an electrochemical simulation study of discharge ...€¦ · - e-verito - e2o plus - e-supro 2017...

Copyright © 2019 Mahindra Electric. All rights reserved.

An electrochemical simulation study of discharge

characteristics of Li-ion batteries

1

Malay JanaEnergy Systems

Mahindra Electric Mobility Limited

Bangalore, India

GT Conference I Jan 27, 2020

Copyright © 2019 Mahindra Electric. All rights reserved.2

Overview of Talk

• Company introduction

• Introduction to Li ion battery

• Battery modeling : Electrochemical modeling Vs. Equivalent circuit

modeling

• Case studies on NMC and LFP batteries:

1. An electrochemical simulation study of temperature dependent

diffusivity on discharge characteristics of NMC cell

2. Effect of cell parameters on the state of charge estimation in LFP cell -

An electrochemical simulation study


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3Copyright © 2019 Mahindra Electric. All rights reserved.

Mahindra’s electric journey


https://www.cataler.co.jp/en/aee2018/electro/lithium.php

4

Introduction

https://www.azom.com/article.aspx?ArticleID=14584

Why battery modelling?

• Replicates the physical cell and can predict the

cell behavior at different operating conditions

much faster than the physical tests

• Manual and technical resources spent for

experiments can be reduced, thereby reducing

cost

Outputs from battery modelling:

• State-of-charge (SOC) and State-of-health (SOH)

estimation

• Modelling the thermo-electric behaviour of batteries

• Algorithm development and system-level optimization

• Real-time simulation for battery management system

design


Equivalent circuit modeling

(Parametrization of battery using R, C parameters)

Electrochemical modeling

(Actual electrochemical reactions considered)

R0

R1 R2

C1 C2OCV

• Simpler and faster

• Accuracy gets compromised at harsh

conditions, such as high C-rate, low

temperature

• Kinetics not involved

• Less information obtained regarding actual

electrochemical reactions

• Based on partial differential equations and finite element

modelling - takes longer computational time

• More complex and intensive than ECM

• Detailed description of input values required - optimization

of these input values should be done to get accurate

results

• Accurate – efficient compared to equivalent circuit

modeling at harsh conditions

https://www.gtisoft.com/blog-post/lithium-ion-battery-modeling-for-the-automotive-engineer/

4

Battery Modeling: An Indispensable Tool


Diffusion in

Electrolyte

Diffusion in Solid

Particles

Butler-VolmerKinetics

+

Physical process involved in Li-ion battery

Set of equations + Boundary condition = Newman Model for Li-ion

Electrochemical Modelling

Electrode reactions are inherently complex as they involve:

• Interfacial charge transfer,

• Mass transport, many species,

• Different timescales,

• Thermodynamics and kinetics,

• Chemical, material and electrical properties.

Complexity increases due to adsorption/desorption or by insertion and extraction and by the presence of two or

three phases.

A. Jokar et. al. J. Power Sources, 2016, 327

Charge

conservation

Copyright © 2019 Mahindra Electric. All rights reserved.Ref: AutoLion User’s Manual 7

Electrochemical Modeling

• Cathode, separator, and anode are discretized in the “thickness”

direction

• In each finite control volume of the cathode, separator and anode,

there is one spherical representation of active material

• Each of these materials are discretized in constant volumes in the

radial direction.

• Function comes as a current flux which has to be multiplied to surface

area of the particles.

Description Equation Discretization

Charge

ConservationSolid-Phase 0 =

𝜕

𝜕𝑥𝜎𝑠𝑒𝑓𝑓 𝜕𝜙𝑠

𝜕𝑥− 𝑗𝐿𝑖 − 𝑎𝑑𝑙𝐶

𝜕(𝜙𝑠 − 𝜙𝑒)

𝜕𝑡Thru-Plane (Anode to Cathode collector) direction

Electrolyte-Phase 0 =𝜕

𝜕𝑥𝜅𝑒𝑓𝑓

𝜕𝜙𝑒

𝜕𝑥+

𝜕

𝜕𝑥𝜅𝐷𝑒𝑓𝑓 𝜕lnce

𝜕𝑥+ 𝑗𝐿𝑖 + 𝑎𝑑𝑙𝐶

𝜕(𝜙𝑠 − 𝜙𝑒)

