1b. Battery Basics and Equivalent Circuit Model.pptx

Modeling and Simulation of Battery Bank from Cell to Pack for Electric Vehicles 2
OUTLINE
1. Batteries
2. Batteries configuration
3. Cell voltage for various types of the batteries
4. Roadmap for battery energy storage
5. CCCV Charging
6. Battery capacity, C rates
7. Battery state of charge
8. Battery state of health
9. Various types of the battery modeling methods
10. Cell level modeling

Introduction
Anode: The electrode where oxidation (loss of electrons) occurs during discharge. Electrons flow from the anode
to the external circuit.
Cathode: The electrode where reduction (gain of electrons) occurs during discharge. Electrons return to the
cathode through the external circuit.
Electrolyte: A substance, often a liquid or gel, that allows ions to move between the anode and cathode. It serves
as a medium for the flow of electric charge.
Separator: A physical barrier that prevents direct contact between the anode and cathode, allowing ions to move
while keeping the electrodes from touching.
CHARGING PROCESS DISCHARGING PROCESS

Source : Ding, Y., Cano, Z.P., Yu, A. et al. Automotive Li-Ion Batteries: Current Status and Future Perspectives. Electrochem. Energ. Rev. 2,
1–28 (2019). https://doi.org/10.1007/s41918-018-0022-z14

Ambient Temperature
Losses
C Rate
Aging
Proper sizing of the storage
Parameter identification
Pre-mature failure prediction for
stack level architecture
State estimation under real-time
conditions
Lifetime improvement under
rigorous drive conditions
Stack level health assessment
Factors affecting EV battery performance
Battery modeling challenges for electric vehicle applications

LCO – Lithium cobalt
oxide battery
NCA - Lithium nickel
cobalt aluminium oxide
NMC - Lithium-Nickel-
Manganese-Cobalt-
Oxide
LMO – Lithium-Ion
manganese oxide
battery
LFP - Lithium iron
phosphate batteries
(LiFePO4 )
LTO - lithium-
titanium-oxide
battery
Source: Miao, Yu, et al. "Current Li-ion battery technologies in electric vehicles and opportunities for
advancements." Energies 12.6 (2019): 1074.

Battery test procedure
Battery
Test
Procedure
Performance
Constant
Current
Variable Power
FUDS
HPPC
DST
Drive Cycle
NEDC
UDDS
EPA US06
IDC
Safety/Abuse
Life cycle
Accelerated
Aging
Baseline Life
Cycle
Need of Battery Modeling :
1. Reduces development
costs,
2. Results in higher user
satisfaction,
3. Reduces development
time,
4. Encourage innovation
and flexible design

Drive Cycles
0 100 200 300 400 500 600
Time [s]
0
10
20
30
40
Velocity
[m/s]
US06
0 200 400 600 800 1000 1200 1400
Time [s]
0
10
20
30
Velocity
[m/s]
UDDS
0 200 400 600 800 1000 1200
Time [s]
0
10
20
30
40
Velocity
[m/s]
NEDC
0 500 1000 1500 2000 2500
Time [s]
0
10
20
30
Velocity
[m/s]
FTP75

CCCV Charging
Constant Current-Constant Voltage (CC-CV) charging is a common charging technique used in lithium-ion
batteries to efficiently and safely charge the battery while maintaining a balance between the charging speed and
the battery's health.
2. Constant Voltage (CV) Charging:
 Once the battery reaches a specified voltage limit (in this case, 4.1 V per cell), the charging process transitions
from CC to CV mode.
 In the CV stage, the charging voltage is held constant at the specified limit while the charging current
decreases as the battery gets closer to full capacity.
 This stage is essential to prevent overcharging the battery, as the constant voltage ensures that the battery
voltage does not exceed the safe limit.
1. Constant Current (CC) Charging:
 In the CC stage, a constant current is applied to the battery module. This means that the charging current
remains constant throughout this phase.
 The purpose of the CC stage is to quickly charge the battery from a low state of charge (SOC) to a certain
voltage level. During this stage, the battery voltage increases gradually as it gets charged.

