Proceedings of the

ITRN2011 31st August – 1st September, University College Cork

Hayes, De Oliveira, Vaughan, Egan: EV Range

RANGE ESTIMATION FOR THE NISSAN LEAF AND TESLA ROADSTER USING SIMPLIFIED POWER TRAIN MODELS

R. Pedro R. de Oliveira University College Cork Sean Vaughan University College Cork John G. Hayes Senior Lecturer

University College Cork Abstract In this paper, simplified EV power train models are used to estimate range for the Nissan Leaf and the Tesla Roadster. The models are compared with published manufacturer specifications for range under various route and driving conditions, and for various drive cycles. The models are validated against test results for the Nissan Leaf and Tesla Roadster vehicles, where the test route topography is modelled using Google Earth and a GPS-based smart-phone application. Excellent correlations are demonstrated between the experimental results and manufacturer data and the vehicle models. Impacts of battery degradation with time and vehicle HVAC loads are considered in the study.

I. INTRODUCTION

In recent years, there has been significant societal interest in the development, production

and sale of electric vehicles. Announcements occur regularly on proposed new product

introductions into the automotive marketplace. Electric vehicles can range from the hybrid-

electric vehicle (HEV) technologies currently on the market such as the Toyota Prius and

Honda Insight to the new production battery electric vehicles (BEV) such as the Nissan Leaf,

the Mitsubishi iMiEV and the Tesla Roadster, to the extended-range electric vehicle (EREV)

Chevy Volt [11]. Key factors in customer acceptance of the new technologies will be the cost

and range of the battery electric vehicles.

Significant information has been published on BEV performance by manufacturers, the

Environmental Protection Agency (EPA), and by the public on the internet. On-going vehicle

testing is providing additional information. The information provided often is not consistent

and some customization is required in order to predict vehicle range under the various

driving conditions. For example, driving range results are presented for the Nissan Leaf on

the company website and are presented in Table I [1]. The nominal range for the EPA LA4

drive cycle is quoted by Nissan and is given at 100 miles. The EPA sticker cites a range of

73 miles based on a standardized five-cycle test [3].

Given the inherent range limitations of BEVs and associated driver anxiety, it is necessary

to estimate vehicle range for varied sets of battery, road and driving conditions. The purpose

of this paper is to present the range estimations using the simplified power train models

developed in [13]. The models are compared to published range information and on-going

road tests.

Hayes, De Oliveira, Vaughan, Egan: EV Range 31st August – 1st September, University College Cork

Proceedings of the

ITRN2011

TABLE I

RANGE ESTIMATES FOR NISSAN LEAF [1]

Driving

condition

Average Speed Temperature Range

Climate

Control

mph km/h °F °C mi km

EPA LA4 20 31 68-86 20-30 100 160 Off

Ideal driving

conditions

38 61 68 20 138 221 Off

Highway, summer 55 88 95 35 70 112 AC

Stop-and-go, winter 15 24 14 -11 62 99 Heat

EPA five-cycle test Varying Varying 73 117 Varying

Vehicle auxiliary loads for heating, ventilation, and air conditioning (HVAC) can restrict

vehicle range significantly. Based on the stop-and-go winter conditions above in Table I, it is

estimated that the maximum heating load is approximately 6 kW for the Nissan Leaf.

Similarly, it appears that that the maximum AC load is 6 kW for the highway summer driving

condition. Thus, driving in extreme temperature conditions can result in significant range

reduction and significant HVAC is required for the passenger cabin and for the batteries.

LiIon batteries require significant thermal management in order to meet the automotive

lifetime specifications and various management approaches are implemented [5, 6].

In [13] an understanding of the vehicle power train and vehicle performance under various

conditions is used to develop a vehicle model. The vehicle range characteristics for various

drive conditions and topographies can then be easily derived. Given the significant

information available in the public domain for the Nissan Leaf and Tesla Roadster, these two

vehicles are initially investigated. Range estimations are available for the Roadster in [10],

while [9] refers to the use of a 4 kW heater for the Roadster.

The simplified electric vehicle models are briefly discussed in Section II. Section III

discusses the drive cycles and simulation results. Section IV presents Nissan Leaf test

results. The Tesla Roadster is discussed in Section V.

II. ELECTRIC VEHICLE MODELS

A significant body of literature and a wide variety of software tools are available for vehicle

modeling [7, 8]. For this study, the power train models are implemented using EXCEL and

are easily implemented using other mathematical software. See [13] for greater detail on the

power train models.

Proceedings of the

ITRN2011 31st August – 1st September, University College Cork

Hayes, De Oliveira, Vaughan, Egan: EV Range

DRIVE CYCLES AND SIMULATION OUTPUTS

There are many types of standardized drive cycles used around the world. The US EPA

uses a combined five-cycle test [3] based on dynamometer testing. There are four basic

cycles: FTP, HFET, US06 and SC03. The fuel economy is based on testing under various

temperature conditions. The FTP cycle is a longer variation of the LA4 drive cycle quoted by

Nissan in their literature. The FTP drive cycle is as shown in Fig. 1.

