hybrid powertrain optimization for plug-in microgrid power
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Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 1 of 28
Hybrid Powertrain Optimization for Hybrid Powertrain Optimization for PlugPlug--In In MicrogridMicrogrid Power GenerationPower Generation
Scott J. MouraScott J. MouraDongsukDongsuk KumKum
Hosam K. Hosam K. FathyFathyJeffrey L. SteinJeffrey L. Stein
May 16, 2007May 16, 2007
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 2 of 28
Introduction & MotivationVision – Vehicle to Grid (V2G)
POWER DISTRIBUTION GRID BUS
BATTERYPOWERPLANT
HYBRID ELECTRIC POWERPLANT
BI-DIRECTIONALPOWER FLOW
FOR LOAD LEVELING
MICROGRID LOAD
BASELOADPOWER FLOW
MOTOR
PLUG-IN HYBRID ELECTRIC VEHICLE
IC ENGINEOR
FUEL CELLUse plug-in hybrid electric vehicles (PHEV) to provide ancillary services to autonomous electric microgrid systems (e.g. hospital backup power, military bases)
Obstacles Current PHEVs do not capitalize on V2G technology
Proposed Solution Develop an optimization approach for the design and control of a PHEV powertrain for microgrid power generation to minimize fuel consumption
BATTERYSIZE
POWERPLANTSIZE
CONTROL ARCHITECHTURE
IC ENGINEOR
FUEL CELLCONTROL SYSTEM
1. What is the optimal design and control?2. Does an optimal system provide significant benefits?
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 3 of 28
Outline• Introduction & Motivation
• Powertrain System Modeling
• Optimization Study
• Constraint Tightening
• Discussion of Results
• Conclusions
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 4 of 28
System Level Block Diagram
Powertrain Syst
em
Power Demand
Rule-based Supervisory Controller
Powertrain System Battery
Battery
Power Demand
Grid PowerDemand Cycle
Sta
te o
f Cha
rge
(S0C
)
ElectricPowerBus
Fuel
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 5 of 28
Grid Power Demand Cycle ModelingRepresentative grid power demand cycle• Adapted from CAISO daily demand forecast data [1]• Applied cubic spline curve fit• Augmented with white Gaussian noise – models stochastic behavior• Scaled for medium size office or apartment complex
[1] California ISO: System Status. http://www.caiso.com/outlook/outlook.html
6am 9am 12am 3am 6pm 9pm 12pm 3pm 6am6
7
8
9
10
11
Time (hour)
Pow
er D
eman
d (k
W)
With NoiseWithout Noise
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 6 of 28
BATTERY
COMPRESSOR
H2 STORAGE TANK
SUPPLY MANIFOLD
COOLER & HUMIDIFIER
COMPRESSOR MOTOR
Air Supply
H2
FUEL CELL STACK
Voltage
CA
THO
DE
SID
E
AN
OD
E S
IDE
POWER BUS
StackCurrent
StackVoltage
Battery Power
Power Output
Powertrain System Model
FCS model adapted from [2]Battery model from ADVISOR library
[2] J. T. Pukrushpan, A. G. Stefanopoulou and H. Peng, Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design. , vol. XVII, Springer, 2004, pp. 161.