𝜕𝑡Thru-Plane (Anode to Cathode collector) direction

Species

Conservation

Electrolyte-Phase

Li+𝜕

𝜕𝑡[𝜀𝑐𝑒] =

𝜕

𝜕𝑥𝐷𝑒𝑒𝑓𝑓 𝜕ce

𝜕𝑥+1 − 𝑡+

0

𝐹𝑗𝐿𝑖 Thru-Plane (Anode to Cathode collector) direction

Active Material Li𝜕𝑐𝑠𝜕𝑡

=1

𝑟2𝜕

𝜕𝑟𝐷𝑠𝑟

2𝜕c𝑠𝜕𝑟

Radial direction

Variables:

x = distance in the thru-plane direction

t = time

σs = solid phase conductivity

ϕs = solid phase potential

ϕe = liquid phase potential

adl = specific interfacial area

Table 1: Summary of Governing Equations

C = specific capacitance

jLi = reaction current of Li

κeff= electrolyte effective ionic conductivityκDeff = effective diffusional conductivity

ce = Li+ concentration in the electrolyte

cs = Li+ concentration in solid

ε = porosity

Deeff = electrolyte phase Li Diffusion coefficient

t+0 = transference number

F = Faraday's constant

r = particle radius


An electrochemical simulation study of temperature

dependent diffusivity on discharge characteristics of NMC cell

8


SluggishFasterElectrochemical kinetics

• High accessible capacity

• Age faster

• Low accessible capacity

• Age slower

Temp (°C) 45 25 0 -10 -20 -30

Normalized capacity (Ah) 105.6 100 88.67 81.80 74.32 53.59

Accessible capacity of Li ion battery is highly dependent on the diffusivity of Li ion, which increases as a function of temperature

https://gpandhuman.com/2018/05/17/the-self-care-battery/

9

Accessible Capacity with Temperature


ACS Appl. Mater. Interfaces 2017, 9, 16, 13999-14005

Arrhenius equation:

• The values of diffusivity multiplier (DM) and hence, the

diffusivity values are optimized for cathode material at

different temperatures

• The optimized DM for 25°C is found to be 1

Validation of electrochemical model

Diffusivity = DM × 10-14 cm2/sec

𝐷 = 𝐷𝑜𝑒−𝐸𝑎𝑘𝑇

D : Li diffusivity

Do : Pre-exponential factor

Eg : Activation energy

T : Absolute temperature

k : Boltzmann constant

10

Diffusivity of Li Ion Battery


Temp

(°C)

Error at

0.1C (V)

Error at

0.33C (V)

Error at

0.5C (V)

Error at

1C (V)

Error at

2C (V)

45 0.02 0.03 0.03 0.04 0.07

25 0.02 0.03 0.03 0.03 0.06

0 0.03 0.04 0.02 - -

• Higher C-rates above 0.5C are considered for

higher temperatures only, as it is not allowed to

draw current at higher C-rate at low temperatures.

• The predicted values of terminal voltages obtained

from electrochemical model are in good agreement

with experimental values.

11

Validation of Electrochemical Modeling


Temp

(°C)

Error at

0.1C (V)

Error at

0.33C (V)

Error at

0.5C (V)

-10 0.04 0.01 0.04

-20 0.04 0.05 0.09

-30 0.04 0.06 0.10

• At low temperatures, especially -20°C and -30°C, the

predicted values of terminal voltages do not match well

with experimental values

• Further optimization needed – diffusivity values might be

SOC dependent

12

Validation of Electrochemical Modeling


• Diffusivity reduces as the temperature decreases

• The effect of C-rates is not significant at temperatures above 0°C

• The diffusivity increases as a function of C-rate at low

temperature

• The reported capacity has been normalized considering the

capacity at 1C rate and 25°C to be 100 Ah

• Higher diffusivity Higher capacity

• The diffusivity becomes higher at higher C-rate at low

temperature due to internal heating, cell capacity reduces

since some of the energy are lost into heat.

13

Diffusivity as a Function of C-rates and Temperatures


1. Discharge behavior of NMC cell have been simulated through

a built-in electrochemical model using AutoLion software.

2. The discharge voltage curves match well with experimental

data having absolute error values within 0.10 V.

3. Diffusivity values increases as a function of temperature.

4. The effect of C-rates on diffusivity becomes significant at low

temperature.

