Fast Charging Strategy Optimization Based

on Electrochemical Model and Dynamic

Programming for a Lithium Ion Battery Cell

Meng Xu, Graduate Student

Xia Wang, Professor

Department of Mechanical Engineering

Oakland University, Rochester, MI

October 4, 2018

Enabling Li-ion Battery Fast Charge?

2

“Range Anxiety” Fast Charge

Challenges of Fast Charge

3

Fast Charge

High temperature Thermal runawayHeat generation

SEI growth Degradation / Capacity fade

Li plating

Charging Strategy Review

4

Constant Current Constant Voltage (CCCV) Charging

A123 26650 LFP Cell Data

Charging Strategy Review

5

• Decrease charging time• Low temperature rise• High charging efficiency

Multistage Constant Current Charging (MCC) (Vo et al. 2014)

Source: T.T. Vo, X. Chen, W. Shen, A. Kapoor, New charging strategy for lithium-ion batteries based on the integration of Taguchi method and state of charge estimation, J. Power Sources 273 (2015) 413-422

Objective

6

• To study the effect of charging protocol on capacity fade and

thermal behavior by developing an electrochemical-thermal-

capacity fade coupled model

• To optimize the charging protocol based on Dynamic

Programming optimization algorithm

Methodology

7

Multi-Step Fast Charging

Protocol

Electrochemical-Thermal-Capacity

Fade Coupled Model

SEI Increase Capacity Fade Li Dendrites Temperature Charging Energy

Efficiency

Dynamic Programming (DP)

Optimization Algorithm

Methodology

8

Model Validation

9

A123 2.3 Ah LFP 26650

MACCOR system 4200

Battery test equipment

Source: T.T. Vo, X. Chen, W. Shen, A. Kapoor, New charging strategy for lithium-ion batteries based on the integration of Taguchi method and state of charge estimation, J. Power Sources 273 (2015) 413-422

15 minutes / 20% ~ 80% SOC Fast Charging Protocols

10

Impact of Cycle Number and Protocol on Capacity Fade

11

• Low-High charging protocols obtain lower capacity fade than High-Low protocols• The 2-step Low-High protocol results in the lowest capacity fade

Dynamic Programming (DP) Optimization

12

0%

32%

48% 48%

64%

16%

32%

64%

80%

48%

Operating Conditions: Charging SOC = 0% ~ 80% Charging time = 30 mins ∆𝑡 = 10 mins Charging step = 3 Charging current

= 0.96C, 1.92C, 2.88C ∆SOC = 16% (0.96C)

Goal: m𝒊𝒏 𝑻(𝟑𝟎𝒎𝒊𝒏, 𝟖𝟎%)

Constrains: 𝑻 < 𝑻𝒎𝒂𝒙, 𝒄𝒆𝒍𝒍

SOC < 80%

𝑻, 𝒕, 𝑺𝑶𝑪𝒊

6 by 4 solution matrix

10 min 30 min20 min0 min

1 2 3 4

1

2

3

4

5

6

𝑻, 𝒕, 𝑺𝑶𝑪𝒊, 𝑺𝑶𝑪𝒊−𝟏

𝟑𝟎𝟓𝑲, 𝟏𝟎, 𝟒𝟖%, 𝟎%

Compare

𝟑𝟏𝟎𝑲, 𝟐𝟎, 𝟒𝟖%, 𝟑𝟐%

𝟑𝟏𝟐𝑲, 𝟐𝟎, 𝟒𝟖%, 𝟏𝟔%

𝑻, 𝟑𝟎𝒎𝒊𝒏, 𝟖𝟎%,64%

Capacity Fade Optimization

13

SEI Potential Optimization

14

Temperature Rise Optimization

15

Optimization at Different Ambient Temperatures

16

Conclusions

17

• An electrochemical-thermal-capacity fade coupled model for a Li-ion battery cell is developed using COMSOL Multiphysics

• The effect of fast-charging protocol on capacity fade with charging-discharging cycles is studied

• A Dynamic Programming Optimization algorithm is developed using COMSOL Livelink - MATLAB to optimize the fast charging protocol

• The cost function include capacity fade, SEI potential, and temperature rise.

Thank you!

Acknowledgement

18

Dr. Benjamin Reichman (BASF Battery Materials - Ovonic)

Enabling Li-ion Battery Fast Charge?