cpλ
nbatt
nfcCompressor Scale
No. of Battery Modules
No. of Fuel Cells
Case Study: Fuel Cell SystemInspired by Lawrence Burns GM Vice-President Research & Development and Strategic Planning Keynote Address, ARC Conference 2004
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 7 of 28
0 5000 10000 150000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Fuel Cell System Efficiency Curve
Requested Power (W)
Effi
cien
cyRule-Based Supervisory Controller
BATTERY ONLY MODE
Ppa
Concept: Use battery to minimize fuel cell operation, yet ensure desirable efficiency
BATTERY ONLY MODE0=fcP
batt demP P=
POWER ASSIST MODE
pa_modefc PP =
batt dem pa_modeP P P= −
FUEL CELL ONLY MODE
chargedemfc PPP +=
batt chargeP P= −
( )deschcharge SOCSOCKP −=where
Pbatt
FUEL CELL ONLY MODE
POWER ASSIST MODE
Ppa
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 8 of 28
Outline• Introduction & Motivation
• Powertrain System Modeling
• Optimization Study
• Constraint Tightening
• Discussion of Results
• Conclusions
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 9 of 28
Optimization Problem FormulationMinimize hydrogen fuel consumption
with respect to6 Design Variables• Number of fuel cells in stack, nfc
• Number of battery modules, nbatt
• Compressor size, λcp
• Power Assist (PA) mode threshold, Ppa
• Battery mode threshold, Pbatt
• Controller Gain, Kch
subject to10 Constraints• Fuel cell stack length• Battery weight• Stack heat generation• Parasitic losses• Fuel cell efficiency• Oxygen excess ratio• Max/Min SOC• Start/End SOC deviation
( ) ( )chbattpacpfcfcH KPPnnmf ,,,,,min2
λ=x
Component Sizes
Control Parameters
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 10 of 28
Optimization Algorithm1. Run multiple experiments to collect
data on physical model
2. Perform monotonicity analysis to determine trends, optima, and reduce the problem
3. Use data to develop a surrogate model (e.g. LSM, ANN, Kriging)
4. Optimize with Sequential Quadratic Programming (SQP)
5. Cross-check solution feasibility with physical model
6. Analyze tradeoff between battery cost and fuel consumption by performing a parametric study
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 11 of 28
Optimization Algorithm
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 12 of 28
64006600
68007000
7200 80008500
90009500
1000010500
0.065
0.07
0.075
0.08
0.085
0.09
0.095
PA Mode Threshold (W)Batt Mode Threshold (W)
H2 C
onsu
mpt
ion
(kg)
250 300 350 400 450 5000.08
0.085
0.09
0.095
Number of Fuel Cells
H2 F
uel C
onsu
mpt
ion
(kg)
Steps1 & 2: DOE & Monotonicity AnalysisModel ReductionNumber of Fuel Cells
Identifying TrendsPower Threshold Values
nfc* = 422 fuel cells
Several constraints may bound Ppa and Pbatt
MINIMUM
MINIMUM
Fuel Cell Stack Length Constraint
Problem reduces to 5 design variables
nfc* = 422 fuel cells
At least two constraints must be active
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 13 of 28
Optimization Algorithm
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 14 of 28
Surrogate Modeling Methods• Least Squares
Method – 4th order Taylor Polynomial
• Feedforward ANN
• Radial Based ANN
Which surrogate model is best?
15 20 25 30 350.075
0.08
0.085
0.09
0.095Surrogate Model Approximation
No. of Battery Modules, nbatt
H2 C
onsu
mpt
ion
(kg)
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.075
0.08
0.085
0.09
0.095
0.1
Compressor Scale, λCP
H2 C
onsu
mpt
ion
(kg)
8000 8500 9000 9500 10000 105000.065
0.07
0.075
0.08
0.085
0.09
Power Assist Mode, Ppa
H2 C
onsu
mpt
ion
(kg)
LSMFFNNRBNNSimulation
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 15 of 28
Mean Square Error
0.0019
0.0022
9.40E-070.00E+00
5.00E-04
1.00E-03
1.50E-03
2.00E-03
2.50E-03
Least Squares MethodTaylor Polynomial
Feed Forward Neural Network Radial Based Neural Network
Step 3: Surrogate Model Evaluation
Surrogate Model used for the
remainder of the study
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 16 of 28
Optimization Algorithm
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 17 of 28
Step 4: Feasibility Analysis
3.33 x 10-160.01Max SOC Deviation
6.6740.666Min SOC
0.70.7Max SOC
3.0463.00Oxygen Excess Ratio
58.7 %57.7 %Fuel Cell Efficiency
1.94 %2.69 %Parasitic Losses
6102 W6094 WStack Heat Generation
55 lbs56 lbsBattery Weight
SimulationSurrogateConstraints
ACTIVE CONSTRAINTFEASIBLE INFEASIBLE
Determine if the surrogate model solution is feasible for the actual simulation
Recall that 2 constraints need to be active to properly bound Ppa and Pbatt
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 18 of 28
Outline• Introduction & Motivation
• Powertrain System Modeling
• Optimization Study
• Constraint Tightening
• Discussion of Results
• Conclusions
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 19 of 28
Constraint Tightening
Case 1: Oxygen Excess Ratio
Case 2: Max SOC Deviation
Boundary Optimum
Surrogate Model Physical Model
Infeasible in Physical Space
Transform to Physical Space
Tighten Constraints on
Surrogate Model
Physical Model
Boundary Optimum
Surrogate Model Physical ModelTransform to
Physical Space
Feasible in Physical Space
STOP
Feasible in Physical Space
Proposed Solution: Make violated constraints more aggressive for the surrogate model to compensate for modeling error
[4] A. Parkinson, "Robust mechanical design using engineering models," Journal of Mechanical Design, vol. 117B, pp. 48-54, 1995.
