# Optimal Planning of Charging for Plug-In Electric Vehicles Focusing on Users’ Benefits

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## Abstract

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## 1. Introduction

_{2}emission, and EV users’ cost is proposed in [18]. The decrease in queue time is also treated as a benefit, especially for motivating EV users in specific situations, such as shopping areas and highways [17,18,19]. Nevertheless, few of those took the cost of battery capacity degradation into account, although such a cost is a non-negligible part of EVs’ total operating costs. The battery is one of the most important parts of the EV and the price of the battery is almost half of the EV price. The batteries’ useful life is greatly affected by different methods of charging and discharging. Many experiments and studies have been performed focusing on the Li-ion battery, but these achievements were not applied in the field of charging management. A battery capacity fading model, which can simulate the battery degradation dynamics in various operating conditions was developed in [20]. The authors of [21] proposed a novel fusion prognostic model, in which the time series prediction model is adopted, and implemented a particle filter algorithm for predicting Li-ion battery life. The CALCE (Center for Advanced Life Cycle Engineering) Battery Group from the University of Maryland quantified the effect of partial cycling on lithium-ion battery capacity fade by means of cycling tests operating on graphite/LiCoO

_{2}pouch cells under diverse state of charge (SOC) ranges, and then developed a model of the battery capacity degradation under partial cycling conditions [22]. Plenty of research efforts have been devoted to study the contributing factors to battery capacity fade. The value of used batteries, which is an important factor to derive the cost of battery capacity degradation, is analyzed in [23,24]. Since the operating SOC range is the most controllable factor, it should be incorporated in the charging planning for reducing EV users’ total operating costs. Furthermore, EV users are likely to pay more attention to the waiting time compared to the operating costs in the aforementioned specific situations [17,19,25,26]. An intention-aware routing system was developed to calculate a routing policy that minimizes their expected journey time in [27]. A planning method based on the queuing theory was proposed to determine the capacity of each EV charging station and minimize the sum of the waiting cost and the charger cost in [28].

## 2. Methodology Description

## 3. Problem Formulation and Transformation

#### 3.1. Cost Model of Battery Capacity Fade

#### 3.1.1. Battery Capacity Degradation Analysis

_{2}pouch cells under different SOC ranges and charge/discharge currents, which is experimentalized and collected by the CALCE battery group at the University of Maryland [31], is adopted in our research. We only focus on the data collected when the batteries are cycled at a current rate of 0.5 C corresponding to level 1 charging. The capacity degradation results for different SOC ranges are shown in Figure 2.

#### 3.1.2. Cost of Battery Capacity Degradation Modeling

_{mean}denotes the mean SOC of the operating SOC range, and ΔSOC means the difference between the maximum and the minimum SOC of the operating SOC range. The number of EFC can be easily derived by this model:

#### 3.2. Electricity Cost

#### 3.3. Grid Load Curve Optimization

- Step 1.
- Initialize the parameters visual distance, step length, population size, crowded degree, and iteration times. The visual distance and step values will decrease as the number of iterations increases. A group of artificial fish M is generated randomly in the water, and the information contained in each fish is a charging start time matrix U of all EVs. Each artificial fish here represents a charging start time scheme for all EVs.
- Step 2.
- Calculate the food concentration of each fish’s position, record the best result on the bulletin board. The food concentration (i.e., the variance of distribution network) load is calculated based on the objective function.
- Step 3.
- Artificial fishes move one step by performing one of the four kinds of behavior, which are cluster behavior, following behavior, foraging behavior, and random behavior, according to their situation.
- Step 4.
- Calculate the food concentration of each fish’s new position. Record the best result to the bulletin board if it is better than the old one.
- Step 5.
- If the ending condition is met, finish the algorithm. If not, go to step 3.

#### 3.4. Queuing Theory for Busy Areas

## 4. Numerical Results

#### 4.1. Regular Routes Planning Simulation

#### 4.1.1. Monte Carlo Method

#### 4.1.2. Results of Regular Routes Simulation

#### 4.2. Irregular Routes Planning Simulation

## 5. Conclusions

- A cost model of battery capacity degradation is developed to estimate the cost of battery capacity degradation, which is usually not paid much attention by EV users. The optimal SOC range planning based on this model enables the the cost of battery degradation to be significantly reduced.
- For regular routes, to keep the operating cost low for the routes, such as commuting, charging time is also shifted to achieve the lowest electricity cost.
- For regular routes, the grid operation is optimized by AFSA with constraints which occur in the process of maximizing EV users’ benefit. In the meantime, the daily load curve in the distribution network can still be flattened markedly.
- For irregular routes, the average queue time is greatly decreased due to the application of queuing theory, and the cost of battery degradation is also reduced by the SOC range planning based on the cost model of battery degradation.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**(

**a**) Battery capacity retention rate versus equivalent full cycles of batteries cycling at 50% mean SOC; (

**b**) battery capacity retention rate versus charging times of batteries cycling at 50% mean SOC; (

**c**) battery capacity retention rate versus equivalent full cycles of batteries cycling at 60% ΔSOC; and (

**d**) battery capacity retention rate versus number of charging times of batteries cycling at 60% ΔSOC.

**Figure 7.**Operating cost comparison of one time charging: (

**a**) costs of battery capacity degradation comparison; and (

**b**) electricity costs comparison.

**Figure 10.**Average waiting time distribution comparison of ordered charging and disordered charging.

**Figure 11.**Cost of battery degradation and average waiting time comparison of ordered charging and disordered charging: (

**a**) cost of battery degradation; and (

**b**) average waiting time.

Vehicle Type | Capacity (kWh) | Consumption (kWh/100 km) | Sales in 2016 |
---|---|---|---|

BYD e6 | 82 | 19.5 | 20605 |

BAIC E-Series EV | 25.6 | 15 | 18814 |

BAIC EU260 EV | 41.4 | 15.9 | 18805 |

Geely Emgrand | 41 | 15.8 | 17181 |

Operating Costs | DC | OC |
---|---|---|

Cost of Battery Degradation (USD) | 0.94 | 0.17 |

Electricity Cost (USD) | 0.51 | 0.46 |

Method | Variance | Peak (kW) | Valley (kW) |
---|---|---|---|

DC | 4098 | 864.0 | 442.2 |

OC | 3885 | 822.7 | 464.7 |

Orignal load | 3016 | 741.0 | 409.4 |

© 2017 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Su, S.; Li, H.; Gao, D.W. Optimal Planning of Charging for Plug-In Electric Vehicles Focusing on Users’ Benefits. *Energies* **2017**, *10*, 952.
https://doi.org/10.3390/en10070952

**AMA Style**

Su S, Li H, Gao DW. Optimal Planning of Charging for Plug-In Electric Vehicles Focusing on Users’ Benefits. *Energies*. 2017; 10(7):952.
https://doi.org/10.3390/en10070952

**Chicago/Turabian Style**

Su, Su, Hao Li, and David Wenzhong Gao. 2017. "Optimal Planning of Charging for Plug-In Electric Vehicles Focusing on Users’ Benefits" *Energies* 10, no. 7: 952.
https://doi.org/10.3390/en10070952