Electrical Circuit Battery Modeling in Simplorer - Ansys

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. 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 


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 


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 

Rself-Discharge = 0 

circuit simulator 

– Current implementation is 

done in Simplorer ® 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 


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 

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 

Impact of discharge rate 

Impact of temperature 


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 


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) 

© 2009 ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary 

Rconv 

Electrical/thermal interaction 

Rcond Rcond 

T1 T2 Tptc 

Ambient 

Rconv Rconv

Simplorer ® Implementation of Gao’s 

Model with PTC and 3 T Nodes 

Implemented 

using VHDL-AMS 


Results –Rate/Temperature Effect 

Added 

Impact of rate 

Impact of temperature 


Results – No Overloading 

• Discharge with a resistor of 10 Ohm. 

• Temperature close to ambient 

Voltage PTC and Battery Temperature 


Results – Overloading 

• Discharge with a resistor of 2 Ohm. 

• Temperature of PTC goes high 

Voltage PTC and Battery Temperature 


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. 


0 

R1 

C1 C2 

R2 R3 

R4 

Foster network 

R5 

R6 

C3 C4 C5 C6

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 




LTI 

Temperature1 

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. 


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 


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 

Foster LTI 

Temperature1 

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 

Battery3 






Fluid Flow 

Region 


LTI Foster Network Model – Simplorer ® 

Implementation of One Pack 

• The LTI Foster network model is within a sub-circuit 

Ccapacity 

C1 

C4 

C7 

C10 

C13 

0 

0 

0 

0 

0 

0 

IBatt 

I7 

I8 

I9 

I10 

I11 

0 

VOC 

E1 

E2 

E3 

E4 

E5 

Rseries 

R1 

R5 

R9 

R13 

R17 

CT_S 

RT_S 

R2 

CT_L 

C2 C3 

R6 

C5 C6 

RT_L 

R3 

R7 

R10 R11 

C8 C9 

R14 

C11 C12 

R15 

R18 R19 

C14 C15 

RLoad 

CONST1 

CONST 

CONST2 

CONST 

CONST3 

CONST 

CONST4 

CONST 

CONST5 

CONST 

CONST6 

CONST 

Y1 

37.50 

25.00 

12.50 

I1 

I2 

I3 

I4 

I5 

I6 

Port1 

Port2 

Port3 

Port4 

Port5 

Port6 

Port7 

Port8 

Port9 

Port10 

Port11 

Port12 

LTI Circuit 

U1 

Simplorer2 


T00 

T01 

T02 

T03 

T04 

T05 

Curve Info 

U1.T00 

TR 

U1.T01 

TR 

U1.T02 

TR 

U1.T03 

TR 

U1.T04 

TR 

U1.T05 

TR 

0.00 

0.00 200.00 400.00 600.00 

Time [s ] 

