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
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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 power
Vehicle velocity [km/h]
between energy sources, when driving along a driving cycle.
Road altitude [m]
60
40
20
0
0
2
4
6
8
10
Distance [km]
12
14
16
Driving cycle: Bus line 17 in Gothenburg.
• Optimal powertrain sizing refers to
sizing of energy and power units that
decrease vehicle price and allow
optimal vehicle operation.
Optimization framework for simultaneous component sizing and
energy management of a hybrid city bus.
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Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)
75
Torque bounds
E fic ency [%]
−5000
0
1000
2000
Speed [rpm]
0
0
10020
200
3000
40
−100
3 00
94 95
92
75
75 92
94
95
95
00
10
6
00 00
92
0
40 0
30
200
0
43000
00
10
94 95
92
75
75 92
94 95
92
94
92
Electrical power [kW]
Torque [Nm]
94
95
75
75
0
Original model
(speed [rpm])
Approximation
(speed [rpm])
100
3000
10
00
60
0
200
92
75
5000
−200
3000
−6000 − 000 −2000
0
2000
Torque [Nm]
Quasi-static model of the EM.
000
Approximated EM model.
50
Fuel power [kW]
Fuel cell hybrid powertrain. EM = electric machine,
FCS = fuel cell system, buffer = battery or supercapacitor.
Efficiency [%]
80
0
30
20
10
0
60
0
20
0
10
20
30
Electrical power [kW]
0
50
Quasi-static model of the FCS.
0
Original model
Approximation
0
10
20
30
Electr cal power [kW]
0
50
Approximated FCS model.
• Objective:
• find optimal sizes of buffer and FCS,
• find optimal power split control,
which minimize hydrogen consumption and investment cost.
N. Murgovski @ Chalmers 2014
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Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)
• Optimal results for a FCHV city bus using
Parameter
Hydrogen price
FCS price
Supercapacitor price
Yearly travel distance
Bus’ service period
Yearly interest rate
supercapacitor as an energy buffer:
Parameter
FCS size
Buffer size
Total cost
Computational time
Value
69.3 kW
0.7 kWh
0.28 e/km
<10 s
Value
4.44 e/kg
34.78 e/kWh
10 000 e/kWh
70 000 km
2 years
5%
Prices and bus specifications.
Optimal results.
0 34
0 35
0.32
0 33
0.36
5
Cost [EUR/km]
Optimum
0.3
FCS power [kW]
7
Cost [EUR/km]
6
3
4
0.3
30
0.31
100
0.3
40
0.3
2
0.3
50
0.3
1
9
60
0.3
50
FCS power [kW]
0.3
0 32
70
0.2
0 34
80
0.3
0 36
9
0.3 .38
0
90
0 38
0.3
5
0.3
4
0.3
3
0.3
100
2
1.5
Buffer energy [kWh]
1
1.5
2
Buffer energy [kWh]
Optimal cost for different sizes of fuel cell system and electric buffer. The shaded region illustrates infeasible component sizes.
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Case study 1: Sizing of a fuel cell hybrid vehicle (FCHV)
60
FCS efficiency [%]
100
0
−50
−100
−150
FCS power
Buffer power
−200
0
5
10
50
Optimal operating points
Distribution [%]
40
30
20
10
15
20
25
30
Time [min]
35
40
45
50
0
0
20
40
FCS power [kW]
FCS and buffer power trajectories.
15
20
25
30
Time [min]
35
Buffer’s state of charge trajectory.
40
45
50
96
Optimal
operating
points
Efficiency [%]
20
0
−2000
93
90
8805
70
State of charge [%]
10
93
90700
50
5
40
6
0
60
70
20
80
90
85 0
8
40
80
Buffer state of charge [%]
85
60
93
90
100
80
9
903
8
805
FCS’s operating points.
100
0
60
930
890
Power [kW]
50
−1000
0
Pack power at terminals [kW]
1000
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 Clean
Energy Systems. Accepted for publication.
N. Murgovski @ Chalmers 2014
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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.
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• Consider A123 battery cell.
• Open circuit voltage is approximated as
affine in state of charge.
• Degradation with respect to cell current
(C-rate) [1].
Open circuit voltage [V]
Case study 2: Battery longevity considerations
3.5
3
Original model
Affine approximation
Operational region
2.5
2
0
20
State of health derivative [1/s]
Number of cycles until end of life
8000
6000
4000
2000
20
80
100
40
60
Internal cell power [W]
Number of cycles until end of life vs. cell power.
x 10
−0.2
−0.4
−0.6
−0.8
−1
0
60
Battery cell open circuit voltage.
−6
0
10000
0
40
State of charge [%]
Original model
Piecewise affine approximation
0
10
20
30
40
50
60
70
Internal cell power [W]
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 for
graphite-LiFePO4 cells. J. Power Sources 2011;196:3942-8.
N. Murgovski @ Chalmers 2014
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Case study 2: Battery longevity considerations
• Optimal results for a FCHV city bus using
Parameter
Hydrogen price
FCS price
Battery price
Yearly travel distance
Bus’ service period
Yearly interest rate
A123 battery as an energy buffer.
Parameter
FCS size
Buffer size (usable)
Total cost
Computational time
Value
44.1 kW
4.4 kWh
0.24 e/km
<10 s
Value
4.44 e/kg
34.78 e/kWh
900 e/kWh
70 000 km
5 years
5%
Prices and bus specifications.
