Electrical Circuit Battery Modeling in Simplorer

Electrical Circuit Battery Modeling in Simplorer®

Xiao Hu Eric Lin Zed Tang Scott Stanton ANSYS Inc October, 2009 © 2009 ANSYS, Inc. All rights reserved.

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ANSYS, Inc. Proprietary

Circuit Model Motivation • Simple enough for system level analysis – Models based on detailed electrochemistry or detailed CFD analysis is too complex and/or too time consuming for system level analysis • Accurate enough for virtual prototyping – Non-linear circuit voltage as a function of SOC – Transient I-V performance – Runtime prediction – Rate dependent capacity – Temperature effect – Accurate transient temperature prediction © 2009 ANSYS, Inc. All rights reserved.

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Outline of Models • Chen’s electrical model – Accurate if temperature and discharge rate is constant • Gao’s modification – Introduces temperature and discharge rate effect – Thermal network model introduced • Foster network thermal modeling – As accurate as CFD or testing • Battery system example

© 2009 ANSYS, Inc. All rights reserved.

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Chen’s Electrical Battery Cell Model • Accounts for non-linear opencircuit voltage • Capable of predicting runtime – Error less than 0.4% • Capable of predicting transient I-V performance – Error less than 30-mV • Can be implemented easily in circuit simulator – Current implementation is done in Simplorer® © 2009 ANSYS, Inc. All rights reserved.

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Rself-Discharge = 0

Reference: M. Chen, G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting Runtime and I-V performance,”IEE Trans. On energy conversion, vol. 21, no. 2, June 2006


Results – Comparison • Pulse discharge and charge.

Results from Simplorer®

Results from Chen

Reference: M. Chen, G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting Runtime and I-V performance,”IEE Trans. On energy conversion, vol. 21, no. 2, June 2006 © 2009 ANSYS, Inc. All rights reserved.

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Experimental Observation • Chen’s model works OK compared with testing data. – Under constant temperature and discharge rate • Rate effect and temperature effect are important to consider

Impact of discharge rate

Reference: L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans, Compon. Packag. Technol., vol. 25, no. 3, pp. 495505, Sep. 2002

Impact of temperature © 2009 ANSYS, Inc. All rights reserved.

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Suggested Modification by Gao • The discharge history is sensitized to rate of discharge and temperature through rate factor and temperature factor Chen’s model Gao’s model

Rate factor

Temperature factor

Reference: L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans, Compon. Packag. Technol., vol. 25, no. 3, pp. 495-505, Sep. 2002 © 2009 ANSYS, Inc. All rights reserved.

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Complete Circuit Model for Li-ion Battery: 1 Cell • Electrical circuit and thermal circuit are coupled • Electrical circuit provides power to thermal circuit • Thermal circuit provides temperature to electrical circuit • Includes Positive Temperature Coefficient (PTC)

Electrical/thermal interaction

Rcond

Rcond

T2

T1 Rconv

Tptc Rconv

Rconv

Ambient © 2009 ANSYS, Inc. All rights reserved.

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Simplorer® Implementation of Gao’s Model with PTC and 3 T Nodes

Implemented using VHDL-AMS


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Results –Rate/Temperature Effect Added

Impact of temperature

Impact of rate


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Results – No Overloading • Discharge with a resistor of 10 Ohm. • Temperature close to ambient

PTC and Battery Temperature

Voltage


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Results – Overloading • Discharge with a resistor of 2 Ohm. • Temperature of PTC goes high

PTC and Battery Temperature

Voltage


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From Thermal Network to Foster Network • Even though the thermal network method works OK, the model has limited accuracy due to the fact that it has only a limited number of thermal nodes, two in the example • A Foster network can be used to replace the thermal network • Foster network is as accurate as CFD or testing • A Foster network is a ladder of RC network shown • The response of the Foster network system is a sum of several exponentially decaying terms.

R1

R2

R3

R4

R5

R6

C1

C2

C3

C4

C5

C6

0

Foster network


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What is an LTI system? • A LTI system is a Linear Time Invariant (LTI) system • Linear means that it satisfies superposition • Time invariant means the behavior will not change if you test it tomorrow • The Foster network is a LTI system

• Battery cooling problem can be treated like a system, in which the inputs are the power generated by individual batteries and the outputs are temperatures at user specified locations • Under certain conditions, such a system is a LTI system

Battery1 Power Battery2 Power Battery3 Power


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Temperature1

LTI

Temperature2 Temperature3


Characteristics of LTI Systems • Impulse (or step) response completely characterize such systems • The Laplace transform of the impulse response is the transfer function of such a system • Any transient response of the system is the convolution of input and the impulse response • If two LTI systems have the same impulse (or step) response (or transfer function), then the two systems have identical behavior. • The output of the two systems are the same provided that the input to the two systems are the same – one can replace one with another even though two systems may have completely different internal structure • Electrical analogy works for mechanical/thermal systems • Both the Foster network and battery system are LTI systems • If we can find resistance and capacitance of the Foster network such that it has the same impulse (or step) response as the battery thermal system, the transient behavior of the battery system can be represented by the Foster network. © 2009 ANSYS, Inc. All rights reserved.