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 20 of 28
START
Perform DOE on physical model
Develop surrogate model
Optimize with SQP
Check if solution is feasible for
physical model
END
Tighten violated
constraints
FEASIBLE
INFEASIBLE
Reduce problem using monotonicity
analysis
Parametric Study
Optimization Algorithm with Constraint Tension1. Run multiple experiments to collect data on
physical model
2. Perform monotonicity analysis to determine trends, optima, and reduce the problem
3. Use data to develop a surrogate model (e.g. LSM, ANN, Kriging)
4. Optimize with Sequential Quadratic Programming (SQP)
5. Cross-check solution feasibility with physical model
6. If solution is not feasible, tighten the violated constraints and go to Step 4
7. Analyze tradeoff between battery cost and fuel consumption by performing a parametric study
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 21 of 28
Outline• Introduction & Motivation
• Powertrain System Modeling
• Optimization Study
• Constraint Tightening
• Discussion of Results
• Conclusions
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 22 of 28
Nominal vs. Optimal Designs
Change in Component Size for Optimal Design
11%
25%
15%
0%
5%
10%
15%
20%
25%
30%
No. of Fuel Cells No. of BatteryModules
Compressor Scale
Perc
enta
ge C
hang
e
• Combined design/control optimization significantly increases fuel efficiency
• All components increase in size
• Number of fuel cells is constrained only by total stack length
• Battery size increases the most
55% decrease in fuelconsumption per month
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 23 of 28
18 19 20 21 22 23 24 25-2
0
2
4
6
8
10
12
14
16
No. of Battery Modules
Add
ition
al F
uel C
onsu
med
per
Mon
th (%
)
Fuel Consumption vs. Battery Size
Parametric Study on Battery Size
Formulate Multi-objective Optimization Problem• Parameterize the number of battery modules
What is the optimal solution that also minimizes battery size?
FEASIBLE
INFEASIBLE
Observations• Decreasing battery size sacrifices
fuel economy
• 20% reduction in battery size 11% increase in fuel consumption
• Tradeoff between battery cost and fuel consumption
nbatt*nbatt
Nominal
Optimal
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 24 of 28
Outline• Introduction & Motivation
• Powertrain System Modeling
• Optimization Study
• Constraint Tightening
• Discussion of Results
• Conclusions
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 25 of 28
Conclusions
What is the optimal control & design?• Increase component sizes• Maximize battery participation
Note: component costs are not considered
Does an optimal system provide significant benefits?• 55% decrease in fuel consumption per month
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 26 of 28
Summary & Future Work
• Developed combined design/control optimization algorithm for PHEV powertrain supplying microgrid power generation
• Applied constraint tightening concept to ensure solution feasibility
• Analyzed tradeoff between fuel consumption and battery cost
Summary
Future Work• Include component cost metrics• Integrate optimal control algorithm to replace rule-based
construction• Generalize case study for any powertrain type and load
demand
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 27 of 28
Acknowledgements & ReferencesThank you for your contributions to this project!
– Jeongwoo Han– Panos Y. Papalambros– Huei Peng– Michael Kokkolaras– James Allison
Key References[1] S. J. Moura, D. Kum. “Plant/Control Optimization of a PEM Hybrid Fuel Cell Vehicle to Grid (V2G)
System.” Design Optimization (ME 555). http://www-personal.umich.edu/~sjmoura/projects.htmlProfessor Panos Y. Papalambros. University of Michigan, Ann Arbor. April 19, 2007.
[2] A. Parkinson, "Robust mechanical design using engineering models," Journal of Mechanical Design, vol. 117B, pp. 48-54, 1995.
[3] J. Han., Optimal design of hybrid and non-hybrid fuel cell vehicles M.S. Thesis, University of Michigan, Ann Arbor, 2000.
[4] J. T. Pukrushpan, A. G. Stefanopoulou and H. Peng, Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design. , vol. XVII, Springer, 2004, pp. 161.
[5] P. Y. Papalambros and D. Wilde. Principles of Optimal Design. Cambridge University Press., 2nd edition, 2000.
Hybrid Powertrain Optimization for Plug-In Microgrid Power GenerationAutomated Modeling Laboratory Slide 28 of 28
QUESTIONS?