Optimal results without battery SOH model.
100
90
50
2
90
94
50
40
30
94
60
60
6
70
Efficiency [%]
Power lim ts
Operating points, without SOH model
Operating points, with SOH model
70
92
State of charge (SOC) [%]
Optimal results with battery SOH model and no
replacements.
96
80
92
10
20
30
0
40
50
Time [min]
Optimal SOC trajectory for a battery with and without
SOH model.
N. Murgovski @ Chalmers 2014
92
96
90
90
−0.1
92 94 96
−0.05
98
0
94
10
30
99
98
20
SOC limits
Wothout SOH model
Woth SOH model
40
99
Optimal SOC trajectory [%]
Battery
Value
47.2 kW
11 kWh
0.29 e/km
≈10 s
94
Parameter
FCS size
Buffer size (usable)
Total cost
Computational time
0
0.05
0.1
Power at cell terminals [kW]
Optimal operating points for a battery with and without
SOH model.
9/16
Case study 2: Battery longevity considerations
• Replacing the battery incurs additional costs. (Although, in certain cases it might be
optimal to replace the battery several times [3].)
• The supercapacitor is a better alternative for this FCHV.
0.45
0.4
Details on convex modeling and more results in
Cost [EUR/km]
0.35
[1] L. Johannesson, N. Murgovski, S. Ebbessen,
B. Egardt, E. Gelso, J. Hellgren. Including a
battery state of health model in the HEV
component sizing and optimal control
problem. IFAC Symposium on Advances in
Automotive Control, Tokyo, Japan, 2013.
0.3
Total cost
Cost for hydrogen
Cost for battery
Cost for FCS
0.25
0.2
[2] X. Hu, L. Johannesson, N. Murgovski, B.
Egardt. Longevity-conscious dimensioning
and power management of a hybrid energy
storage system for a fuel cell hybrid electric
bus. Journal of Applied Energy, 2014,
Submitted.
0.15
0.1
0.05
0
0
2
4
6
8
Number of battery replacements
Cost vs. number of battery pack replacements.
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[3] N. Murgovski, L. Johannesson, B. Egardt.
Optimal battery dimensioning and control of
a CVT PHEV powertrain. IEEE Transactions
on Vehicular Technology, 2014. Accepted for
publication.
10/16
Case study 3: Plug-in hybrid electric vehicle (PHEV) in a series
configuration
• Dual buffer consisting of Saft VL 45E
Electric grid
battery and Maxwell BCAP2000 P270
supercapacitor.
Auxiliary load
Ultracapacitor Battery
• Can charge at 7 bus stops for 10 s, or
EM
Buffer
10 min before starting the route.
50
100
150
92 90
85
85
90
92
0 85 85
92
ICE
85
GEN
EGU
8
Plug-in HEV powertrain in a series configuration.
EGU = Engine generator unit, GEN = Generator.
90
92
0
Generator power [kW]
Efficiency [%]
500
1000
1500
2000
Speed [rpm]
Engine generator unit (EGU).
Altitude [m] Veloc ty [km/h]
Fuel tank
90
85
0
Torque limits
−1
−2
0
92
92
Torque [kNm]
Efficiency [%]
10
1
9090
20
85
2
30
Electric machine (EM).
60
0
20
0
60
Fast−charge docking stations
0
20
0
0
2
6
8
10
12
1
16
Distance [km]
Driving cycle with charging opportunities.
N. Murgovski @ Chalmers 2014
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Case study 3: Plug-in hybrid electric vehicle (PHEV) in a series
configuration
• 2 design parameters: battery and
supercapacitor size.
• 2 states: battery and supercapacitor SOC.
• Magnitude of charging power is an
optimization variable.
• Engine is turned on when demanded
Parameter
Diesel price
Battery price
Supercapacitor price
Yearly travel distance
Bus’ service period
Yearly interest rate
Maximum charging power
Value
1.6 e/l
500 e/kWh
10 000 e/kWh
80 000 km
5 years
5%
200 kW
Prices and bus specifications.
power exceeds a certain threshold.
• Optimal results:
Charging scenario
Supercapacitor energy [kWh]
Usable battery energy [kWh]
Total cost [e/km]
Diesel fuel consumption [l/km]
Charging power [kW]
7 chargers
0.8
2.4
0.32
0.16
200
1 charger
0.4
15.6
0.16
0
121
Optimal results for the two charging scenarios.
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Battery SOC [%]
Supercapacitor SOC [%]
Case study 3: Plug-in hybrid electric vehicle (PHEV) in a series
configuration
100
100
80
80
60
60
40
20
0
−10
100
Power limits
7 chargers
1 charger
Infrastructure with 7 chargers
Infrastructure with 1 charger
0
10
20
30
40
50
80
−4
−2
0
2
−0.5
0
0.5
80
60
60
40
40
10 s charging intervals
10 min charging interval
SOC limits
20
0
−10
0
100
0
10
20
Time [min]
30
20
40
50
0
−1
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. Sjöberg. Dimensioning and control of a thermally constrained double buffer plug-in
HEV 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 control
issues regarding vehicle electrification. IEEE Control Systems Magazine, vol. 34, no. 2, pp. 32-49, 2014.
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(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 on
Vehicular 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 Transactions
on Vehicular Technology, 2014. Accepted for publication.
N. Murgovski @ Chalmers 2014
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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. IFAC
World Congress, Cape Town, South Africa, 2014.
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