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Combined design and control optimization of hybrid vehicles- Recent developments through case studies -

Nikolce Murgovski

Department of Signals and Systems,Chalmers University of Technology

Gothenburg, Sweden

May 2014

Outline

Powertrain sizing and energy management of hybrid vehicles. Case study 1: Sizing of a fuel cell hybrid vehicle. CONES: Matlab code for convex optimization in electromobility studies. Case study 2: Battery longevity considerations. Case study 3: Plug-in hybrid electric vehicle (PHEV) in a series configuration. HEV in a parallel configuration. Planetary gear HEV (used in Toyota Prius).

N. Murgovski @ Chalmers 2014 2/16

Powertrain sizing and energy management of hybrid vehicles


Hybrid vehicles include one or more energy buffers (battery, supercapacitor,flywheel) to reduce losses.

The objective of the energy management controller is to optimally arbitrate powerbetween energy sources, when driving along a driving cycle.

Vehi

cle

velo

city

[km/

h]

Distance [km]

0 2 4 6 8 10 12 14 160

20

40

60Road altitude [m]

Driving cycle: Bus line 17 in Gothenburg.

Optimal powertrain sizing refers tosizing of energy and power units thatdecrease vehicle price and allowoptimal vehicle operation.

Optimization framework for simultaneous component sizing andenergy management of a hybrid city bus.

Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)


Fuel cell hybrid powertrain. EM = electric machine,FCS = fuel cell system, buffer = battery or supercapacitor.

0 1000 2000 30005000

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5000

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75 75 75

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75 75 75

92

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Torq

ue [N

m]

Speed [rpm]

Torque boundsE fic ency [%]

Quasi-static model of the EM.

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W]

Original model(speed [rpm])Approximation(speed [rpm])

Approximated EM model.

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ienc

y [%

]

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Quasi-static model of the FCS.

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pow

er [k

W]

Electr cal power [kW]

Original modelApproximation

Approximated FCS model.

Objective: find optimal sizes of buffer and FCS, find optimal power split control,

which minimize hydrogen consumption and investment cost.



Optimal results for a FCHV city bus usingsupercapacitor as an energy buffer:

Parameter ValueHydrogen price 4.44e/kgFCS price 34.78e/kWhSupercapacitor price 10 000e/kWhYearly travel distance 70 000 kmBus service period 2 yearsYearly interest rate 5 %

Prices and bus specifications.

Parameter ValueFCS size 69.3 kWBuffer size 0.7 kWhTotal cost 0.28e/kmComputational time



0 5 10 15 20 25 30 35 40 45 50200

15010050

050

100

Pow

er [k

W]

Time [min]

FCS powerBuffer power

FCS and buffer power trajectories.

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Time [min]

Buffe

r sta

te o

f cha

rge

[%]

Buffers state of charge trajectory.

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FCS power [kW]

FCS

effic

ienc

y [%

]

Optimal operating pointsDistribution [%]

FCSs operating points.

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Stat

e of

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rge

[%]

Pack power at terminals [kW]

OptimaloperatingpointsEfficiency [%]

Buffers operating points.

Further details in

[1] N. Murgovski, X. Hu, L. Johannesson, B. Egardt. Combined design and control optimization of hybrid vehicles. Handbook of CleanEnergy Systems. Accepted for publication.

CONES: Matlab code for convex optimization in electromobility studies


CONES: Convex programming framework in electromobility studies. Optimization examples with realistic vehicle design and control problems. Available online http://publications.lib.chalmers.se/publication/

192858-cones-matlab-code-for-convex-optimization-in-electromobility-studies. Coded in Matlab. Uses CVX, a Matlab-based modeling system for convex optimization. Examples are continuously added for powertrain design and energy management of

electrified vehicles.

Case study 2: Battery longevity considerations


Consider A123 battery cell. Open circuit voltage is approximated as

affine in state of charge. Degradation with respect to cell current

(C-rate) [1].State of charge [%]

Ope

n cir

cuit

volta

ge [V

]

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2.5

3

3.5

Original modelAffine approximationOperational region

Battery cell open circuit voltage.

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Internal cell power [W]

Num

ber o

f cyc

les

until

end

of lif

e

Number of cycles until end of life vs. cell power.

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0.8

0.6

0.4

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0x 106

Internal cell power [W]

Stat

e of

hea

lth d

eriva

tive

[1/s]

Original modelPiecewise affine approximation

Derivative of battery cell state of health.

[1] Wang J, Liu P, Hicks-Garner J, Sherman E, Soukiazian S, Verbrugge M, Tataria H, Musser J, Finamore P. Cycle-life model forgraphite-LiFePO4 cells. J. Power Sources 2011;196:3942-8.



Optimal results for a FCHV city bus usingA123 battery as an energy buffer.

Parameter ValueHydrogen price 4.44e/kgFCS price 34.78e/kWhBattery price 900e/kWhYearly travel distance 70 000 kmBus service period 5 yearsYearly interest rate 5 %


Parameter ValueFCS size 44.1 kWBuffer size (usable) 4.4 kWhTotal cost 0.24e/kmComputational time



Replacing the battery incurs additional costs. (Although, in certain cases it might beoptimal to replace the battery several times [3].)

