# Evaluation Method to Select Pure Electric Buses Based on Road Operation Tests

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## Abstract

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## 1. Introduction

_{2}reduction targets defined by political legislation [1]. Electric buses have globally attracted attention for urban applications because of their outstanding environmental protection performance, driving stability, and economic performance. The 30th Electric Vehicle Symposium, which was held on the 9–11 October 2017, explored different types of vehicles, including pure electric, hybrid, fuel cell, energy conservation, environmental protection, and other types of new energy vehicles, and covered a range of topics, such as auto parts development, new technology applications, policy guidance for new product marketing, and industrial upgrading [2].

## 2. Performance Measurement Indexes

#### 2.1. Construction of the Index System

#### 2.2. Data Collection

## 3. Index Calculation and Data Level

#### 3.1. Quantitative Indexes

#### 3.1.1. Calculation of the Reliability Indexes

#### 3.1.2. Calculation of the Economic Index

- $\mathrm{G}$ = purchase cost (¥10,000)
- ${\mathrm{G}}_{1}$ = bus price (¥10,000)
- ${\mathrm{G}}_{2}$ = taxes (¥10,000)
- ${\mathrm{G}}_{3}$ = other fees (¥10,000)
- ${\mathrm{G}}_{4}$ = average subsidization per bus (¥ 10,000)

- q = electricity consumption per 1000 seats·kilometers (kWh/1000seats·km)
- Q = electricity consumption during testing (kWh)
- S = test mileage (km)
- n = the number of the seat (seats)

- w = maintenance cost per 100 km (¥)
- W = maintenance cost during test (¥)
- S = test mileage (km)

#### 3.1.3. Security Indexes Calculation

- T = average temperature difference after braking (°C)
- x = number of test samples (time)
- $\mathsf{\Delta}\mathrm{T}$ = temperature rise after braking (°C)

- $\mathsf{\eta}$ = failure rate (time/100 km)
- N = total number of failures under test mileage
- S = test mileage (km)

#### 3.2. Semi-Qualitative Indexes

#### 3.2.1. Calculation of the Environmental Adaptability Indexes

- $\mathsf{\epsilon}$ = environmental impact coefficient
- q = electricity consumption per 100 km (kWh/100 km)
- n = number of test samples

#### 3.2.2. Failure Severity Calculation

- $\mathsf{\Delta}\mathrm{t}$ = average failure maintenance time (min)
- t = single maintenance time (min)
- N = total number of failures under the test mileage

#### 3.3. Qualitative Indexes

## 4. Comprehensive Evaluation

#### 4.1. Determination of the Weights by the AHP Method

- $\mathsf{\lambda}$ = non-zero eigenvalue
- n = the number of the indexes

#### 4.2. Determination of the Evaluation Set and Subjection Function

- $\mathrm{a}$ = total number of experts who evaluate index ${\mathrm{u}}_{\mathrm{i}\mathrm{j}}$
- ${\mathrm{a}}_{\mathrm{k}}$ = number of experts who give grade k to index ${\mathrm{u}}_{\mathrm{i}\mathrm{j}}$

- i = number of indicators of Class 1
- j = number of indicators of Class 2
- k = number of data levels of each indicator

#### 4.3. Determination of the Fuzzy Evaluation Matrix

#### 4.4. Results and Discussion

## 5. Case Study

- W = (0.307, 0.203, 0.132, 0.307, 0.051)
- W1 = (0.128, 0.356, 0.222, 0.072, 0.222)
- W2 = (0.529, 0.309, 0.162)
- W3 = (0.379, 0.158, 0.108, 0.070, 0.285)
- W4 = (0.162, 0.309, 0.529)
- W5 = (0.311, 0.575, 0.114)

^{′}

_{i1}, R

^{′}

_{i2}, R

^{′}

_{i3}, R

^{′}

_{i4}, R

^{′}

_{i5}(i = 1, 2).

