# Effect of Low Temperature on Electric Vehicle Range

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions globally [2] (pp. 142–146), the automotive industry is set to play an important role in mastering this global task. In recent decades, emission standards for passenger cars have been introduced in the largest automotive sales markets, with the aim of reducing the carbon footprint of road transportation [3]. The rising number of electric vehicles (EVs) available on the market in recent years [4] is evidence that manufacturers are choosing to electrify their fleets in order to comply with new legal requirements. However, despite the increase in the supply of EVs, vehicle registration statistics show that electric vehicles have yet to be fully accepted by the customer [4]. In the particular case of battery electric vehicles (BEVs), the limited driving range per charge, coupled with the associated range anxiety, is one of the biggest barriers for customers today against adopting EVs [5,6,7,8,9].

## 2. Article Contributions and Layout

**Study of a modern first-generation and a state-of-the-art BEV model.**

**Evaluation of the impact of heating on a BEVs range.**

**Assessment of the impact of recuperation limitation on a BEVs range.**

**Deduction of requirements for an electrothermal recuperation (ETR) system.**

## 3. Database

#### 3.1. BMW i3—Designed Route Data

#### 3.2. Tesla Model 3—Designed Route Data

## 4. Method of Analysis

#### 4.1. Heating Analysis—Heating Energy Share

_{Bat}.

_{Dis}in Equation (1). The heating energy share was defined like this because it allows us to separate the impact of heating from the impact of (limited) recuperation on the vehicles’ energy consumption and thus its range. Since the computed share reflects the relation between a trip’s actual energy demand and the energy portion required for heating throughout the trip, it translates directly to an equally high reduction in the vehicle’s range due to heating for the trip.

#### 4.2. Recuperation Analysis—Determination of Regenerative Braking Power Limitations

#### 4.3. Recuperation Analysis—Regnerative Braking Energy Share

_{Bat}.

_{Chr}is the battery charge current. Since the computed energy share RS represents the regenerated energy in relation to the actual energy demand of the traction system for a trip, RS translates to an equally high range increase through recuperation for the respective trip compared to the same trip without using regenerative braking at all. Consequently, when losing the capability to recuperate due to low temperatures, the gained range increase through recuperation gets lost, which would result in a range reduction of RS for the respective trip. However, since heating is not considered in RS, the determined range reductions are theoretical.

#### 4.4. Recuperation Analysis—Regenerative Braking Perfromance Analysis

#### 4.4.1. Data Preprocessing

#### 4.4.2. Drivetrain Moment of Inertia

_{Comp}. A mean material density was derived for the rotor and tires, which are multi-material components, based on the components’ outer dimensions and target weights. With the densities assigned to the component models, the CAD program returned the single components‘ moments of inertia around their rotational axis I

_{Comp}:

_{DT}was then calculated using:

_{Rot}, first spur gear I

_{G}

_{1}, second and third spur gear I

_{G}

_{2}.

_{3}, fourth spur gear I

_{G}

_{4}, left driveshaft I

_{DS}.

_{L}, right driveshaft I

_{DS}.

_{R}, rear axle brake disc I

_{BD}.

_{RA}, front axle brake disc I

_{BD}.

_{FA}, rim I

_{Rim}, and tire I

_{Tire}. The gear ratios of the first and second gearbox stages are indicated by i

_{1}and i

_{2}. The moments of inertia of the gears and rotor include the inertia of the shafts on which they are mounted. The result of the drivetrain inertia calculation is 10.42 kg∙m

^{2}for the reverse-engineered CAD model.

#### 4.4.3. Regenerative Braking Potential

_{x}.

_{veh}, the altitude signal h, and vehicle characteristics such as the drag coefficient c

_{d}.

_{veh}. The driving resistance represents the force responsible for the vehicle’s change in velocity throughout a trip. Since steep slopes are not present on the roads driven on by the vehicles in the datasets, a positive total driving resistance means the vehicle must supply power for propulsion, whereas a negative driving resistance means the vehicle has to supply braking power to explain the observed change in velocity. This characteristic of the total driving resistance is used to identify phases within a trip where braking power is required. The required braking power could potentially be provided by the electric machines of the vehicle to regenerate energy. Therefore, the computed negative driving resistance is referred to as regenerative braking potential.

_{DR}(Equation (5)) is smaller than zero and when the traction system current I

_{TS}(Equation (11)) is smaller than or equal to zero.

