Maximizing Net Present Value of a Series PHEV by Optimizing

Battery Size and Control

R.Vijayagopal, A.Rousseau, J.Kwon

Argonne National Laboratory&

P.Maloney

MathWorks

SAE 2010-01-2310

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Overview Problem statement

NPV, Optimum battery size

Vehicle specifications & usage assumptions Real world drive cycles Battery assumptions Financial assumptions

Modeling and Simulation Autonomie capabilities

Optimization Approach & Process

Results

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Option 1: Invest $ in PHEV battery, save gasoline

Option 2: Get 7% interest on $, but pay for gasoline

Compared to a 30mpg conventional vehicleHigher initial investment (cost of battery)Lesser gasoline expenses in future

Is the NPV of the savings higher than the additional investment ?

Net Present Value of a PHEV

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70007000

7000 7000 7000

80008000

8000

8000 8000

1000

0

10000

10000 10000

1100

0

11000

11000

12000

12000

Battery Storage Capacity (kWh)

Bat

tery

Dis

char

ge P

ower

(kW

)

2 4 6 8 10 12 14 16 18 20

10

20

30

40

50

60

70

Gasoline Savings Vary with Battery Sizeoperational cost savings compared to a 30mpg vehicleLarger the battery, higher the gasoline savings

Smaller battery saves about $7000 or less

Large battery can save over $12000

12k

Larger the battery, higher the initial investment

5

Optimum Battery Size

ConventionalMicro HEV

Mild HEV

Strong HEV

Plug In HEV

Bigger battery: higher investment, higher returns ?

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Problem StatementMaximize Net Present Value (NPV) of a PHEV

By varying battery capacity & discharge power Optimum control parameters for each battery capacity & power

While considering• Real world drive cycles (30) instead of the FTP cycles• Net Savings (reduced gasoline use & increased electricity use)• Battery ageing and its effects on the fuel consumption• Vehicle ageing and its effect on vehicle usage

PHEV battery vs. other investment options

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Vehicle AssumptionsMidsize sedanSeries PHEV modeled in Autonomie

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Battery Cost : Present & Future

10003000

3000

30005000

5000

50007000

7000

70009000

9000

900011000

11000

1100013000

13000

Battery Storage Capacity (kWh)

Bat

tery

Dis

char

ge P

ower

(kW

)

2 4 6 8 10 12 14 16 18 20

10

20

30

40

50

60

70

80

500

1000

1000

1500

1500

1500

2000

2000

2000

2500

2500

2500

3000

30003500

Battery Storage Capacity (kWh)

Bat

tery

Dis

char

ge P

ower

(kW

)

2 4 6 8 10 12 14 16 18 20

10

20

30

40

50

60

70

80

$8k $2kDOE target is roughly a

quarter of the present cost

Cost of battery: Now

$/kWh = 32 x P/E + 600 $/kWh = 20 x P/E + 125

Cost of battery: DOE target

End of Life : 2000 cycles (~6 years)Present cost $/kWh = 32 x battery power to energy ratio + 600DOE target $/kWh = 20 x battery power to energy ratio + 125

pow

er

energyenergySAE 2010-01-2310

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Simultaneous Optimization of Battery Size & Control Parameters

OFF threshold

ON threshold

Pow

er d

eman

d at

whe

el

Engine OFF

Engine ON

time

Battery spec range

2 kWh 20 kWh

8 kW

80 kW

energy

pow

er

Battery sizing determines the constraints for the controller

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Inputs for NPV Calculation

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NPV Calculation.

Assumptions

Gasoline cost $3.24/gallon

Electricity cost $0.1/kWh

1 charge per day

85% charger efficiency

Conventional fuel efficiency ~30mpg

Used 300 days a year

NPV is maximized by varying the battery

energy, power ratings and the vehicle control

parameters

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Optimization Problem StatementMaximizing NPV over the lifetime of the vehicle

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Define vehicle Vary battery sizes Optimize control parameters

Real world drive cyclesPost Processing Gasoline savings

Over conventional vehicle

Calculate savings Yearly miles & $ saved NPV over 15 years

Autonomie Simulation

mpg $ saved

$ NPV over

15 years

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Use Rapid Accelerator for Execution Speed on all Drive-Cycles

Use Parallel Computing To Make Execution Speed Scalable and Controllable

Use Direct Search Optimization for Robustness to Local Minima

SearchSystematicallySteps Through The Search Parameter Space

HEV Optimization Approach

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Initialize Optimization Parameters

Generate N Parameter Variations With Pattern Search

Run all Real-World Drive-Cycle Simulations PerParallel Computing Worker For Each of The N Variations

Size Pattern Search Mesh Smaller Than Tolerance?