19Source: https://techflourish.com

1% market share

• Cost• “Range anxiety”

Fast charging Li-ion batteries …

Typical Lithium Ion Cells

20

Coin/Button Cell

Cylindrical Cell

Prismatic Cell

Pouch Cell

Load

Positive

Li+

Li+

Lithium Ion Electrochemical Cell

e-

Positive Electrode:

𝐿𝑖𝑥𝐶6𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

𝒙𝑳𝒊+ + 𝒙𝒆− + 𝐶6

𝐿𝑖1−𝑥𝑀𝑂2 + 𝑥𝐿𝑖+ + 𝑥𝑒−𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

𝐿𝑖𝑀𝑂2

Negative Electrode:

Separator Negative

e-

I I

I

Cu

rren

t C

oll

ecto

r

Cu

rren

t C

oll

ecto

r 𝐿𝑖𝑀𝑂2

𝐶6

Electrolyte

Al foil

Cu foil

21

Typical Lithium Ion Battery Models

22

Predictability

CP

U T

ime

Li+rprn

Discharge

r

x

x r

P2D Electrochemical Model

23

𝑥𝐿𝑝𝑜𝑠 𝐿𝑠𝑒𝑝 𝐿𝑛𝑒𝑔

𝑥 = 0𝑟 𝑟

e-

Separator Negative Electrode

I

Cu

rren

t C

olle

cto

r

Cu

rren

t C

olle

cto

r

Load

Charge Conservation in x: 𝛻 ∙ 𝒊𝑙 = 𝛼𝑣𝑖𝑙𝑜𝑐𝛻 ∙ 𝒊𝑠 = −𝛼𝑣𝑖𝑙𝑜𝑐;𝛻 ∙ 𝒊𝑠 + 𝛻 ∙ 𝒊𝑙 = 0;

Mass Conservation in x: 𝜖𝑙𝜕𝑐𝑙𝜕𝑡

+ 𝛻 ∙ 𝑵𝑙 =𝛼𝑣𝑖𝑙𝑜𝑐𝐹

Mass Conservation in r:𝜕𝑐𝑠𝜕𝑡

+ 𝛻 ∙ −𝐷𝑠𝜕𝑐𝑠𝜕𝑟

= 0

Electrochemical Kinetics: 𝑖𝑙𝑜𝑐 = nF𝑘0𝑐𝑙𝑐𝑠𝛼𝑎(1 − 𝑐𝑠,𝑚𝑎𝑥)

1−𝛼𝑎 𝐶𝑅𝑒𝑥𝑝𝛼𝑎𝐹𝜂

𝑅𝑇− 𝐶𝑂𝑒𝑥𝑝

−𝛼𝑐𝐹𝜂

𝑅𝑇

∅𝑠(𝑥, 𝑡)∅𝑙(𝑥, 𝑡)

c𝑠(𝑟, 𝑡)c𝑙(𝑥, 𝑡)

𝐿𝑖1−𝑥𝑀𝑂2 + 𝒙𝑳𝒊+ + 𝒙𝒆−𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

𝐿𝑖𝑀𝑂2

e-e-

Electrolyte

Positive Electrode

𝒊𝒔

e-

Li+Li+e-

𝐿𝑖𝑥𝐶6𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒

𝒙𝑳𝒊+ + 𝒙𝒆− + 𝐶6

e-Li+ Li+

e-

Li+

𝒊𝒍

Li+e- 𝛻 ∙ 𝒊𝑠

𝛻 ∙ 𝒊𝑙

𝑖𝑙𝑜𝑐

𝑟

Thermal Model

24

Capacity Fade Model

25

Source: Ekström, Henrik, and Göran Lindbergh. "A model for predicting capacity fade due to SEI formation in a commercial graphite/LiFePO4 cell." Journal of The Electrochemical Society 162, no. 6 (2015): A1003-A1007.

• In addition to the main graphite-lithium intercalation reaction on the negative electrode, the parasitic lithium/solvent reduction reaction is also included in the model:

15 min 20 ~ 80% SOC Fast Charging Cycles

26

SEI Thickness Increase Cycle 1 – Cycle 3

27

• SEI increases with cycles• Low-High protocols have thinner SEI at cycle 3

Low-High

High-Low

Impact of Cycle Number and Protocol on Capacity Fade

28

• Low-High charging protocols obtain lower capacity fade than High-Low protocols• The 2-step Low-High protocol results in the lowest capacity fade • Utilization range shifts in the negative electrode

Optimization at Different Ambient Temperatures

29