for thermal analysis since it is as accurate as CFD. ⢠Advantages of Simplorer. â Circuit simulator for the electrical and thermal circuits. â Customizable using ...
Electrical Circuit Battery Modeling in Simplorer®
Xiao Hu Eric Lin Zed Tang Scott Stanton ANSYS Inc October, 2009 © 2009 ANSYS, Inc. All rights reserved.
1
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.
2
ANSYS, Inc. Proprietary
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.
3
ANSYS, Inc. Proprietary
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.
4
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
ANSYS, Inc. Proprietary
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.
5
ANSYS, Inc. Proprietary
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.
6
ANSYS, Inc. Proprietary
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.
7
ANSYS, Inc. Proprietary
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.
8
ANSYS, Inc. Proprietary
Simplorer® Implementation of Gao’s Model with PTC and 3 T Nodes
Implemented using VHDL-AMS
© 2009 ANSYS, Inc. All rights reserved.
9
ANSYS, Inc. Proprietary
Results –Rate/Temperature Effect Added
Impact of temperature
Impact of rate
© 2009 ANSYS, Inc. All rights reserved.
10
ANSYS, Inc. Proprietary
Results – No Overloading • Discharge with a resistor of 10 Ohm. • Temperature close to ambient
PTC and Battery Temperature
Voltage
© 2009 ANSYS, Inc. All rights reserved.
11
ANSYS, Inc. Proprietary
Results – Overloading • Discharge with a resistor of 2 Ohm. • Temperature of PTC goes high
PTC and Battery Temperature
Voltage
© 2009 ANSYS, Inc. All rights reserved.
12
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
13
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
14
Temperature1
LTI
Temperature2 Temperature3
ANSYS, Inc. Proprietary
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.
15
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
16
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
17
Temperature1
Foster LTI
Temperature2 Temperature2
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
18
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
19
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
20
ANSYS, Inc. Proprietary
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.
21
ANSYS, Inc. Proprietary
An Example of Sixty Cells in Serial and Parallel
Five cells
© 2009 ANSYS, Inc. All rights reserved.
22
ANSYS, Inc. Proprietary
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.
23
ANSYS, Inc. Proprietary
Battery in a Control System with a Motor Controller
Battery
© 2009 ANSYS, Inc. All rights reserved.
24
ANSYS, Inc. Proprietary
Results – Motor Performance Velocity Command
Ansoft LLC
induction_machine_DC_BusCap
2800.00
Measured Rotor Speed
Ansoft LLC
induction_machine_DC_BusCap
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
induction_machine_DC_BusCap
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]
© 2009 ANSYS, Inc. All rights reserved.
25
ANSYS, Inc. Proprietary
Results – Battery Performance
Battery Voltage
Ansoft LLC
induction_machine_DC_BusCap
Battery Current
Ansoft LLC
200.00
induction_machine_DC_BusCap
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
© 2009 ANSYS, Inc. All rights reserved.
200.00
Battery Current
26
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
27
ANSYS, Inc. Proprietary
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
© 2009 ANSYS, Inc. All rights reserved.
28
ANSYS, Inc. Proprietary