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
N. Murgovski @ Chalmers 2014 3/16
• 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)
N. Murgovski @ Chalmers 2014 4/16
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.
Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)
N. Murgovski @ Chalmers 2014 5/16
• 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.
Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)
N. Murgovski @ Chalmers 2014 6/16
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
N. Murgovski @ Chalmers 2014 7/16
• 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
N. Murgovski @ Chalmers 2014 8/16
• 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.
Case study 2: Battery longevity considerations
N. Murgovski @ Chalmers 2014 9/16
• 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 %
Prices and bus specifications.
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.
Case study 2: Battery longevity considerations
N. Murgovski @ Chalmers 2014 10/16
• 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
N. Murgovski @ Chalmers 2014 11/16
• 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.
Case study 3: Plug-in hybrid electric vehicle (PHEV) in a seriesconfiguration
N. Murgovski @ Chalmers 2014 12/16
• 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
Prices and bus specifications.
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.
Case study 3: Plug-in hybrid electric vehicle (PHEV) in a seriesconfiguration
N. Murgovski @ Chalmers 2014 13/16
−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
N. Murgovski @ Chalmers 2014 14/16
• 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
N. Murgovski @ Chalmers 2014 15/16
• 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.