0

10

20

30

40

50

60

0 500 1000 1500 2000

Time (s)

Sp

eed

(m

ph

)

Speedmph

Fig. 1. EPA FTP drive cycle

The five-cycle tests are based on the internal combustion engine and many of the

variations on the testing do not appear directly applicable to EVs. The authors of this paper

are calculating the EPA range based on slight modifications of the procedures described in

Section III of [3]. The formulae from [3] are used to generate a range or fuel consumption

and are as outlined below. The formulae include an adjustment factor of 9.5 % to allow for

non-dynamometer effects. An additional assumption of an adjustment of 20 % for battery

degradation is also made by the authors. A feature of the Nissan Leaf is that the long-life

mode can be enabled in order to set the maximum state of charge at 80 % and so extend

battery life [12].

The model is used to generate the mileage available using the specified battery energy.

The energies required for traction and braking are easily calculated. Using regenerative

braking, a certain proportion of the braking energy is regenerated. As mentioned, the

calculation of the five-cycle fuel economy is dependent on various temperatures, starting,

soak, and running conditions. The authors in this study neglect the effects of starting and the

calculation of the rating is purely based on the running fuel economy. These assumptions

are reasonable for an EV.

The mileage and fuel economy ratings for the city, highway, and combined five-cycle tests

are simplified in this study from those presented in [3] and are as follows:

=0.905×1

City FERunning FC

(1)

where the factor 0.905 represents the adjustment factor due to real road conditions, FC is the fuel consumption in kWh/mile, and FE is the fuel economy in mile/kWh or range in miles for a given battery pack size. The city Running FC is given by

0.89 0.11 0.18=0.82× + +

1 1+0.133×1.083 -

Running FCFTP US06 FTP

SC03 FTP

(2)

where FTP, US06, HFET, and SC03 represent the fuel consumption in kWh/mile for the

related drive cycle.

Similarly, the Highway mileage range and fuel economy ratings are developed as follows:

=0.905×1

Highway FERunning FC

(3)

Hayes, De Oliveira, Vaughan, Egan: EV Range 31st August – 1st September, University College Cork

Proceedings of the

ITRN2011

The Highway Running FC is given by

0.79 0.21=1.007× +

1 1+0.133×0.377 -

Running FCUS06 HFET

SC03 FTP

(4)

The 5-cycle fuel economy and range is then simply the addition of the City and Highway

driving ranges.

=0.43 0.575 cycleFE City FE Highway FE (5)

The following table calculates the consumption and mileage based on regenerating 30 %

of the braking energy. The SC03 drive cycle is calculated using continuous full HVAC power.

TABLE II

CONSUMPTION AND RANGE FOR THE NISSAN LEAF

Cycle kWh/mile Range Range, 80%

LA4 0.24 101 81

FTP 0.24 100 80

HFET 0.22 110 88

US06 0.32 74 59

SC03 0.53 45 36

City 0.24 99 79

Highway 0.27 88 70

5-cycle 0.26 93 74

VUT 0.25 97

The results presented in Table II show an excellent correlation with the published data. For

30 % regeneration of braking energy, the model predicts a range of 101 miles correlating

well to the Nissan prediction of 100 miles. A range of 74 miles is the model prediction for the

EPA 5-cycle range. Allowing for a battery degradation to 80%, this correlates well to the EPA

sticker range of 73 miles. The SC03 test under full HVAC indicates that a range less than 40

miles is likely with a degraded or long-life-mode battery and full HVAC at extreme

temperatures.

Based on the model developed above, graphs of range versus speed are generated for

the Nissan Leaf as shown in Fig.2.

The curves show the ideal vehicle range for a fixed speed as the upper curve, the middle

curve assumes a significant HVAC load of 6 kW for the Leaf for extreme temperature

conditions. There is a significant reduction in vehicle range as has been suggested in the

Nissan Leaf literature. The lower curve reduces the extreme temperature range to 80 % to

allow for battery degradation with time or long-life mode. As can be seen, the HVAC can

have a very significant impact on the achievable range. Overall range will reduce with time

due to battery degradation.

The graph also shows the range for the LA4 and EPA drive cycles at their respective

average speeds. The LA4 range of about 100 miles for the Leaf can drop to about 44 miles

with full HVAC and close to 35 miles with battery degradation or long-life mode.

Proceedings of the

ITRN2011 31st August – 1st September, University College Cork

Hayes, De Oliveira, Vaughan, Egan: EV Range

0

50

100

150

200

0 10 20 30 40 50 60 70 80

Speed (mph)

Ra

ng

e (

mile

s)

Const Speed

Const Speed+HVAC

Const Speed+HVAC,80%

LA4

LA4+HVAC

LA4+HVAC,80%

EPA

VUT

Fig. 2. Nissan Leaf range

On-going tests with a Nissan Leaf have resulted in a range of 97 miles. This data point

correlates well with the nominal 100 mile range. This point is shown on the graph of Fig. 2

and Table II as VUT for vehicle under test.