- The calculation of fuzzy evaluation matrices of Bus 1 (B
_{1}):$$\begin{array}{l}{{\mathrm{R}}^{\prime}}_{11}={\mathrm{W}}_{1}\xb7{\mathrm{R}}_{11}=\left(\begin{array}{cccc}0.222& 0.67& 1& 0.872\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{12}={\mathrm{W}}_{2}\xb7{\mathrm{R}}_{12}=\left(\begin{array}{cccc}0.162& 0.232& 0.6031& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{13}={\mathrm{W}}_{3}\xb7{\mathrm{R}}_{13}=\left(\begin{array}{cccc}0.117& 0.537& 0.879& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{14}={\mathrm{W}}_{4}\xb7{\mathrm{R}}_{14}=\left(\begin{array}{cccc}0.838& 0.838& 0.968& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{15}={\mathrm{W}}_{5}\xb7{\mathrm{R}}_{15}=\left(\begin{array}{cccc}0.336& 0.564& 0.093& 0.008\end{array}\right)\\ {\mathrm{R}}_{1}=\left({{\mathrm{R}}^{\prime}}_{11}{{\mathrm{R}}^{\prime}}_{12}{{\mathrm{R}}^{\prime}}_{13}{{\mathrm{R}}^{\prime}}_{14}{{\mathrm{R}}^{\prime}}_{15}\right)=\left(\begin{array}{cccc}0.222& 0.67& 1& 0.872\\ 0.162& 0.232& 0.6031& 1\\ 0.117& 0.537& 0.879& 1\\ 0.838& 0.838& 0.968& 1\\ 0.336& 0.564& 0.093& 0.008\end{array}\right)\\ {\mathrm{B}}^{1}=\mathrm{W}\xb7{\mathrm{R}}_{1}=\left(0.391\text{\hspace{1em}}0.610\text{\hspace{1em}}0.848\text{\hspace{1em}}0.910\right)\end{array}$$ - The calculation of fuzzy evaluation matrices of Bus 2 (B
_{2}):$$\begin{array}{l}{{\mathrm{R}}^{\prime}}_{21}={\mathrm{W}}_{1}\xb7{\mathrm{R}}_{21}=\left(\begin{array}{cccc}0.275& 0.510& 0.658& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{22}={\mathrm{W}}_{2}\xb7{\mathrm{R}}_{22}=\left(\begin{array}{cccc}0.033& 0.162& 0.511& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{23}={\mathrm{W}}_{3}\xb7{\mathrm{R}}_{23}=\left(\begin{array}{cccc}0& 0.376& 0.817& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{24}={\mathrm{W}}_{4}\xb7{\mathrm{R}}_{24}=\left(\begin{array}{cccc}0& 0.205& 0.471& 1\end{array}\right)\\ {{\mathrm{R}}^{\prime}}_{25}={\mathrm{W}}_{5}\xb7{\mathrm{R}}_{25}=\left(\begin{array}{cccc}0.274& 0.522& 0.197& 0.007\end{array}\right)\\ {\mathrm{R}}_{2}=\left({{\mathrm{R}}^{\prime}}_{21}\text{}{{\mathrm{R}}^{\prime}}_{22}\text{}{{\mathrm{R}}^{\prime}}_{23}\text{}{{\mathrm{R}}^{\prime}}_{24}\text{}{{\mathrm{R}}^{\prime}}_{25}\right)=\left(\begin{array}{cccc}0.275& 0.510& 0.658& 1\\ 0.033& 0.162& 0.511& 1\\ 0& 0.376& 0.817& 1\\ 0& 0.205& 0.471& 1\\ 0.274& 0.522& 0.197& 0.007\end{array}\right)\\ {\mathrm{B}}^{2}=\mathrm{W}\xb7{\mathrm{R}}_{2}=\left(0.105\text{}0.329\text{}0.568\text{}0.950\right)\end{array}$$

- The final performance score of Bus 1:$${\mathrm{S}}_{1}={\mathrm{B}}_{1}\xb7\mathrm{P}=6$$
- The final performance score of Bus 2:$${\mathrm{S}}_{2}={\mathrm{B}}_{2}\xb7\mathrm{P}=3.493$$

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Class 1 Indexes | Class 2 Indexes |
---|---|

Reliability indexes ${\mathrm{u}}_{1}$ | Power weight ratio, ${\mathrm{u}}_{11}$ |

Driving mileage, ${\mathrm{u}}_{12}$ | |

Total battery cycle times, ${\mathrm{u}}_{13}$ | |

Battery capacity, ${\mathrm{u}}_{14}$ | |

Battery attenuation amplitude, ${\mathrm{u}}_{15}$ | |

Cost indexes ${\mathrm{u}}_{2}$ | Vehicle purchase cost, ${\mathrm{u}}_{21}$ |

Electricity consumption per 1000 seats·km, ${\mathrm{u}}_{22}$ | |

Maintenance cost per 100 km, ${\mathrm{u}}_{23}$ | |

Adaptability indexes ${\mathrm{u}}_{3}$ | Temperature adaptability, ${\mathrm{u}}_{31}$ |

Line adaptability, ${\mathrm{u}}_{32}$ | |

Special weather adaptability, ${\mathrm{u}}_{33}$ | |

Initial electric quantity adaptability, ${\mathrm{u}}_{34}$ | |

Air conditioner adaptability, ${\mathrm{u}}_{35}$ | |

Security indexes ${\mathrm{u}}_{4}$ | Average temperature difference of brake, ${\mathrm{u}}_{41}$ |

