# Effect of Ambient Temperature on Electric Vehicles’ Energy Consumption and Range: Model Definition and Sensitivity Analysis Based on Nissan Leaf Data

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## Abstract

**:**

## 1. Introduction

_{2}emissions [1]. Because of the related environmental concerns, in recent years, innovative technologies have been progressively gaining a share in the automotive industry, aiming at both improving the power train conversion efficiency and reducing the dependence on fossil fuels. Solutions are mainly based on the adoption of new vehicle concepts that make use of green energy carriers such as electricity or hydrogen, as in electric or hybrid vehicles [2,3,4].

## 2. Model Description

^{®}, following the approach first proposed by Larminie and Dicks [36] and subsequently adopted and further improved by other researchers [19,37,38,39,40]. The proposed model is based on a critical analysis of the main assumptions made in existing models of the different components, aiming at identifying the best compromise between accuracy and the possibility to build up a straightforward and effective tool for the simulation of commercial electric vehicles, whose construction and operating data are often difficult to obtain from car manufactures. To this end, the analysis is particularly focused on the Nissan Leaf, and Table 1 shows the main assumptions adopted in the most relevant up-to-date published Nissan Leaf models. Last column of the table reports the assumptions used in the present study.

_{I}, which represents a fictitious mass taking into account the inertia of rotating components, can be expressed as follows:

_{Wheels}can be either positive or negative. In the first case, the battery pack provides energy to the motor. In the second case, representative of the regenerative braking mode, the energy flows from the wheels to the generator to charge the battery, as shown in Figure 1. Thus, P

_{Motor,out}is expressed by the following:

_{tr}is the transmission efficiency and η

_{rb}is the regenerative braking efficiency, which identifies the percentage of the total braking power that can actually be recovered, as per the following equation:

_{rb}have been proposed, as already reported in Table 1. In the work of [38], all the available regenerative energy is assumed to be returned to the battery as long as the regenerative power is lower than or equal to 20 kW; Genikomsakis and Mitrentsis [37] express η

_{rb}as a function of the vehicle speed and consider the recoverable power subject to the braking torque limitation of the electric motor/generator. Maia et al. [40] introduce a braking torque reduction factor, a function of some collection of variables that represent the instantaneous driving parameters (acceleration, jerk, road inclination). In the present analysis, the approach proposed by the authors of [1] was applied, where the regenerative braking efficiency η

_{rb}is assumed to be a function of acceleration (always negative when braking). The following exponential relationship, calibrated on empirical data on regenerative braking energy efficiency for a Chevy Volt vehicle, has thus been used:

_{Motor,in}(Figure 1) is computed on the basis of the efficiency of motor/generator η

_{m}:

_{m}is a general function of both instantaneous speed and torque of motor/generator, in the present study, the more general approach, proposed by the authors of [37], has been employed, in which the motor/generator efficiency is a piecewise function of the load. The efficiency is finally corrected with a size coefficient that, in the case of the Nissan Leaf motor with a rated power of 80 kW, is 0.988. The resulting efficiency values employed in this study are reported in Table 2.

_{Bat}takes into account also the power consumed by the accessories as per the following equation:

_{Acc}is assumed to be a linear decreasing function of the ambient temperature, ranging from a maximum value of 6000 W at T

_{amb}= −15 °C to a minimum value of 200 W at T

_{amb}= 20 °C, when the HVAC system is turned off.

_{Bat}, the input or output current flows, occurring during battery charging (regenerative braking) and discharging (motoring), can be evaluated by solving the battery equivalent circuit according to the following Equation (8) [36,40]:

_{int}and E are the internal resistance and the open circuit potential, respectively. According to the authors of [40], E can be expressed as a function of the SOC as per Equation (9), while the values of R

_{int}in charging and discharging can be defined as a piecewise function of SOC, as reported in Table 3.

_{p}is given by the following:

_{p}= 71.1 Ah.

