) summer, (

**c**) autumn, (

**d**) winter.

**Figure 10.**Optimized daily load curves of the given network by applying the proposed charging strategy; (

**a**) spring, (

**b**) summer, (

**c**) autumn, (

**d**) winter.

**Figure 11.**Optimized daily note voltage curves of the given network by applying the proposed charging strategy; (

**a**) spring, (

**b**) summer, (

**c**) autumn, (

**d**) winter.

**Figure 12.**Optimal charging strategy for a selected domestic electric vehicle in different seasons; (

**a**) spring, (

**b**) summer, (

**c**) autumn, (

**d**) winter.

**Table 1.**The standard deviations and mathematical expectations of users’ return time in different seasons.

Parameters | Spring | Summer | Autumn | Winter |
---|---|---|---|---|

μ_{end} | 17:48 ^{1} | 18:00 ^{1} | 17:26 ^{1} | 17:10 ^{1} |

σ_{end} | 3.60 | 3.59 | 3.60 | 3.62 |

^{1}17:48, 18:00, 17:26 and 17:10 need to be converted to 17.8, 18.0, 17.43 and 17.17, respectively, when calculating the probability of return time from the last trip.

Standardized Charging Loads | Spring | Summer | Autumn | Winter |
---|---|---|---|---|

Standardized Maximum Charging Loads | 1 | 1.37 | 1.07 | 1.23 |

Standardized Average Charging Loads | 1 | 1.30 | 1.03 | 1.19 |

Seasons and Cases | Daily Network Demands (MW·h) | Network Loss (MW·h) | Loss Rate (%) | |
---|---|---|---|---|

Spring | Case 1 ^{1} | 57.61 | 1.66 | 2.88 |

Case 2 ^{1} | 59.94 | 1.96 | 3.27 | |

Case 3 ^{1} | 59.94 | 1.86 | 3.10 | |

Case 4 ^{1} | 59.94 | 1.88 | 3.14 | |

Summer | Case 1 ^{1} | 75.10 | 2.85 | 3.79 |

Case 2 ^{1} | 78.13 | 3.25 | 4.16 | |

Case 3 ^{1} | 78.13 | 3.05 | 3.90 | |

Case 4 ^{1} | 78.13 | 3.12 | 3.99 | |

Autumn | Case 1 ^{1} | 58.08 | 1.69 | 2.91 |

Case 2 ^{1} | 60.48 | 1.99 | 3.29 | |

Case 3 ^{1} | 60.48 | 1.89 | 3.13 | |

Case 4 ^{1} | 60.48 | 1.90 | 3.14 | |

Winter | Case 1 ^{1} | 65.31 | 2.18 | 3.34 |

Case 2 ^{1} | 68.04 | 2.63 | 3.87 | |

Case 3 ^{1} | 68.04 | 2.50 | 3.67 | |

Case 4 ^{1} | 68.04 | 2.54 | 3.73 |

^{1}Case 1: Not considering electric vehicle charging loads at all; Case 2: Considering electric vehicle charging loads and seasonal factors, but not considering any electric vehicle charging strategy; Case 3: Considering electric vehicle charging loads, seasonal factors, and the proposed electric vehicle charging strategy, and Case 4: Considering electric vehicle charging loads and the proposed electric vehicle charging strategy, but not considering seasonal factors.

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**MDPI and ACS Style**

Zhao, Y.; Che, Y.; Wang, D.; Liu, H.; Shi, K.; Yu, D.
An Optimal Domestic Electric Vehicle Charging Strategy for Reducing Network Transmission Loss While Taking Seasonal Factors into Consideration. *Appl. Sci.* **2018**, *8*, 191.
https://doi.org/10.3390/app8020191

**AMA Style**

Zhao Y, Che Y, Wang D, Liu H, Shi K, Yu D.
An Optimal Domestic Electric Vehicle Charging Strategy for Reducing Network Transmission Loss While Taking Seasonal Factors into Consideration. *Applied Sciences*. 2018; 8(2):191.
https://doi.org/10.3390/app8020191

**Chicago/Turabian Style**

Zhao, Yuancheng, Yanbo Che, Dianmeng Wang, Huanan Liu, Kun Shi, and Dongmin Yu.
2018. "An Optimal Domestic Electric Vehicle Charging Strategy for Reducing Network Transmission Loss While Taking Seasonal Factors into Consideration" *Applied Sciences* 8, no. 2: 191.
https://doi.org/10.3390/app8020191