800.00 1000.00 1200.00 

batt00_P_input 



0 

0 

0 

0 

0 

0 

+ 

V 

VM1 

+ 

V 

VM2 

+ 

V 

VM4 

+ 

V 

VM3 

+ 

V 

VM5 

+ 

V 

VM6 

R1 R2 R4 R5 

R8 R7 R6 R3 

R9 R10 R11 R12 

R16 R15 R14 R13 

R17 R18 R19 R20 

R24 R23 R22 R21 

C1 C2 C4 C5 

C8 C7 C6 C3 

C9 C10 C11 C12 

C16 C15 C14 C13 

C17 C18 C19 C20 

C24 C23 C22 C21 

+ 

V 

VM24 

+ 

V 

VM23 

+ 

V 

VM21 

+ 

V 

VM22 

+ 

V 

VM20 

+ 

V 

VM19 

+ 

V 

+ 

V 

R48 R47 R46 R45 

R41 R42 R43 R44 

R40 R39 R38 R37 

R33 R34 R35 R36 

R32 R31 R30 R29 

R25 R26 R27 R28 

C48 C47 C46 C45 

C41 C42 C43 C44 

C40 C39 C38 C37 

C33 C34 C35 C36 

C32 C31 C30 C29 

C25 C26 C27 C28 

+ 

V 

VM25 

+ 

V 

VM26 

+ 

V 

VM28 

+ 

V 

VM27 

+ 

V 

VM29 

+ 

V 

VM30 

R49 R50 R51 R52 

R56 R55 R54 R53 

R57 R58 R59 R60 

R64 R63 R62 R61 

R65 R66 R67 R68 

R72 R71 R70 R69 

C49 C50 C51 C52 

C56 C55 C54 C53 

C57 C58 C59 C60 

C64 C63 C62 C61 

C65 C66 C67 C68 

C72 C71 C70 C69 




+ 

V 

VM48 

+ 

V 

VM47 

+ 

V 

VM45 

+ 

V 

VM46 

+ 

V 

VM44 

+ 

V 

VM43 

+ 

V 

+ 

V 

R96 R95 R94 R93 

R89 R90 R91 R92 

R88 R87 R86 R85 

R81 R82 R83 R84 

R80 R79 R78 R77 

R73 R74 R75 R76 

C96 C95 C94 C93 

C89 C90 C91 C92 

C88 C87 C86 C85 

C81 C82 C83 C84 

C80 C79 C78 C77 

C73 C74 C75 C76 

+ 

V 

VM49 

+ 

V 

VM50 

C97 C98 C99 C100 

+ 

V 

VM52 

C104 C103 

+ 

V 

VM51 

+ 

V 

VM53 

+ 

V 

VM54 

R97 R98 R99 R100 

R104 R103 R102 R101 

R105 R106 R107 R108 

R112 R111 R110 R109 

R113 R114 R115 R116 

R120 R119 R118 R117 

+ 

V 

VM72 

+ 

V 

VM71 

+ 

V 

VM69 

C102 C101 

C105 C106 C107 C108 

+ 

V 

VM70 

+ 

V 

VM68 

+ 

V 

VM67 

+ 

V 

VM8 

VM17 

VM32 

VM41 

VM56 

C112 C111 

C136 C135 C134 C133 

C129 C130 C131 C132 

+ 

V 

VM65 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

VM7 

VM18 

VM31 

VM42 

VM55 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

VM9 

VM16 

VM33 

VM40 

VM57 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

VM10 

VM15 

VM34 

VM39 

VM58 

C110 C109 

C113 C114 C115 C116 

+ 

V 

VM66 

+ 

V 

VM64 

C128 C127 

+ 

V 

VM63 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

VM12 

VM13 

VM36 

VM37 

VM60 

C120 C119 

+ 

V 

VM61 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

+ 

V 

VM11 

VM14 

VM35 

VM38 

VM59 

C118 C117 

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 

+ 

V 

VM62 

C126 C125 

C121 C122 C123 C124

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 


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 


An Example of Sixty Cells in Serial and Parallel 

Five cells 


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 

Voltage Current 


Battery in a Control System with a Motor 

Controller 

Battery 


2600.00 

2400.00 

2200.00 

2000.00 

1800.00 

1600.00 

Results – Motor Performance 

Ansoft LLC induction_machine_DC_BusCap 

2800.00 

Curve Info 

Vel_com 

Velocity Command 

0.00 200.00 400.00 600.00 800.00 1000.00 

Time [s] 

Velocity Command 

TR 

Vel_com 


250.00 

Curve Info 

ASM_2.MI [NewtonMeter] 

200.00 

150.00 

100.00 

50.00 

0.00 

Torque 


2800.00 

Curve Info 

0.00 200.00 400.00 600.00 800.00 1000.00 

Time [s] 

Measured Rotor Speed 

Torque 


ASM_2.N [rpm] 

2600.00 

2400.00 

2200.00 

2000.00 

1800.00 

1600.00 

ASM_2.MI 

TR 

0.00 200.00 400.00 600.00 800.00 1000.00 

Time [s] 

Measured Rotor Speed 

TR 

ASM_2.N

Results – Battery Performance 


200.00 

Curve Info 

VM2.V [V] 

175.00 

150.00 

125.00 

100.00 

75.00 

50.00 

25.00 

0.00 

Battery Voltage 

Rotor speed 

0.00 200.00 400.00 600.00 800.00 1000.00 

Time [s] 

Battery Voltage 

TR 

VM2.V 


300.00 

Curve Info 

0.00 200.00 400.00 600.00 800.00 1000.00 

Time [s] 

Battery Current 


AM4.I [A] 

250.00 

200.00 

150.00 

100.00 

50.00 

0.00 

Battery Current 

AM4.I 

TR

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 


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

Electrical Circuit Battery Modeling in Simplorer - Ansys

Create successful ePaper yourself

Delete template?

Save as template?