_{i}, the charge removed during discharging or added during charging is computed as follows:

_{n}, after n time steps, can be obtained as follows:

## 3. Model Validation

_{max}= 91 km/h, v

_{av}= 32 km/h) and Simplified FUDS (SFUDS) (v

_{max}= 87 km/h, v

_{av}= 31 km/h). FUDS, developed into the Federal Urban Driving Schedule, is one of the most well-known standard driving cycles, based on real urban traffic flows in Los Angeles. SFUDS is a simplified version of this cycle, commonly employed for the analysis of electric vehicles performance [36,43]. Compared with FUDS, it is characterized by a similar average speed, the same proportion of stationary time, and the same maximum acceleration and braking, thus providing generally very similar results when used for simulating vehicle range. The analysis was also extended to two additional driving cycles, namely the New European Driving Cycle (NEDC) (v

_{max}= 120 km/h, v

_{av}= 32 km/h) and FIGE cycle, named after the German FIGE Institute, (v

_{max}= 91 km/h, v

_{av}= 59 km/h), which differ from the urban nature of the reference experimental data. In fact, NEDC consists of four repeated ECE-15 urban driving cycles and one extra-urban driving cycle, while different driving conditions are represented by FIGE, which includes urban, rural, and motorway driving. All the considered driving cycles are reported in Figure 2. Simulations are carried out considering an external ambient temperature ranging from −15 to +20 °C. Accessories consumption varies linearly from 6000 W at −15 °C with heating at full power to 200 W at 20 °C when the heating is switched off. Simulations start with battery fully charged and end at SOC = 0.1.

## 4. Sensitivity Analysis

_{rb}(Equation (4)).

- (a)
- η
_{rb}= 0: no braking power recovered, that is, the entire braking power is wasted by mechanical brakes. - (b)
- η
_{rb}= 1: the whole braking power available at the wheels is converted into electricity according to the generator operating efficiency. - (c)
- ${\eta}_{rb}={\left[{e}^{\left(\frac{0.0411}{\left|a\left(t\right)\right|}\right)}\right]}^{-1}$ according to the authors of [1]; this case has been also assumed as the reference case in the present model.
- (d)
- η
_{rb}as a function of the vehicle speed according to the model proposed in the work of [37] and given by the following:$$\{\begin{array}{c}{\eta}_{rb}=0\mathrm{if}v5\frac{km}{h}\\ {\eta}_{rb}=0.0834v-0.417\mathrm{if}5v17\frac{km}{h}\\ {\eta}_{rb}=1\mathrm{if}v17\frac{km}{h}\end{array}$$In addition, the maximum recoverable braking power is subject to the driving/braking torque limitation of the electric motor/generator. - (e)
- Maximum regenerative power limited to 20 kW according to the authors of [38], that is, all the available regenerative power P
_{Wheels}is fed into the electric generator as long as its value does not exceed 20 kW.

_{rb}= 1). On the contrary, neglecting the contribution of the regenerative braking energy, as in case (a) (η

_{rb}= 0), results in a significant reduction of the driving range. For instance, at an ambient temperature of 20 °C, the range reduces with respect to the reference case from 160 km to 120 km (−25%) in the case of SFUDS, from 158 km to 115 km (−27%) in the case of FUDS, from 154 km to 124 km (−20%) in the case of NEDC, and from 172 km to 160 km (−6%) in the case of FIGE.

_{rb}= 0, while they reach asymptotically case (b) of η

_{rb}= 1 as the value of the limiting regenerative power increases. The black dashed line represents the hypothesis assumed in the work of [38] of a maximum regenerative power of 20 kW. It can be observed that with FIGE and SFUDS driving cycles, the ranges obtained with case (e) are very close to case (b) η

_{rb}= 1, while the highest difference (about 5 km) is observed only with NEDC.

## 5. Conclusions

_{max}= 91 km/h, v

_{av}= 32 km/h) and SFUDS (v

_{max}= 87 km/h, v

_{av}= 31 km/h) driving cycles, showing a good agreement with the experimental data, with these cycles’ features similar to those of the reference routes, particularly in terms of average and maximum speeds. The analysis was further extended to FIGE and NEDC cycles, thus also considering extra urban, rural, and motorway driving profiles.