The supercapacitor is a better alternative for this FCHV.

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0.05

0.1

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0.2

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0.3

0.35

0.4

0.45

Cost

[EUR

/km]

Number of battery replacements

Total costCost for hydrogenCost for batteryCost for FCS

Cost vs. number of battery pack replacements.

Details on convex modeling and more results in

[1] L. Johannesson, N. Murgovski, S. Ebbessen,B. Egardt, E. Gelso, J. Hellgren. Including abattery state of health model in the HEVcomponent sizing and optimal controlproblem. IFAC Symposium on Advances inAutomotive Control, Tokyo, Japan, 2013.

[2] X. Hu, L. Johannesson, N. Murgovski, B.Egardt. Longevity-conscious dimensioningand power management of a hybrid energystorage system for a fuel cell hybrid electricbus. Journal of Applied Energy, 2014,Submitted.

[3] N. Murgovski, L. Johannesson, B. Egardt.Optimal battery dimensioning and control ofa CVT PHEV powertrain. IEEE Transactionson Vehicular Technology, 2014. Accepted forpublication.

Case study 3: Plug-in hybrid electric vehicle (PHEV) in a seriesconfiguration


Dual buffer consisting of Saft VL 45Ebattery and Maxwell BCAP2000 P270supercapacitor.

Can charge at 7 bus stops for 10 s, or10 min before starting the route.

Auxiliary load

Buffer

Battery Ultracapacitor

Electric grid

EGU

EM

GEN ICE Fuel tank

Plug-in HEV powertrain in a series configuration.EGU = Engine generator unit, GEN = Generator.

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20

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Generator power [kW]

Effic

ienc

y [%

]

Engine generator unit (EGU).

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Speed [rpm]

Torq

ue [k

Nm]

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Torque limits

Efficiency [%]

Electric machine (EM).

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60

Velo

cty

[km/

h]

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0

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Altit

ude

[m]

Distance [km]

Fastcharge docking stations

Driving cycle with charging opportunities.



2 design parameters: battery andsupercapacitor size.

2 states: battery and supercapacitor SOC. Magnitude of charging power is an

optimization variable. Engine is turned on when demanded

power exceeds a certain threshold. Optimal results:

Parameter ValueDiesel price 1.6e/lBattery price 500e/kWhSupercapacitor price 10 000e/kWhYearly travel distance 80 000 kmBus service period 5 yearsYearly interest rate 5 %Maximum charging power 200 kW


Charging scenario 7 chargers 1 chargerSupercapacitor energy [kWh] 0.8 0.4Usable battery energy [kWh] 2.4 15.6Total cost [e/km] 0.32 0.16Diesel fuel consumption [l/km] 0.16 0Charging power [kW] 200 121

Optimal results for the two charging scenarios.



10 0 10 20 30 40 500

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Supe

rcap

acito

r SO

C [%

]

Infrastructure with 7 chargersInfrastructure with 1 charger

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Time [min]

Batte

ry S

OC

[%]

10 s charging intervals10 min charging intervalSOC limits

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60

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Power limits7 chargers1 charger

1 0.5 0 0.50

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Cell power [kW]Optimal buffer operation for the two charging scenarios. The shaded region in the right plots depicts efficiency greater than 90 %.

Further details in

[1] N. Murgovski, L. Johannesson, A. Grauers, J. Sjoberg. Dimensioning and control of a thermally constrained double buffer plug-inHEV powertrain. 51st IEEE Conference on Decision and Control, Maui, Hawaii, 2012.

[2] B. Egardt, N. Murgovski, M. Pourabdollah, L. Johannesson. Electromobility studies based on convex optimization: design and controlissues regarding vehicle electrification. IEEE Control Systems Magazine, vol. 34, no. 2, pp. 32-49, 2014.

(P)HEV with a parallel powertrain configuration


Convex optimization can also be applied to parallel HEVs. Heuristics are used for gear selection. When using continuously variable transmission (CVT), the optimization can also find the

optimal gear ratio trajectory.

HEV with a parallel powertrain configuration.ICE = Internal combustion engine.

HEV with a continuously variable transmission (CVT).

Further details in

[1] M. Pourabdollah, N. Murgovski, A. Grauers, B. Egardt. Optimal sizing of a parallel PHEV powertrain. IEEE Transactions onVehicular Technology, vol. 62, no. 6, pp. 2469-2480, 2013.

[2] N. Murgovski, L. Johannesson, B. Egardt. Optimal battery dimensioning and control of a CVT PHEV powertrain. IEEE Transactionson Vehicular Technology, 2014. Accepted for publication.

HEV with a planetary gear


Convex optimization can also be applied to HEVs with a planetary gear unit. Heuristics are used for engine on/off.

Toyota Prius - power split device

Series-parallel HEV powertrain with a planetary gear as a power-split device.

Further details in

[1] N. Murgovski, X. Hu, B. Egardt. Computationally efficient energy management of a planetary gear hybrid electric vehicle. IFACWorld Congress, Cape Town, South Africa, 2014.

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