# Efficient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy

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## Abstract

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## 1. Introduction

## 2. Literature Review

_{2}, people’s effort to develop the eco-friendly technology is getting bigger too. Between various eco-friendly resources, electric vehicles with wireless power transmission attract attention [10]. Therefore, there are researches to improve the power receiver technology [11], plans to set wireless charging infrastructure [12], or locate wireless charging lanes for vehicles that can maximize recharged electricity while maintaining small road congestion [13]. However, in order to apply wireless power transmission technology to transportation, it is necessary to transmit a large amount of electric power with high efficiency through a relatively large air-gap. Huh et al. presented a new inductive power transfer system (IPTS) for electric cars with a large air-gap and narrow rail width. They tested the efficiency of their proposed power transfer technology from 10 cm to 20 cm of air-gap and announced that maximum efficiency is 74% at 27 kW output [14]. Wang et al. described the theoretical and practical design issues associated with inductive power transfer systems, and verified the developed theory using a practical electric vehicle battery charger. They proposed a new approach to the design of the main resonant circuit, and the proposed method minimized the deviation of the design expectation due to phase or frequency shift [15]. Huang et al. proposed a hands-free inductive power transmission system for charging batteries in electric vehicles. They explained how to design a power regulator that can guarantee a high efficiency and continuous power flow even though the distance between the bottom of the vehicle and the charge pad may vary depending on the vehicle type [16]. The studies of wireless power transmission technology applied to electric trams are as follows. Fujii and Mizuma [17] analytically studied the characteristics of new electromagnetic devices with propulsion and non-contact power collection capabilities for future wireless trams. The devices they designed operate as linear motors or linear transformers, using finite element method (FEM) and special integral equations method (IEM) for analysis. Lee et al. [18] proposed wireless power transfer (WPT) as a way to effectively solve the energy supply problem of electric railway (ER). To develop such systems, design optimization has been described as a solution that optimizes objective functions (e.g., system mass, transfer efficiency and air-gap) while satisfying constraints such as electromagnetic field (EMF), magnetic saturation and induction. In this paper, an optimization framework for railway WPT system was developed by connecting optimization module and electromagnetic commercial software. In addition, because estimating the SOC (state of charge) of a battery is one of the important techniques in wireless charging electric trams, Miyamoto et al. [19,20] performed investigations about that subject.

## 3. Problem Description

#### 3.1. Problem Statement

_{capa}, then the actual battery utilization area is between I

_{min}and I

_{max}[20,24]. As a result, the maximum battery capacity should be determined considering all those situations.

_{min}and I

_{max}, and even if the electric power is supplied by the regenerative braking and the wireless charging, the battery charging level cannot exceed I

_{max}. In this case, the supplied electricity cannot be charged, and it is lost. Therefore, when the wireless charging electric tram starts to operate in the first station, it is best to determine the target battery charging level, I

_{target}, as the optimal value between I

_{min}and I

_{max}. Then, it can prevent the loss of the electricity supplied by regenerative braking and wireless charging.

#### 3.2. Overall Procedure

#### 3.2.1. Data Collection

#### 3.2.2. Battery Consumption Calculation

#### 3.2.3. Optimal System Design

#### 3.2.4. Real Application

## 4. Mathematical Model

#### 4.1. Notation

Index | ||

i | : | Set of segments; overall route is divided by I number of segments (i = 1,2, 3…, I) |

Decision variables | ||

I_{capa} | : | Maximum capacity of battery installed in wireless charging electric tram [kWh] |

I_{target} | : | Target battery charging level before operation at first station [kWh] |

k_{inverter}(i) | : | 0–1 binary decision variable; if the inverter is allocated in ith segment, then value of 1, otherwise, value of 0 |

k_{cable}(i) | : | 0–1 binary decision variable; if the inductive cable is allocated in ith segment, then value of 1, otherwise, value of 0 |

Variables | ||

n_{inverter} | : | Total number of inverters applied in overall system [unit] |

n_{cable} | : | Total length of inductive cable applied in overall system [meter] |

I_{max} | : | Upper limit of battery utilization area regarding maximum battery capacity [kWh] |

I_{min} | : | Lower limit of battery utilization area regarding maximum battery capacity [kWh] |

I (0) | : | Initial battery charging level before operation at first station [kWh] |

I(i) | Battery charging level after passing ith segment [kWh] | |

Input parameters | ||

n_{tram} | : | Total number of wireless charging electric trams in overall system [unit] |

c_{battery} | : | Battery cost per unit kWh [$/kWh] |

c_{inverter} | : | Unit inverter cost [$/unit] |

c_{cable} | : | Inductive cable cost per unit length [$/meter] |

α_{max} | : | Ratio of upper limit of battery utilization area regarding maximum battery capacity |

α_{min} | : | Ratio of lower limit of battery utilization area regarding maximum battery capacity |

k_{cable}(0) | : | Initial value for allocation of inductive cable, which is set as 0 |

s(i) | : | Electricity supply by wireless charging in ith segment [kWh] |

r(i) | : | Electricity supply by regenerative braking in ith segment [kWh] |

l(i) | : | Length of ith segment [meter] |

#### 4.2. Model Formulation

## 5. Numerical Example

#### 5.1. System Parameters

^{2}, −1 m/s

^{2}and 20 m/s, respectively.

#### 5.2. Computational Result

## 6. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Notation | Meaning | Value |
---|---|---|

N_{tram} | Number of wireless charging electric tram [unit] | 5 |

c_{battery} | Battery cost per unit kWh [$/kWh] | $50,000 |

c_{inverter} | Unit inverter cost [$/unit] | $5000 |

c_{cable} | Inductive cable cost per unit length [$/meter] | $200 |

α_{max} | Ratio of upper limit of battery utilization area | 0.8 |

α_{min} | Ratio of lower limit of battery utilization area | 0.2 |

l(i) | Length of ith segment [meter] | 20 |

Content | Value |
---|---|

Total investment cost | $1,125,725 |

The optimal battery capacity | 3.2389 kWh |

Target battery charging level before operation at first station | 1.7997 kWh |

Total number of inverters | 8 units |

Total length of inductive cable | 1380 m |

Location of 1st inductive cable | 0 m–420 m |

Location of 2nd inductive cable | 580 m–680 m |

Location of 3rd inductive cable | 960 m–1040 m |

Location of 4th inductive cable | 1340 m–1400 m |

Location of 5th inductive cable | 1640 m–1720 m |

Location of 6th inductive cable | 1960 m–2040 m |

Location of 7th inductive cable | 2320 m–2400 m |

Location of 8th inductive cable | 2680 m–3160 m |

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**MDPI and ACS Style**

Ko, Y.D.; Oh, Y.
Efficient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy. *Sustainability* **2020**, *12*, 2920.
https://doi.org/10.3390/su12072920

**AMA Style**

Ko YD, Oh Y.
Efficient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy. *Sustainability*. 2020; 12(7):2920.
https://doi.org/10.3390/su12072920

**Chicago/Turabian Style**

Ko, Young Dae, and Yonghui Oh.
2020. "Efficient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy" *Sustainability* 12, no. 7: 2920.
https://doi.org/10.3390/su12072920