_{rb}, has been assessed. In particular, the results available in literature are found to be very close to the assumption of η

_{rb}= 1.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Notations | |

A | Frontal area, m^{2} |

a | Acceleration, m/s^{2} |

BEV | Battery electric vehicle |

C | Battery capacity, Ah |

C_{d} | Drag coefficient |

C_{p} | Peukert capacity, Ah |

$\mathsf{\Delta}CR$ | Removed/added charge, Ah |

E | Open circuit voltage, V |

FIGE | FIGE (Forschungsinstitut Geräusche und Erschütterungen) Institute, Aachen, Germany |

FUDS | Federal Urban Driving Schedule |

G | Gear ratio |

g | Gravity acceleration, m/s^{2} |

HVAC | Heating, ventilation, and air-conditioning |

I | Current, A |

k | Peukert constant |

m_{c} | Vehicle mass with battery pack (curb weight), kg |

m_{I} | Vehicle equivalent mass increase due to the angular moments of the rotating components |

m_{v} | Total vehicle mass including occupants (gross weight), kg |

NEDC | New Eu |

P | Power, W |

R_{int} | Battery internal resistance, Ω |

SFUDS | Simplified Federal Urban Driving Schedule |

SOC | State of charge |

t | Time, t |

v | Velocity, m/s |

Subscripts | |

Acc | Accessories |

Bat | Battery |

av | Average |

max | Maximum |

i | i-th time step |

Greek symbols | |

α | Slope angle of the road |

ρ | Air density, kg/m^{3} |

η_{m} | Electric motor/generator efficiency |

η_{rb} | Regenerative braking efficiency |

η_{tr} | Transmission and gear efficiency |

µ_{rr} | Rolling resistance coefficient |

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**Figure 4.**Driven range as a function of the Peukert constant k in the case of ambient temperature of 20 °C.

**Figure 5.**Driven range as function of the Peukert constant k in the case of ambient temperature of 0 °C.

**Figure 6.**Driven range as function of the Peukert constant k in the case of ambient temperature of −15 °C.

**Figure 7.**Impact of different regenerative braking assumptions on range in the case of SFUDS driving cycle.

**Figure 8.**Impact of different regenerative braking assumptions on range in the case of FUDS driving cycle.

**Figure 9.**Impact of different regenerative braking assumptions on range in the case of NEDC driving cycle.

**Figure 10.**Impact of different regenerative braking assumptions on range in the case of FIGE driving cycle.

**Figure 11.**Driving range as a function of the limit on the maximum power for regenerative braking at 20 °C.

**Table 1.**Summary of the main assumptions adopted in various Nissan Leaf published models. SOC—state of charge.

Reference | [37] | [38] | [39] | [40] | [1] | [19] | Assumed Here |
---|---|---|---|---|---|---|---|

Nominal battery energy | 24 kWh | 24 kWh | 24 kWh | Capacity of 65 Ah times open circuit voltage as by Equation (9) with SOC at nominal conditions | - | 24 kWh | Capacity of 65 Ah times open circuit voltage as by Equation (9) with SOC at nominal conditions [40] |

Battery efficiency | 95% | Based on charge efficiency of 85% and R_{int} = 0.11 Ω | Based on round trip efficiency of 85% and R_{int} = 0.1 Ω | Based on round trip efficiency of 97% and R_{int} = as by Table 3 | 90% | - | Based on internal resistance as by Table 3 [40] and Peukert battery model with k = 1.03 [41] |

Rolling coefficient | 0.008 | Vehicle load forces expressed as function of vehicle speed | 0.008 | 0.007 | 1.75 × 10^{−3} (0.0328v + 4.575) | 0.012 | 1.75 × 10^{−3} (0.0328v + 4.575) [1] |

Drag coefficient | 0.29 | 0.28/0.29 | 0.28 | 0.28 | 0.29 | 0.28 | |

Frontal area, m^{2} | 2.19 | 2.19 | 2.29 | 2.3316 | 2.27 | 2.3 | |

Air density, kg/m^{3} | 1.25 | - | 1.25 | 1.2256 | 1.2 | Function of temperature | |

Transmission efficiency | 0.97 | 0.97 | 0.97 | 0.83 | 0.92 | Included in overall power train efficiency of 80% | 0.97 |