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Electrical Model Plus LTI Foster Network • Electrical circuit part is unchanged • Thermal network model is replaced with the Foster network – The Foster network is curve fitted to have the same impulse (or step) response as the battery thermal system using CFD. • Battery circuit model provides power to Foster network and Foster network returns temperature to battery circuit model – This aspect is similar to the thermal network approach


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Complete Circuit Model for Li-ion Battery: 1 Pack • Electrical circuit and Foster network are coupled • Electrical circuit provides power to Foster network • Foster network provides temperature to electrical circuit

Electrical/thermal interaction

Battery1 Power Battery2 Power Battery3 Power


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Temperature1

Foster LTI

Temperature2 Temperature2


Example • The thermal model is replaced by a LTI Foster network • The Foster network is curve fitted to have the same impulse response as CFD. • Using step response for curve fitting is also OK. • The LTI Foster network is then as accurate as CFD

Battery5 Battery4 Battery3 Battery2 Battery1 Battery0

Fluid Flow Region


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LTI Foster Network Model – Simplorer® Implementation of One Pack • The LTI Foster network model is within a sub-circuit Rseries

RT_S

RT_L I1 Port1

R1

R2

R4

R5

R8

R7

R6

R3

R9

R10

R11

R12

R16

R15

R14

R13

R17

R18

R19

R20

R24

R23

R22

C1

C2

C4

C5

C8

C7

C6

C3

C9

C10

C11

C12

C16

C15

C14

C13

C17

C18

C19

C20

C24

C23

C22

V

V

VM11

+

V

VM12

+

V

VM10

+

V

VM9

+

V

VM7

+

V

VM8

+

V

VM6

+

V

VM5

+

V

VM3

+

VM4

V

V

VM2

+

+

VM1

T00

R21

batt00_P_input

Port2

C21

0

R48

R47

R46

R45

R41

R42

R43

R44

R40

R39

R38

R37

R33

R34

R35

R36

R32

R31

R30

R29

R25

R26

R27

C48

C47

C46

C45

C41

C42

C43

C44

C40

C39

C38

C37

C33

C34

C35

C36

C32

C31

C30

C29

C25

C26

C27

V

VM14

+

+

V

VM13

V

+

+

VM15

V

VM16

V

VM18

+

+

+

VM17

V

VM19

V

VM20

V

VM22

+

VM21

R28

batt01_P_input

T01

0

VM23

V

+

VM24

+

Port3

V

I2

+

CONST

V

VOC

V

IBatt

CT_L

+

CONST1 CT_S

+

Ccapacity

C28

0

Port4

Port5

R49

R50

R51

R52

R56

R55

R54

R53

R57

R58

R59

R60

R64

R63

R62

R61

R65

R66

R67

R68

R72

R71

R70

C49

C50

C51

C52

C56

C55

C54

C53

C57

C58

C59

C60

C64

C63

C62

C61

C65

C66

C67

C68

C72

C71

C70

V

VM35

+

V

+

+

VM36

V

VM34

V

+

+

VM33

V

VM31

V

+

+

VM32

V

VM30

V

VM29

+

V

VM27

+

+

V

VM28

V

VM26

V

VM25

I3

+

R3

R2

+

R1

R69

batt02_P_input

C1

I4

U1

Port7

R96

R95

R94

R93

R89

R90

R91

R92

R88

R87

R86

R85

R81

R82

R83

R84

R80

R79

R78

R77

R73

R74

R75

C96

C95

C94

C93

C89

C90

C91

C92

C88

C87

C86

C85

C81

C82

C83

C84

C80

C79

C78

C77

C73

C74

C75

V

VM38

+

V

+

+

VM37

V

VM39

V

+

+

VM40

V

VM42

V

+

+

VM41

V

VM43

V

VM44

+

V

+

VM46

+

VM45

V

VM47

V

VM48

V

LTI Circuit

Port6

CONST

+

E1

0

C3 +

I7

C69

T02

CONST2 C2

R76

batt03_P_input

Simplorer2

C76

0

T03

R97

R98

R99

R100

R104

R103

R102

R101

R105

R106

R107

R108

R112

R111

R110

R109

R113

R114

R115

R116

R120

R119

R118

C97

C98

C99

C100

C104

C103

C102

C101

C105

C106

C107

C108

C112

C111

C110

C109

C113

C114

C115

C116

C120

C119

C118

V

VM59

+

V

+

+

VM60

V

VM58

V

+

+

VM57

V

VM55

V

+

+

VM56

V

VM54

V

VM53

+

V

VM51

+

+

V

VM52

V

+

+

Port8

VM50

V

VM49

0

R117

batt04_P_input

I5 R7

R6

0

C4

CONST3 C5

E2

C6

V

VM62

+

V

+

+

VM61

V

VM63

V

+

+

VM64

V

VM66

V

+

+

VM65

V

VM67

V

VM68

+

V

+

VM70

+

VM69

V

VM71

V

+

VM72

V

T04

I8

C117

Port9

+

R5

R144

R143

R142

R141

R137

R138

R139

R140

R136

R135

R134

R133

R129

R130

R131

R132

R128

R127

R126

R125

R121

R122

R123

R124

C144

C143

C142

C141

C137

C138

C139

C140

C136

C135

C134

C133

C129

C130

C131

C132

C128

C127