5. This electrochemical model can be used to predict cell

behavior at different operating conditions – thermal and battery

management systems

Optimum temperature range

http://dc-ts.com/advanced-battery-thermal-management-system/14

Summary


Effect of cell parameters on the state of charge estimation-An

electrochemical simulation study


• Materials of battery components

• Cell configuration and accessory

parts

• Interfacial definitions

• Thermal features

Necessary inputs and checks

Simulation

Software

Capacity,

Porosity comparable to

actual Li-ionCheck!!

• Discharge profile

• Thermal profile

• SEI growth profile

• Cell Life

• Many other details of the cell

Optimization of several parameters

Basic discharge and thermal profile

Refinement

Optimizing Parameters:

• Mass Loading

• Electrode thickness

• OCV at 100% SoC

• N/P ratio

• Particle size

Pre-processing

Simulation Software: GT Suite AutoLion

16

Modelling of LFP Battery


Discharge Profile of LFP @ 25 °C

• Optimized data obtained by fixing the particle

size to 5 micron for anode and 0.25 micron for

LFP

• Simulation with bigger particle sizes exhibits

lower capacity and viz-a-viz

• Voltage lag is evident for all the conditions

• Voltage lag is addressed by changing

resistance

17

Validation of Discharge Profile


Cell Resistance

Film resistance Contact resistance

𝑂ℎ𝑚′𝑠 𝐿𝑎𝑤: −𝜎𝑠𝑒𝑓𝑓 𝜕Φ𝑠

𝜕𝑥= 𝑖𝑠

𝜕(𝜀𝑒𝑐𝑒)

𝜕𝑡= 𝛻 ∙ 𝐷𝑒

𝑒𝑓𝑓𝛻𝑐𝑒 +

1 − 𝑡+0

𝐹𝑎𝑠𝑗

𝜕(𝜀𝑠𝑐𝑠)

𝜕𝑡=𝐷𝑠

𝑟2

𝜕 𝑟2𝜕𝑐𝑠𝜕𝑟

𝜕𝑟

18

Influence of Cell Resistances

𝑖 = 𝑖0. [expαᴧ 𝑛𝐹

𝑅𝑇η − exp(−

α𝑐 𝑛𝐹

𝑅𝑇η)


• Improvement in curve fitting by optimizing

the resistance values in the simulation

• Both the different types resistance

parameters used

• Better understanding of the effect of

different type of resistances

Discharge Profile of LFP @ 25 °C by optimizing resistance

19

Correction to Voltage Mismatch


@ 25°C @ 1C

Validation for Other C-rates and Temperatures

25°C 45°C

• The voltage profile obtained from the electrochemical model matches well with experimental data


Amb. Temp.

(°C)

C-rate SOCTest,

%

SOCModel_

CR, %

SOCModel_

FR, %

25 1 100 100 100

0.5 101.7 100.4 100.4

0.3 102.7 100.8 101.4

45 1 102.5 100.4 101

0.5 102 100.8 101.7

0.3 102.2 100.8 101.8

Amb.

Temp. (°C)

C-rate ΔTempTest

, %ΔTempModel

_CR, %ΔTempMode

l_FR, %

25 1 7.51 7.7 5.8

0.5 4.7 3.6 2.8

0.3 2.9 2 1.6

45 1 6 4.6 4.4

0.5 3.3 2.2 2.2

0.3 1.5 1.4 1.3

SOC values from experimental testing and

prediction from the model

Temperature rise experimental testing and

prediction from the model

Reference

21

Predicted SOC and Temperature Rise

Capacity match

• Model predicted (contact resistance) temperature

rise values are close to experimental values


1. Effect of cell parameters such as particle size, electrode resistance on discharge behaviour is

investigated

2. Particle size is crucial, higher surface area results in higher capacity and also higher extent of

SEI formation

3. Battery degradation is closely associated to the particle size and the changes in resistances

4. These results can be used to design cell as per our OEM’s requirement

5. These models can also be used to predict the cycle life and pin down the cause of capacity

degradation

22

Summary


Thank Youfor staying charged

23

ACKNOWLEDGEMENT

Dr. Deya Das

Dr. Subhra Gope

Dr. Suman Basu

an electrochemical simulation study of discharge ...€¦ · - e-verito - e2o plus - e-supro 2017...

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