Gear ratio, G | 8.2 | 7.9377 | 7.94/8.19 | 7.937 | - | - | 7.94 |

Tire radius, m | 0.316 | 0.315 | 0.316 | 0.309 | - | 0.31 | |

Maximum motor power, kW | 80 | 80 | 80 | 80 | - | - | 80 |

Motor /generator efficiency | Function of load | Based on a per-phase equivalent circuit electric model | 89%–96% (Motor + controller efficiency) | Varying between 85% and 95% as function motor torque and speed | 91% | Included in overall power train efficiency of 80% | Function of load, according to authors of [37] |

Power consumption of accessories (cabin air conditioning excluded), W | 300 | 180 | 200 | 269 | 700 | 400 | 200 |

Vehicle mass (curb weight), kg | - | 1521 | 1498/1691 | 1521 | 1521 | 1521 | 1521 |

Vehicle mass including occupants (gross weight), kg | 1663 | 1701 | - | 1761 | 1595/1640 | 1601 /1731 | 1600 |

Fictitious vehicle mass increase due to the inertia of rotating components, kg | 0.05∙m_{c} | - | - | ${m}_{c}\left(0.04+0.0025{G}^{2}\right)$ | - | 0.03∙m_{c} | ${m}_{c}\left(0.04+0.0025{G}^{2}\right)$ [40] |

Regenerative braking model | Speed-dependent regeneration efficiency; limit on maximum generator torque | Limited to maximum braking power of 20 kW | 100% regenerative braking at all vehicle speeds | Regenerative coefficient based on a fuzzy logic model | ${\eta}_{rb}={\left[{e}^{\left(\frac{0.0411}{\left|a\left(t\right)\right|}\right)}\right]}^{-1}$ | Not considered | ${\eta}_{rb}={\left[{e}^{\left(\frac{0.0411}{\left|a\left(t\right)\right|}\right)}\right]}^{-1}$ [1] |

**Table 2.**Motor/generator efficiency [37].

Part Load Fraction | η_{m}, % | |
---|---|---|

Motor | Generator | |

0.01 | 58.72 | 56.62 |

0.02 | 72.24 | 70.63 |

0.05 | 83.89 | 83.02 |

0.1 | 88.67 | 88.20 |

0.2 | 91.28 | 91.04 |

0.3 | 92.12 | 91.98 |

0.4 | 92.71 | 92.56 |

0.5 | 93.31 | 93.14 |

0.6 | 93.91 | 93.71 |

0.7 | 94.51 | 94.29 |

0.8 | 94.43 | 94.74 |

0.9 | 93.67 | 94.07 |

1 | 92.91 | 93.41 |

SOC | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
---|---|---|---|---|---|---|---|---|---|---|

R_{int}—charging, Ω | 0.0830 | 0.0830 | 0.0892 | 0.0997 | 0.1051 | 0.0894 | 0.0919 | 0.1135 | 0.1026 | 0.0997 |

R_{int}—discharging, Ω | 0.0620 | 0.0620 | 0.0587 | 0.0691 | 0.0593 | 0.0928 | 0.0906 | 0.0664 | 0.0892 | 0.0250 |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Iora, P.; Tribioli, L.
Effect of Ambient Temperature on Electric Vehicles’ Energy Consumption and Range: Model Definition and Sensitivity Analysis Based on Nissan Leaf Data. *World Electr. Veh. J.* **2019**, *10*, 2.
https://doi.org/10.3390/wevj10010002

**AMA Style**

Iora P, Tribioli L.
Effect of Ambient Temperature on Electric Vehicles’ Energy Consumption and Range: Model Definition and Sensitivity Analysis Based on Nissan Leaf Data. *World Electric Vehicle Journal*. 2019; 10(1):2.
https://doi.org/10.3390/wevj10010002

**Chicago/Turabian Style**

Iora, Paolo, and Laura Tribioli.
2019. "Effect of Ambient Temperature on Electric Vehicles’ Energy Consumption and Range: Model Definition and Sensitivity Analysis Based on Nissan Leaf Data" *World Electric Vehicle Journal* 10, no. 1: 2.
https://doi.org/10.3390/wevj10010002