combined design and control optimization of hybrid vehicles · buffer’s operating points. further...

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.

Veh

icle

vel

ocity

[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 3000−5000

0

5000

75

75 75 75

75

75 75 75

92

92 92 92

92

92 92 92

94

94 94

9494 94

95

95 95

9595 95

Tor

que

[Nm

]

Speed [rpm]

Torque boundsE fic ency [%]

Quasi-static model of the EM.

−6000 − 000 −2000 0 2000 000−200

−100

0

100

200

10010

00

200

20

00

200

300

300

300

400

400

400

600

0

600

1000

1000

300

3000

Torque [Nm]

Ele

ctric

al p

ower

[kW

]

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

Approximated EM model.

0 10 20 30 0 500

10

20

30

0

50

Effi

cien

cy [%

]

Electrical power [kW]

Quasi-static model of the FCS.

0 10 20 30 0 500

20

0

60

80

Fue

l 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 <10 s

Optimal results.

1 1.5 250100

0.3

0 32

0 34

0 36

0 38

Buffer energy [kWh]FCS power [kW]

Cos

t [E

UR

/km

] 0.29

0.3

0.3

0.31

0.31

0.32

0.32

033

0.33

0.33

034

0.34

0.34

035

0.35

0.35

0.36

0.36 0.370.38

0.39

Buffer energy [kWh]

FC

S p

ower

[kW

]

1 1.5 2

30

40

50

60

70

80

90

100

Cost [EUR/km]Optimum

Optimal cost for different sizes of fuel cell system and electric buffer. The shaded region illustrates infeasible component sizes.



0 5 10 15 20 25 30 35 40 45 50

−200

−150

−100

−50

0

50

100

Pow

er [k

W]

Time [min]

FCS powerBuffer power

FCS and buffer power trajectories.

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

Time [min]

Buf

fer

stat

e of

cha

rge

[%]

Buffer’s state of charge trajectory.

0 20 40 600

10

20

30

40

50

60

FCS power [kW]

FC

S e

ffici

ency

[%]

Optimal operating pointsDistribution [%]

FCS’s operating points.

−2000 −1000 0 10000

20

40

60

80

100

0

50

70

70

70

80

80

0

80

80

885

85

85

85

9090

90

9090

90

9393

93

93

93

96

6

Sta

te o

f cha

rge

[%]

Pack power at terminals [kW]

OptimaloperatingpointsEfficiency [%]

Buffer’s 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.

http://publications.lib.chalmers.se/publication/192858-cones-matlab-code-for-convex-optimization-in-electromobility-studies

http://publications.lib.chalmers.se/publication/192858-cones-matlab-code-for-convex-optimization-in-electromobility-studies

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 ci

rcui

t vol

tage

[V]

0 20 40 60 80 1002

2.5

3

3.5

Original modelAffine approximationOperational region

Battery cell open circuit voltage.

0 20 40 600

2000

4000

6000

8000

10000

Internal cell power [W]

Num

ber

of c

ycle

s un

til e

nd o

f life

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

0 10 20 30 40 50 60 70−1

−0.8

−0.6

−0.4

−0.2

0x 10

−6

Internal cell power [W]

Sta

te o

f hea

lth d

eriv

ativ

e [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 <10 s

Optimal results without battery SOH model.

Parameter ValueFCS size 47.2 kWBuffer size (usable) 11 kWhTotal cost 0.29e/kmComputational time ≈10 s

Optimal results with battery SOH model and noreplacements.

0 10 20 30 40 5030

40

50

60

70

Time [min]

Opt

imal

SO

C tr

ajec

tory

[%]

SOC limitsWothout SOH modelWoth SOH model

Optimal SOC trajectory for a battery with and withoutSOH model.

90

9090

9292

92

922

9494

94

9494

966

96

96

98

9899

99

Sta

te o

f cha

rge

(SO

C)

[%]

Power at cell terminals [kW]

Battery

−0.1 −0.05 0 0.05 0.10

10

20

30

40

50

60

70

80

90

100Efficiency [%]Power lim tsOperating points, without SOH modelOperating points, with SOH model

Optimal operating points for a battery with and withoutSOH model.



• 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.

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Cos

t [E

UR

/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.

0 50 100 1500

10

20

30

Generator power [kW]

Effi

cien

cy [%

]

Engine generator unit (EGU).

85

85 85 8858585

85

9090

90

90

90

90

9292

92

92

92

92

Speed [rpm]

Tor

que

[kN

m]

0 500 1000 1500 2000

−2

−1

0

1

2

Torque limits

Efficiency [%]

Electric machine (EM).

0

20

0

60

Vel

octy

[km

/h]

0 2 6 8 10 12 1 160

20

0

60

Alti

tude

[m]

Distance [km]

Fast−charge 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

20

40

60

80

100

Sup

erca

paci

tor

SO

C [%

]

Infrastructure with 7 chargersInfrastructure with 1 charger

−10 0 10 20 30 40 500

20

40

60

80

100

Time [min]

Bat

tery

SO

C [%

]

10 s charging intervals10 min charging intervalSOC limits

−4 −2 0 20

60

80

100

Power limits7 chargers1 charger

−1 −0.5 0 0.50

20

40

60

80

100

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.

http://eahart.com/prius/psd/

combined design and control optimization of hybrid vehicles · buffer’s operating points. further...

Documents