Vehicle failure rate, ${\mathrm{u}}_{42}$ | |

Vehicle fault severity, ${\mathrm{u}}_{43}$ | |

Service indexes ${\mathrm{u}}_{5}$ | Driving convenience, ${\mathrm{u}}_{51}$ |

Comfort, ${\mathrm{u}}_{52}$ | |

After-sale service, ${\mathrm{u}}_{53}$ |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

C (kWh) | C ≥ 250 | 150 ≤ C < 250 | 100 ≤ C < 150 | C < 100 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

f | f ≥ 12 | 10 ≤ f < 12 | 8 ≤ f < 10 | f < 8 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

L (km) | L ≥ 250 | 200 ≤ L < 250 | 150 ≤ L < 200 | L < 150 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

r | r ≥ 2000 | 1000 ≤ r < 2000 | 500 ≤ r < 1000 | r < 500 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

δ | δ < 10% | 10% ≤ δ < 15% | 15% ≤ δ < 20% | δ ≥ 20% |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

$\mathrm{G}$ (units: ¥10,000) | $\mathrm{G}$ ≤ 60 | 60 < G ≤ 80 | 80 < $\mathrm{G}$ < 120 | $\mathrm{G}$ ≥ 120 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

$\mathrm{q}$ (kWh/1000 seats·km) | q ≤ 25 | 25 < q ≤ 40 | 40 < q < 50 | q ≥ 50 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

w (yuan) | w ≤ 10 | 10 < w ≤ 20 | 20 < w < 30 | w ≥ 30 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

T (°C) | T < 5 | 5 ≤ T < 10 | 10 ≤ T < 15 | T ≥ 15 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

η | η < 0.002 | 0.002 ≤ η < 0.005 | 0.005 ≤ η < 0.008 | η ≥ 0.008 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

ε | ε ≤ 0.1 | 0.1 < ε ≤ 0.3 | 0.3 < ε < 0.6 | ε ≥ 0.6 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

∆t (min) | ∆t ≤ 5 | 5< ∆t ≤ 30 | 30 < ∆t ≤ 60 | ∆t > 60 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

Score range | 16–20 | 11–15 | 6–10 | 1–5 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

Score range | 13–15 | 9–13 | 5–8 | 0–4 |

Grade Division | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

Score range | 16–20 | 11–15 | 6–10 | 1–5 |

Numerical Rating | Connotation |
---|---|

1 | Factor i is equally important to factor j |

3 | Factor i is slightly more important than factor j |

5 | Factor i is clearly more important than factor j |

7 | Factor i is strongly more important than factor j |

9 | Factor i is extremely more important than factor j |

2,4,6,8 | Intermediate values |

Reciprocal | ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$: factor i compared with factor j, ${\mathrm{a}}_{\mathrm{j}\mathrm{i}}$: factor j compared with factor i, ${\mathrm{a}}_{\mathrm{j}\mathrm{i}}=1/{\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ |

A | ${\mathrm{B}}_{1}$ | ${\mathrm{B}}_{2}$ | … | ${\mathrm{B}}_{\mathrm{n}}$ |

${\mathrm{B}}_{1}$ | 1 | ${\mathrm{a}}_{12}$ | … | ${\mathrm{a}}_{1\mathrm{n}}$ |

${\mathrm{B}}_{2}$ | ${\mathrm{a}}_{21}$ | 1 | … | ${\mathrm{a}}_{2\mathrm{n}}$ |

… | … | … | … | … |

${\mathrm{B}}_{1\mathrm{n}}$ | ${\mathrm{a}}_{\mathrm{n}1}$ | ${\mathrm{a}}_{\mathrm{n}2}$ | … | 1 |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

Grade | 1 | 2 | … | K |
---|---|---|---|---|

$\mathrm{f}\left({\mathrm{u}}_{\mathrm{i}\mathrm{j}}\right)$ | $\left({\mathrm{f}}_{1},{\mathrm{f}}_{2}\right]$ | $\left({\mathrm{f}}_{2},{\mathrm{f}}_{3}\right]$ | … | $\left({\mathrm{f}}_{\mathrm{K}},{\mathrm{f}}_{\mathrm{K}+1}\right]$ |

Index | Bus 1 | Bus 2 | |
---|---|---|---|

Reliability (${\mathrm{u}}_{1}$) | Power to weight ratio (${\mathrm{u}}_{11}$) | 9.5 | 7 |

Driving mileage (${\mathrm{u}}_{12}$) | 225 | 170 | |

Total battery cycle times (${\mathrm{u}}_{13}$) | 2000 | 2000 | |

Battery capacity (${\mathrm{u}}_{14}$) | 324 | 324 | |

Battery attenuation amplitude (${\mathrm{u}}_{15}$) | 14.87 | 14.87 | |

Economic (${\mathrm{u}}_{2}$) | Vehicle purchase cost (${\mathrm{u}}_{21}$) | 110 | 110 |