Report Results

NoYes

Typical Run Results: 4hrs on Quad-Core PC, ~1000 Simulations

HEV Optimization Process

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0

0

0

0

500

500

500

500

1000

1000

1000

1000

2000

2000

2000

20002400

2400

240026

00

2600

2800Battery Storage Capacity (kWh)

Bat

tery

Dis

char

ge P

ower

(kW

)

2 4 6 8 10 12 14 16 18 2010

20

30

40

50

60

70

NPV Variation with Battery Size considering Present day battery costs

High initial cost reduces the NPV of the future savings

Smaller battery gives better savings

Pow

er (k

W)

Energy (kWh)SAE 2010-01-2310

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4000

4000

4000 40004000

4500

4500

4500

4500 4500

5000

50005000

5000 5000

5500

5500

5500

5500

5800

5800

5800

5800

6020

6020

6020

6080

Battery Storage Capacity (kWh)

Batte

ry D

isch

arge

Pow

er (k

W)

2 4 6 8 10 12 14 16 18 20

10

20

30

40

50

60

70

NPV Variation with Battery Size considering DOE Target battery costs

Gasoline savings will provide more than 7% return on investmentNPV > $6000

Smaller battery too saves money

Pow

er (k

W)

Energy (kWh)

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Summary Developed a process for maximizing the NPV of a

PHEV, by optimization of battery size & control parameters Shows the need for reducing the initial investment to

make PHEVs attractive

Demonstrated the benefits of Autonomie & the parallel computing and optimization capabilities in MATLAB®

Ability to run large studies in a shorter time frame Analysis and optimization capabilities

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Questions

Contact detailswww.autonomie.netArgonne National Laboratory

arousseau@anl.govram@anl.gov

The MathWorks Inc.

peter.maloney@mathworks.com

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The Transportation Energy Data handbook, 28th edition, shows that at least a third of all cars live for 15 yrs or more.

http://www-cta.ornl.gov/data/chapter3.shtml Newer cars, better built ? Duration long enough to cover 240,000km (150,000 miles)

Why is vehicle life set at 15 yrs

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Why is driving distance reduced after 6 yrsDriving distance reduces with vehicle age. (ref: http://www-nrd.nhtsa.dot.gov/Pubs/809952.pdf)

This is factored in for this study, by reducing the driving distanceafter the initial 6 yrs

64km (40 miles) is a fair estimate for the average daily driving distance

As per NHTSA and as per Kansas City dataref SAE 2009-01-1383

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Battery Beyond its End of Life (EOL)Capacity fade is noticeableMay have more limitations, but still useful

Number of discharge cycles

Batt

ery

capa

city

%

120

100

60

20% over sizing to meet End Of Life performance criteria

40% of capacity is not used as depth of discharge is restricted during daily drives

Battery ‘End Of Life’

Capacity fade is noticeable after battery EOL.

Designed Capacity

Rated Capacity

Usable Capacity 60% of total

Vehicle ‘End Of Life’

40

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Drive cycle characteristicsReal world cycles (30 cycles chosen arbitrarily from a set of over 100 cycles)30 vehicles, 1 day, 380 trips (trip = event between Key ON - OFF)

Longest trip: Distance : 94km in about 1 hour

Shortest trip: Distance: 0.2km in about 1 minute

Daily cycle durations too varied from a few minutes a day to a couple of hours a day.

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Interpretation of the resultsAnalyzing the impact of the initial assumptions The study was done with a long term estimate of the battery cost.

This reduces the initial investment

Larger battery has a larger potential for gasoline savings This increases the income in future years

Battery replacement is not warranted in this case due to reduced use of vehicle as it gets older. This avoids future investments on the vehicle.

All these factors together results in the presented optimum sizeIf any of these assumptions change, the result will be different.

Eg: with short term cost estimates, the battery size drops to the lower limits used in the study. This explains the need for tax incentives for PHEVs with larger batteries.

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Battery AssumptionsBattery life : 2000 cycles (replacement is optional)Battery cost :Present cost $/kWh = 32 x battery power to energy ratio + 600DOE target $/kWh = 20 x battery power to energy ratio + 125

SAE 2010-01-2310

Maximizing Net Present Value of a Series PHEV by Optimizing Battery Size and ControlOverviewNet Present Value of a PHEVGasoline Savings Vary with Battery Size�operational cost savings compared to a 30mpg vehicleOptimum Battery SizeProblem StatementVehicle AssumptionsBattery Cost : Present & FutureSimultaneous Optimization of Battery Size & Control ParametersInputs for NPV CalculationNPV CalculationOptimization Problem StatementAutonomie SimulationHEV Optimization ApproachHEV Optimization ProcessNPV Variation with Battery Size �considering Present day battery costsNPV Variation with Battery Size �considering DOE Target battery costsSummaryQuestionsWhy is vehicle life set at 15 yrsWhy is driving distance reduced after 6 yrsBattery Beyond its End of Life (EOL)Drive cycle characteristicsInterpretation of the resultsBattery Assumptions