electro thermal battery pack with model order reduction · • cell level – electrodes ......

Efficient electro‐thermal battery pack simulation with model order reduction

Lucas KostetzerEvgeny Rudnyi

Outline

• Battery simulation introduction• Model order reduction by projection• Case studies

– MIMO, 99 inputs– Electro‐thermal pack model– Expansion pass– MOR switch

• Summary

Monday, October 08, 2012 2012 Automotive Simulation World Congress 2

Battery simulation

• Cell level– Electrodes design– User: Cell producers

• Pack level– Battery management systems (BMS)– User: OEM, Auto makers

• Vehicle level– Complete system integration– User: OEM, Auto makers


0.00 250.00 500.00 750.00 1000.00 1250.00Time [s]

0.00

25.00

50.00

75.00

100.00

125.00

Y1

[km

_per

_hou

r]

-4.00

-3.00

-2.00

-1.00

-0.00

1.00

2.00

Veh

icle

.AC

C [m

_per

_s2]

GearChange_CompleteVehicleSpeed ANSOFT

Battery simulation

• Cell level– Electrodes design– User: Cell producers

• Pack level– Battery management systems (BMS)– User: OEM, Auto makers

• Vehicle level– Complete system integration– User: OEM, Auto makers

Monday, October 08, 2012 2012 Automotive Simulation World Congress 4 0.00 250.00 500.00 750.00 1000.00 1250.00

Time [s]

0.00

25.00

50.00

75.00

100.00

125.00

Y1

[km

_per

_hou

r]

-4.00

-3.00

-2.00

-1.00

-0.00

1.00

2.00

Veh

icle

.AC

C [m

_per

_s2]

GearChange_CompleteVehicleSpeed ANSOFT

Battery pack level: Electrical predictions

• Model for each cell– Limitng current– Heat generation– SOC

• No need of 3D local effects in pack level– System level model are indicated

• P2D, Newman• Impedance (circuits)


C1

R1

UOCV

I1

RI

R2

C2

0

Li+

eLi+

Li+ Li+

LixC6LixC6 Lix-Metal-oxideLix-Metal-oxidee

Jump

Battery pack level: Thermal predictions

• Cooling system models– CFD, FEM

• Heat sources– Battery cells– Power electronics

• Cell temperatures– Local, 3D


Electro‐Thermal simulation for BMS

• Cell electrical model– f(Temp,SOC , I, ….)

• Battery pack thermal model– Hot spots

• Spatial resolution


Cell electrical model

Battery pack thermal model

Heat Temperature

System level simulation

Low CPU cost ‐ >Reduced order model

Bring 3D thermal model to system level

• ANSYS MOR Techniques for linear problems: • Transfer function based (or LTI method)• System matrix based Presentation focus

Monday, October 08, 2012 2012 Automotive Simulation World Congress

MOR for ANSYS

• Projection onto low‐dimensional subspace zx V

x V

z

=

uxx BKE

uzz BVKVVEVV TTT

E

Er

Advantage: NO transient solution with the original FEM model is necessary Highly accurate (linear systems) As accurate as the original FEM model

MOR’s task


Implicit Moment Matching

• Padé approximation• Matching first moments for the transfer

function

• Implicit Moment Matching:– via Krylov Subspace

0

0 )( ii ssmH

mi mi,red , i 0,,r

BKsEsH 1)(

0

0, )( iredired ssmH

s0 0

V span{(K1E,K1b)}

uxx BKE


Example: battery pack FEM

• Part of a battery pack– 4 Cells (pouch)– Cooling by 3 air channels

• 3D FEM model in ANSYS– Uniform heat generation in

each cell• 1D fluid channels

– Coupling by heat transfer coefficient

FLUID116


Reduced vs full solution

Reduced Full

Simulation time [s] 4000 4000 (100 time steps)

Dimension 40 (10 x Input) 48500 elements

CPU time [s] <1 ~20 min

0000

Cell1Cell2Cell3Cell4 T_Ref

HVALUE=0

HVALUE=0

HVALUE=0

VALUE=20HVALUE=10

0.00 1000.00 2000.00 3000.00 4000.00Time [s]

0.00

0.50

1.00

Tem

pera

ture

[cel

]

Curve InfoTCell1.T

TR

ansys_Cell1ImportedError <1%

Step response of 1W per cell


Industrial battery pack model

• Pouch cells

• Cooling by Air– Rectangular channels Battery cell Fluid channel

Cutting detail

Simplified CFD domainMonday, October 08, 2012 2012 Automotive Simulation World Congress

How to use 1D CFD elementCFD (CAD cut) 1D CFD + Thermal simulation (complete CAD)

Average film coefficient

FLUID1163D thermal transient


More complex battery pack model

• 3 layers of 33 cells – 99 inputs

• Numerics– FEM: 68000 DOFs– Dimension of reduced

order model: 10*99• Results (4000s)

– Simplorer: 5mim 48s– Full solution: 80 min

1W/per cell step response

MOR


C1

R1

UOCV

I1

RI

R2

C2

0

Electro‐thermal battery modeling: cell model

• Circuit based (empirical)– One model per cell– Temperature dependent


)(),(

),(),(),(

),(),(

2

1

2

1

IferFactorButlerVolmTIfDifFactor

TSOCftTSOCftTSOCfR

TSOCfrTSOCfr

I

OCV

I

URtC

RtC

RDifFactorrR

erFactorButlerVolmrR

2

22

1

11

22

11

Look‐up tables from experimentsCircuit elements

Resistors

Capacitors

Voltage source

Electro‐thermal battery modeling: Example

• Series connection of 4 cells

Cell model Battery pack

Heat

Temperature


Recover the Temperature field

• From system results back to 3D whenever desired– Expansion pass

x V

z

=

A

B

C


1W/per cell step response, and recovering instants

Recover the Temperature field ‐ Validation

A B C

REDUCED

FULL


When Fluid flow changes

• Co‐simulation– CFD solver + Simplorer

• Transfer function based– LTD

• Projection techniques:– Parametric MOR– ROM switch

Control

TemperatureVelocity


BACKGROUND – ROM switch

IIIIII

IIIIIIIII

zVzVzVzV

:assume

Vzx

x V

z

=

BuKxxE

BuVKVzVzEVV TTT

ROM = Reduced Order Model

IITIIII zVVz


ROM switch example

• Example– ROM1: with fluid velocity V– ROM2: with fluid velocity V*0.001

• Validation• ROM1 (green), ROM 2 (blue), ANSYS (red)

• Differences are smaller than the line thickness

vv*0.001

Switch instant

Full solution (red)


Summary

• Efficient electro‐thermal simulation by reduction of THERMAL models

• MOR with projection techniques by moment matching– Automatic MOR from ANSYS to Simplorer

• Complex models with more inputs are feasible• Field values (Temperature) recovering from system solution

• ROM switch for changing conditions in the system matrices (velocity)


Acknowledgments

• Evgeny Rudnyi– CADFEM GmbH

• Xiao Hu– ANSYS Inc

• AiF ZIM– Funding project KF2613901WD0


electro thermal battery pack with model order reduction · • cell level – electrodes ......

Documents