C126

C125

C121

C122

C123

C124

batt05_P_input

Port10 I6

CONST

0

Port11 T05

0

Port12

RLoad

R9

R10

R11

37.50 Curve Info U1.T00

TR C7

CONST4 I9

C8

E3

TR

C9 CONST

TR TR TR

0

TR

U1.T01 U1.T02 U1.T03 U1.T04 U1.T05

25.00 R13

R15

R14

CONST5 I10

C11

E4

Y1

C10 C12

CONST

12.50 0

R17

R18

R19

C13

CONST6 I11

E5

C14

C15 CONST

0.00 0.00

0

200.00

400.00

600.00 Time [s]

800.00

1000.00

1200.00

0


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LTI Foster Network Model Results •

Results from the Foster network are so close to Fluent that they are on top of each other

Battery 0

Battery 1

Battery 2

Battery 3

Battery 4

Battery 5


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System Level Circuit Model for Li-ion Battery

• Cells connected in series and parallel combinations to form packs • Packs are then connected series and parallel combinations to form final configuration © 2009 ANSYS, Inc. All rights reserved.

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An Example of Sixty Cells in Serial and Parallel

Five cells


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Results – Voltage and Current • The peak voltage is approximately 16 V – Result of serial connection of four batteries • The peak current drawn is approximately 3.25 Amp compared with 0.4 Amp for single battery case. And yet the runtime is almost doubled. – Result of parallel connection of 15 batteries – Estimated to be 0.4/(3.25/15)x8000 sec without rate factor consideration

Current

Voltage © 2009 ANSYS, Inc. All rights reserved.

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Battery in a Control System with a Motor Controller

Battery


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Results – Motor Performance Velocity Command

Ansoft LLC

induction_machine_DC_BusCap

2800.00

Measured Rotor Speed

Ansoft LLC


2800.00

Curve Info

Curve Info

Vel_com

ASM_2.N

TR

TR

2600.00

2400.00

2400.00

Vel_com

ASM_2.N [rpm]

2600.00

2200.00

2200.00

2000.00

2000.00

1800.00

1800.00

1600.00

1600.00 0.00

200.00

400.00

600.00

800.00

1000.00

0.00

200.00

400.00

Time [s]

600.00

800.00

1000.00

Time [s]

Measured Rotor Speed

Velocity Command Torque

Ansoft LLC


250.00 Curve Info ASM_2.MI TR

ASM_2.MI [NewtonMeter]

200.00

150.00

Torque

100.00

50.00

0.00 0.00

200.00

400.00

600.00

800.00

1000.00

Time [s]


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Results – Battery Performance

Battery Voltage

Ansoft LLC


Battery Current

Ansoft LLC

200.00


300.00

Curve Info

Curve Info

AM4.I

VM2.V

TR

TR

175.00

250.00 150.00

200.00

AM4.I [A]

VM2.V [V]

125.00

100.00

150.00

Rotor speed

75.00

100.00 50.00

50.00 25.00

0.00 0.00

200.00

400.00

600.00

800.00

0.00

1000.00

0.00

Time [s]

400.00

600.00

800.00

1000.00

Time [s]

Battery Voltage


200.00

Battery Current

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Conclusions • Electrical battery models implemented in Simplorer® have demonstrated its capability to capture battery non-linear voltage, transient I-V performance, etc. • Models have been tested in system environment using a control system with a motor controller • Circuit model can be coupled with thermal network model to include temperature effects on battery performance • Foster network has demonstrated its capability to replace CFD for thermal analysis since it is as accurate as CFD • Advantages of Simplorer – – – – –

Circuit simulator for the electrical and thermal circuits. Customizable using VHDL-AMS Multi-domain system level simulation quite easy and efficient Communicates with ANSYS CFD/Mechanical and Maxwell. Simplorer 8.1 automatically extracts the Foster network parameters


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Appendix : list of papers • M. Chen, G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting Runtime and I-V performance,” IEEE Trans. On energy conversion, vol. 21, no. 2, June 2006 • L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans, Compon. Packag. Technol., vol. 25, no. 3, pp. 495-505, Sep. 2002


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