_{Acc}is the acceleration power (Equation (6)), P

_{Aer}is the aerodynamic drag power (Equation (7)), P

_{Rol}is the rolling resistance power (Equation (8)), and P

_{Slo}is the slope resistance power (Equation (9)).

_{veh}is the vehicle mass, I

_{DT}is the moment of inertia of the rotating drivetrain parts, r

_{dyn}is the dynamic tire radius, a

_{x}.

_{veh}is the vehicle’s longitudinal acceleration, and v

_{x.veh}is the vehicle’s longitudinal velocity.

_{Air}is the density of air, c

_{d}.

_{veh}is the vehicle’s drag coefficient, and A

_{veh}is the vehicle’s cross-sectional front area.

_{Rol}is the rolling resistance coefficient, Δs is the distance covered within a time step by the vehicle, and Δh is the change in altitude of the vehicle within a time step.

_{RBP}is determined according to Equation (10) and the regenerative braking energy potential E

_{RBP}is defined according to Equation (12)

#### 4.4.4. Trip Parameters

_{Ref}and the regenerative braking energy share of any trip on an identical route with the same vehicle RS

_{x}. Even though the MRR represents the difference between energy portions, the analysis setup allows for the translation of this difference to an equally high range reduction. The reason for this assumption is that RS is a value that is normalized by the respective trips’ actual energy demands and both considered RS values relate additionally to the identical route with the same length and driven by the same driver. However, it needs to be mentioned that the trip characteristics (velocity and acceleration) on the respective route can still vary due to traffic differences and variations in powertrain efficiency. Therefore, the absolute energy demand of the traction system that serves as a reference value for RS might not be identical for two trips on the same route driven by the same driver, which results in some uncertainty regarding the accuracy of the MRR. Still, due to the analysis setup, the MRR gives a good indication of practical range reductions due to limited recuperation on a specific route.

## 5. Results and Discussion

#### 5.1. Heating—Energy Demands and Range Implications

#### 5.2. Regenerative Braking—Limitation and Range Implications

_{RBP}and the unused regenerative braking energy potential E

_{RBP}(Section 4.4.3). To emphasize the difference of the regenerative braking limitation on the presented trips, an exemplary section in Figure 8a,b and Figure 10a–c is enlarged.

#### 5.3. Requirements for Direct Use of Regenerative Braking Power

_{Bat}≤ 0 °C), recuperation currents only occur between 1 s and 3 s and between 5 s and 10 s in the BMW i3. This is primarily due to the small database in this range. In contrast, the Tesla dataset shows recuperations below 0 °C for every time range up to 20 s. However, beyond this, no effect of temperature on the duration of recuperation phases can be detected. Only rarely is a recuperation phase longer than 20 s, while 95% of the phases are shorter.

- Response times in the lower millisecond range: The system should have a fast response and a short ramp-up time to capture short recuperation phases below 1 s.
- Power transformation of up to 20 kW: The system should be able to transform up to 20 kW of electric power into heating power.

## 6. Conclusions and Outlook

- Heating energy demands can cut a BEV’s range by almost one third.
- While the ambient temperature has a significant impact on the heating energy demands, other factors such as weather conditions are likely to impact the heating energy demands as well.
- A BEV’s maximum regenerative braking power capability depends on the battery temperature.
- Regenerative braking power limitations apply to the battery temperature range below 10 °C and the limitations increase with lower battery temperatures.
- At a battery temperature of −4 °C, regenerative braking is disabled entirely (Tesla Model 3).
- Theoretically, a BEV’s range could be cut by up to 42.2% if regenerative braking would be disabled for a whole trip (battery temperature stays below −4 °C throughout the trip).
- Practically, based on the available data, range reductions due to limited recuperation of up to 21.7% were identified.
- In total, range reductions of approximately. 50% are possible at low temperatures due to the combination of both heating energy demands and limited recuperation.
- Technical requirements for an ETR-system to reduce the identified range losses were found to be a fast response time in the lower millisecond range and a power capability of 20 kW.
- Restrictions regarding the achievable range regain with such a system still apply due to the limited energy storage capability of the heating circuit and the inability of the heater to utilize peak recuperation potential powers.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Component | Part (Figure 3) | Property in Unit | Value | Property of |
---|---|---|---|---|

Electric machine rotor | 1 | Lamination outer diameter in mm | 149 | Tesla Model 3 |

Lamination inner diameter in mm | 70 | Tesla Model 3 | ||

Lamination stack length in mm | 134 | Tesla Model 3 | ||

Weight in kg ^{1} | 17.0 | Tesla Model 3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0661 | Tesla Model 3 | ||

