Hybrid Powertrain Optimization for Plug-In Microgrid Power ...

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


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?


Outline• Introduction & Motivation

• Powertrain System Modeling

• Optimization Study

• Constraint Tightening

• Discussion of Results

• Conclusions


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


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


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


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







• Conclusions


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


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


Optimization Algorithm


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


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


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


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







• Conclusions


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.


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







• Conclusions


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


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







• Conclusions


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


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


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.


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