Electricity consumption per 1000 seats·km (${\mathrm{u}}_{22}$) | 38 | 35 | |

Maintenance cost per 100 km (${\mathrm{u}}_{23}$) | 0 | 8 | |

Adaptability (${\mathrm{u}}_{3}$) | Temperature adaptability (${\mathrm{u}}_{31})$ | 0.09 | 0.13 |

Line adaptability (${\mathrm{u}}_{32}$) | 0.05 | 0.23 | |

Special weather adaptability (${\mathrm{u}}_{33}$) | 0.71 | 0.76 | |

Initial electric quantity adaptability (${\mathrm{u}}_{34}$) | 0.32 | 0.34 | |

Air conditioner adaptability (${\mathrm{u}}_{35})$ | 0.31 | 0.37 | |

Security (${\mathrm{u}}_{4}$) | Average temperature difference of brake (${\mathrm{u}}_{41})$ | 11 | 9 |

Vehicle failure rate (${\mathrm{u}}_{42})$ | 0 | 0.0035 | |

Vehicle fault severity (${\mathrm{u}}_{43})$ | 0 | 177 |

Index | Grade 1 | Grade 2 | Grade 3 | Grade 4 | ||
---|---|---|---|---|---|---|

Service (${\mathrm{u}}_{5}$) | Driving convenience (${\mathrm{u}}_{51})$ | Bus 1 | 7 | 8 | 0 | 0 |

Bus 2 | 4 | 9 | 2 | 0 | ||

Comfort (${\mathrm{u}}_{52}$) | Bus 1 | 5 | 9 | 1 | 0 | |

Bus 2 | 5 | 8 | 2 | 0 | ||

After-sale service (${\mathrm{u}}_{53})$ | Bus 1 | 0 | 7 | 7 | 1 | |

Bus 2 | 0 | 4 | 10 | 1 |

Indexes | Grade 1 | Grade 2 | Grade 3 | Grade 4 |
---|---|---|---|---|

${\mathrm{u}}_{11}$ | [12,∞) | [10,12) | [8,10) | [0,8) |

${\mathrm{u}}_{12}$ | [250,∞) | [200,250) | [150,200) | [0,150) |

${\mathrm{u}}_{13}$ | [2000,∞) | [1000,2000) | [500,1000) | [0,500) |

${\mathrm{u}}_{14}$ | [250,∞) | [150,250) | [100,150) | [0,100) |

${\mathrm{u}}_{15}$ | [0,0.1) | [0.1,0.15) | [0.15,0.2) | [0.2,1] |

${\mathrm{u}}_{21}$ | [0,60) | [60,80) | [80,120) | [120,∞) |

${\mathrm{u}}_{22}$ | [0,25) | [25,40) | [40,50) | [50,∞) |

${\mathrm{u}}_{23}$ | [0,10) | [10,20) | [20,30) | [30,∞) |

${\mathrm{u}}_{31}~{\mathrm{u}}_{35}$ | [0,0.1) | [0.1,0.3) | [0.3,0.6) | [0.6,∞) |

${\mathrm{u}}_{41}$ | [0,5) | [5,10) | [10,15) | [15,∞) |

${\mathrm{u}}_{42}$ | [0,0.002) | [0.002,0.005) | [0.005,0.008) | [0.008,∞) |

${\mathrm{u}}_{43}$ | [0,10) | [10,30) | [30,60) | [60,∞) |

${\mathrm{u}}_{51}$ | [16,20] | [11,15] | [6,10) | [1,5] |

${\mathrm{u}}_{52}$ | [13,15] | [9,12] | [5,8] | [0,4] |

${\mathrm{u}}_{53}$ | [16,20] | [11,15] | [6,10] | [1,5] |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; He, J.; Lu, W.; Yan, X.; Cheng, C.
Evaluation Method to Select Pure Electric Buses Based on Road Operation Tests. *World Electr. Veh. J.* **2020**, *11*, 4.
https://doi.org/10.3390/wevj11010004

**AMA Style**

Liu Y, He J, Lu W, Yan X, Cheng C.
Evaluation Method to Select Pure Electric Buses Based on Road Operation Tests. *World Electric Vehicle Journal*. 2020; 11(1):4.
https://doi.org/10.3390/wevj11010004

**Chicago/Turabian Style**

Liu, Yanzhong, Jie He, Wenhui Lu, Xintong Yan, and Cheng Cheng.
2020. "Evaluation Method to Select Pure Electric Buses Based on Road Operation Tests" *World Electric Vehicle Journal* 11, no. 1: 4.
https://doi.org/10.3390/wevj11010004