Spur gear 1 ^{2} | 2 | Diameter in mm | 50 | BMW i3 |

Width in mm | 40 | BMW i3 | ||

Number of teeth | 24 | BMW i3 | ||

Weight in kg | 1.0 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0002 | BMW i3 | ||

Spur gear 2 and 3 ^{2} | 3 | Diameter in mm | 167|75 | BMW i3 |

Width in mm | 40 | BMW i3 | ||

Number of teeth | 80|31 | BMW i3 | ||

Weight in kg | 4.6 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0110 | BMW i3 | ||

Spur gear 4 including differential ^{2} | 4 | Diameter in mm | 218 | BMW i3 |

Width in mm | 40 | BMW i3 | ||

Number of teeth | 90 | BMW i3 | ||

Weight in kg | 6.5 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0410 | BMW i3 | ||

Drive shafts (left|right) ^{3} | 5|6 | Diameter in mm | 30 | BMW i3 |

Length in mm | 583.5|768.5 | BMW i3 | ||

Weight in kg | 5.1|6 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0010|0.0020 | BMW i3 | ||

Brake disc front axle | 7 | Diameter in mm | 280 | BMW i3 |

Thickness in mm | 20 | BMW i3 | ||

Weight in kg | 5.2 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0600 | BMW i3 | ||

Brake disc rear axle | 8 | Diameter in mm | 280 | BMW i3 |

Thickness in mm | 8.2 | BMW i3 | ||

Weight in kg | 4.1 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.0490 | BMW i3 | ||

Rim | 9 | Dimension | 5J × 19 ET | BMW i3 |

Weight in kg | 11.0 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.3290 | BMW i3 | ||

Tire | 10 | Dimension | 175/60 R19 | BMW i3 |

Weight in kg | 6.0 | BMW i3 | ||

Predicted moment of inertia in kg·m^{2} | 0.6340 | BMW i3 |

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**Figure 2.**(

**a**–

**c**) Gaussian smoothing (b = 16) of the measured signals for Rural Trip 04 as an example (Tesla Model 3).

**Figure 3.**Drivetrain CAD model. Numbers refer to Table A1.

**Figure 6.**Recuperated energy in relation to the traction system energy demand—Tesla Model 3 and BMW i3.

**Figure 7.**Velocity profile (

**a**), battery temperature profile (

**b**), and battery SOC profile (

**c**) of the BMW i3 FTM Trips 07 and 06.

**Figure 9.**Velocity profile (

**a**), battery temperature profile (

**b**), and battery SOC profile (

**c**) of the Tesla Model 3 on Rural Trips R01, R02, and R05.

**Figure 10.**Tesla Model 3 regenerative braking performance on Rural Trips R01 (

**a**), R02 (

**b**), and R05 (

**c**).

Property | BMW i3 | Tesla Model 3 |
---|---|---|

Vehicle mass in kg | 1195 | 1750 |

Drag coefficient | 0.29 | 0.23 |

Rolling resistance coefficient | 0.008 | 0.011 |

Cross sectional front area in m^{2} | 2.38 | 2.37 |

Max. power in kW | 125 | 239 |

Drive topology | Rear Axle— Single Motor | Rear Axle— Single Motor |

Machine type | PMSM | PMSM |

Gearbox type | Two-Stage Spur | Two-Stage Spur |

Total gear ratio | 9.7 | 9.0 |

Tire size | 175/60 R19 | 235/45 R18 |

Dynamic tire radius in m | 0.336 ^{1} | 0.325 ^{1} |

Powertrain moment of inertia in kg·m^{2} | 10.42 ^{2} | 10.42 ^{2} |

Battery size (gross/net) in kWh | 22/18.8 | 55/50 |

Cell chemistry | NMC | LFP |

Heater | Layer | PTC |

^{1}Computed with flat4 Dynamic Tire Radius Calculator [42];

^{2}For determination and assumptions, see Section 4.3.