III. EXPERIMENTAL DATA AND THE NISSAN LEAF

In this section, a model of the Nissan Leaf is created and compared with test results from

on-going road tests. The test route daily taken by the driver is approximately 60 km roundtrip

on roads with some steep slopes and a mix of urban and suburban driving. Google Maps

and Google Earth were found to be very useful tools in estimating the vehicle power

consumption. A GPS-based mobile app, View Ranger, is also used to track the location,

elevation, and speed. A plot of elevations is shown in Fig. 3.

Fig. 3. Google Earth elevations

The route drive cycle was generated, factoring in elevations, and the mild weather driving

was estimated to have a fuel consumption of 0.16 kWh/mile. This correlates well with the

0.155 kWh/mile recorded by the Nissan Leaf for a vehicle range of just less than 100 miles.

An independent measurement of the supplied grid energy resulted in an energy consumption

of 0.175 kWh(AC)/mile. Further testing is required to determine the effects of elevation and

HVAC on the fuel consumption.

IV. TESLA ROADSTER

Tesla Motor Company has published various data and information on the range of their

vehicles. The following fuel consumption and range curves are presented in [10]. A Tesla

model is generated to correlate to the above graphs and the parameters are input to the

drive cycles similar to the Nissan Leaf above. The predictions for fuel consumption and

range are shown in Table III. A higher regeneration level of 50 % is assumed for the Tesla

with 4 kW HVAC for the SC03 test. Plots of range versus speed are shown in Fig. 6. The

vehicle under test has similar range to the US06 drive cycle, as shown in the bottom row of

Table III.

Hayes, De Oliveira, Vaughan, Egan: EV Range 31st August – 1st September, University College Cork

Proceedings of the

ITRN2011

Wh/mile vs. Speed

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

mph

Wh

/mil

e

Fig. 4. Tesla Roadster fuel economy [10]

Range vs. Speed

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

mph

mil

es

Fig. 5. Tesla Roadster Range [10]

TABLE III

CONSUMPTION AND RANGE FOR THE TESLA ROADSTER

Cycle kWh/mile Range Range, 80%

LA4 0.22 242 194

FTP 0.22 243 194

HFET 0.22 245 196

US06 0.30 175 140

SC03 0.41 129 103

City 0.22 243 195

Highway 0.26 204 164

5-cycle 0.24 221 177

VUT 0.32 166

Proceedings of the

ITRN2011 31st August – 1st September, University College Cork

Hayes, De Oliveira, Vaughan, Egan: EV Range

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60 70 80

Speed (mph)

Ra

ng

e

Const Speed

Const Speed+HVAC

Const Speed+HVAC,80%

LA4

LA4+HVAC

LA4+HVAC,80%

EPA

Fig. 6. Tesla Roadster range

V. CONCLUSIONS

In this paper, simplified EV power train models are used to estimate range for the Nissan

Leaf and Tesla Roadster. The models are compared with published manufacturer

specifications for range under various route and driving conditions, and for various drive

cycles. The test route topography is modeled using Google Earth and a GPS-based mobile

app. Excellent correlations are demonstrated between the experimental results,

manufacturer data and the model predictions. Impacts of battery degradation with time and

vehicle HVAC loads are considered in the study.

ACKNOWLEDGMENT

The authors wish to thank Prof. Gerry Wrixon for the Nissan Leaf road testing, and Peter

Harte and Celine McInerney for the Tesla Roadster testing.

REFERENCES

[1] Nissan Motor Corporation website, www.nissanusa.com [2] Environmental Protection Agency website, www.epa.gov [3] US EPA, “Fuel Economy of Motor vehicle Revisions to Improve Calculation of Fuel

Economy Estimates,” December 2006. [4] http://www.fueleconomy.gov/feg/fe_test_schedules.shtml [5] C. Park, A.K. Jaura, “Dynamic Thermal Model of Li-Ion Battery for Predictive Behavior in

Hybrid and Fuel Cell Vehicles,” SAE 2003-01-2286. [6] C. Mi, L. Ben, D. Buck, N. Ota, “Advanced Electro-Thermal Modeling of Lithium-Ion

Battery System for Hybrid Electric Vehicle Applications,” IEEE VPPC 2007. [7] M. Ehsani, Y. Gao, A. Emadi, Modern Electric, Hybrid Electric and Fuel Cell Vehicles:

Fundamentals, Theory, and Design, 2nd

Edition, CRC Press, 2009. [8] AVL, www.avl.com [9] B. Randall, “Blowing hot and cold,” www.teslamotors.com/blog/blowing-hot-and-cold.

Dec. 2006. [10] J.B. Staubel, CTO, “Roadster efficiency and range,”

www.teslamotors.com/blog/roadster-efficiency-and-range, Dec. 2008. [11] E.D Tate, M.O. Harpster, P.J. Savagian, “The electrification of the automobile: from

conventional hybrid to plug-in hybrids, and extended-range electric vehicles,” SAE 2008-01-0458.

[12] 2011 Nissan Leaf Owner’s Manual [13] J.G. Hayes, R.P.R. de Oliveira, S. Vaughan, M.G. Egan, “Simplified Electric Vehicle

Power Train Models and Range Estimation,” IEEE Vehicular Power and Propulsion Conference, Chicago, September, 2011.