Signal | Symbol | BMW i3 | Tesla Model 3 |
---|---|---|---|

Time in s | t | X | X |

Longitudinal vehicle speed in m/s | v_{x}._{veh} | X | X |

Elevation in m | h | X | X |

Battery current in A | I_{Bat} | X | X |

Battery voltage in V | U_{Bat} | X | X |

Battery temperature in °C | T_{Bat} | X | X |

Battery SOC in % | SoC | X | X |

DCDC current in A | I_{DCDC} | X | |

DCDC voltage in V | U_{DCDC} | X | |

Heater current in A | I_{Heat} | X | X |

Heater voltage in U | U_{Heat} | X | X |

Ambient temperature in °C | T_{Amb} | X | X |

Cabin temperature in °C | T_{Cab} | X | X |

Property | BMW i3 | Tesla Model 3 |
---|---|---|

Number of trips | 68 | 44 |

Distance in km | 1340.8 | 637.8 |

Ambient temperature range in °C | −3.5|33.5 | −6.0|24.0 |

Battery temperature range in °C | −1.5|32.0 | −4.5|26.0 |

SOC range in % | 15.4|88.5 | 15.5|99.5 |

Property | FTM Route |
---|---|

Route * | |

Distance in km | 19.2 |

Duration in min | 26.3 |

Average velocity in km/h | 43.8 |

Number of trips | 9 |

Battery temp. range in °C | 1|15 |

SOC range in % | 20.0|86.1 |

Property | City | Rural | Highway |
---|---|---|---|

Route * | |||

Distance in km | 8.1 | 20.1 | 35.2 |

Number of trips | 3 | 5 | 5 |

Average duration in min | 22 | 24 | 25 |

Average velocity in km/h | 22.3 | 51.4 | 83.7 |

Battery temp. range in °C | −6.0|5.0 | −2.5|24.0 | −9.5|25.0 |

SOC range in % | 34.0|99.5 | 27.8|99.2 | 7.7|99.1 |

Parameter | BMW i3 | Tesla Model 3 | ||||
---|---|---|---|---|---|---|

Trip Name | FTM07 | FTM06 | FTM01 | R01 | R02 | R05 |

Ambient temperature in °C | 1 | 3.5 | 8.5 | −1.5 | 2 | 23.5 |

Weather conditions | sunny | few clouds | cloudy | sunny | light snowfall | cloudy |

Total energy consumption in kWh | 4.52 | 4.30 | 4.23 | 4.27 | 4.43 | 3.41 |

Heating energy in kWh | 0.88 | 0.55 | 0.58 | 0.60 | 1.05 | 0.09 |

HS—Heating share in % | 19.45 | 12.79 | 13.71 | 14.05 | 23.70 | 2.64 |

Trip Parameter | FTM Trip 07 | FTM Trip 06 |
---|---|---|

Consumed energy—traction system in kWh | 3.64 | 3.75 |

Regenerated energy—actual in kWh | 0.58 | 0.91 |

Regenerated energy—potential in kWh | 1.13 | 1.35 |

RS—Regenerative braking share in % | 15.93 | 24.26 |

RP—Regenerative braking performance in % | 51.33 | 67.40 |

PRS—Potential regenerative braking share in % | 31.04 | 36.00 |

MRR—Measured range reduction in % | 8.33 | Reference |

URP—Unused range potential in % | 15.11 | 11.74 |

Trip Parameter | Rural Trip 01 | Rural Trip 02 | Rural Trip 05 |
---|---|---|---|

Consumed energy—traction system in kWh | 3.51 | 3.21 | 3.18 |

Regenerated energy—actual in kWh | 0.23 | 0.55 | 0.90 |

Regenerated energy—potential in kWh | 1.02 | 1.25 | 1.01 |

RS—Regenerative braking share in % | 6.60 | 17.13 | 28.30 |

RP—Regenerative braking performance in % | 22.55 | 44.00 | 89.11 |

PRS—Potential regenerative braking share in % | 29.06 | 38.94 | 31.76 |

MRR—Measured range reduction in % | 21.70 | 11.17 | Reference |

URP—Unused range potential in % | 22.46 | 21.81 | 3.46 |

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## Share and Cite

**MDPI and ACS Style**

Steinstraeter, M.; Heinrich, T.; Lienkamp, M.
Effect of Low Temperature on Electric Vehicle Range. *World Electr. Veh. J.* **2021**, *12*, 115.
https://doi.org/10.3390/wevj12030115

**AMA Style**

Steinstraeter M, Heinrich T, Lienkamp M.
Effect of Low Temperature on Electric Vehicle Range. *World Electric Vehicle Journal*. 2021; 12(3):115.
https://doi.org/10.3390/wevj12030115

**Chicago/Turabian Style**

Steinstraeter, Matthias, Tobias Heinrich, and Markus Lienkamp.
2021. "Effect of Low Temperature on Electric Vehicle Range" *World Electric Vehicle Journal* 12, no. 3: 115.
https://doi.org/10.3390/wevj12030115