CCCV Charging
3. Completion of Charging:
 The CV stage continues until the battery's state of charge (SOC) reaches a predetermined level, typically
around 90% in this example.
 Once the battery SOC reaches the desired level, the charging process is halted, and the battery is considered
fully charged.
4. Discharging Phase:
 After reaching full charge, the battery can be discharged using a constant current (CC) method to return its
SOC to the initial level (10% in this case).
 Discharging the battery through the CC method ensures a controlled and consistent discharge rate until the
desired SOC is achieved, completing one cycle of the charging and discharging process.
openExample('simscapebattery/BatteryCCCVExample')

CCCV Charging
0 2000 4000 6000 8000 10000
Time (s)
3.6
3.8
4
4.2
Volt
Battery Voltage
0 2000 4000 6000 8000 10000
Time (s)
-10
0
10
20
Amp
Charging current
0 2000 4000 6000 8000 10000
Time (s)
40
60
80
100
SoC
%
Battery State of Charge

CCCV Charging

Battery Capacity
Battery capacity is defined as the total amount of electricity generated due to
electrochemical reactions in the battery and is expressed in ampere hours. For example, a
constant discharge current of 1 C (5 A) can be drawn from a 5 Ah battery for 1 hour.
Q .1 An automobile battery might have a 200 Ah rating. How long can this battery supply 20
amperes?
The actual ampere-hours delivered varies with battery age and condition, temperature and discharge
rate.

C RATES
A C-rate is a measure of the rate at which a battery is discharged relative to its maximum
capacity. A 1C rate means that the discharge current will discharge the entire battery in 1
hour.
C Rating Time Amp
1C 1Hour
2C
5C
10
C Rating Time Amp
1C/2 = 0.5C
C/5 = 0.2C
C/10 = 0.1C
12
Volt,
50
Ah

12 Volt, 50 Ah Battery connected with a DC load . Load current is 10 ampere. Calculate the %SoC of
the battery after 3hr .
Total Coulombs are available in batteries are based on Ah rating
Coulombs used =
SoC (used )=
CoulombsUsed
Total coulombs
× 100

An expression of the present battery capacity as a percentage of maximum capacity. SOC is
generally calculated using current integration to determine the change in battery capacity over time.
12 Volt, 50 Ah Battery connected with a DC load . Load current is 10
ampere. Calculate the %SoC of the battery after 3hr .

Measuring State of Charge in Electric Vehicles
 Electric vehicles (EVs) provide a cleaner alternative to traditional combustion engine vehicles by
using electricity as power source.
 This alternative power source allows the EVs to reduce the reliance on fossil fuels and cut down on
greenhouse gas emissions and air pollution. EVs operate by using electric motors powered by
batteries, which are the heart of any EV.
 These batteries determine the EV range, performance, and environmental footprint. However,
managing the battery inside an EV is complex due to the inherent characteristics of the battery itself,
including the battery energy density and weight, the thermal management, aging and degradation,
and the estimation of the SOC and state of health (SOH).
 The ability to track the SOC is crucial for managing battery systems efficiently and in applications
where the battery performance and longevity are critical.

Battery Capacity
Battery capacity is defined as the total amount of electricity generated due to electrochemical
reactions in the battery and is expressed in ampere hours. For example, a constant discharge
current of 1 C (5 A) can be drawn from a 5 Ah battery for 1 hour.
Q .1 An automobile battery might have a 200 Ah rating. How long can this battery supply 20 amperes?
The actual ampere-hours delivered varies with battery age and condition, temperature and discharge
rate.

C Rates
A C-rate is a measure of the rate at which a battery is discharged relative to its maximum
capacity. A 1C rate means that the discharge current will discharge the entire battery in 1
hour.
C Rating Time Amp
1C 1Hour
2C
5C
10
C Rating Time Amp
1C/2 = 0.5C
C/5 = 0.2C
C/10 = 0.1C
12
Volt,
50
Ah

SOH - State of Health
0 200 400 600 800 1000
Number of Cycles
0
25
50
75
100
State
of
Health
(%)
Battery State of Health over Time
State of Health (SoH) is a key indicator used to
describe the overall condition of a battery, particularly
in terms of how much capacity and performance it has
retained compared to its original state. SoH provides a
percentage value that reflects how much usable capacity
the battery has left.
SoH=
CurrentCapacity
NominalCapacity
∗100
0 10 20 30 40 50 60 70
Time (hours)
25
50
75
100
State
of
Charge
(SoC)
%
Battery Charging and Discharging Cycles

BATTERY STATE OF CHARGE (SOC)
 Battery State of Charge (SoC) is a measure that indicates the remaining energy or capacity of a
battery as a percentage of its total capacity.
 It quantifies how much charge is left in a battery relative to its full charge capacity, providing
insight into the current energy storage level.
SOC=
RemainingCapacity
TotalCapacity
∗100

𝑆𝑂𝐶 𝑓𝑖𝑛𝑎𝑙=𝑆𝑂𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 −
∫𝐼 (𝑡)𝑑𝑡
𝑄𝑟𝑎𝑡𝑒𝑑
∗ 100
A 12V lithium-ion battery has a capacity of 10 Ah. Initially, the battery is fully charged (100%
SOC). During use, a current of 2 A is discharged for 2 hours. Assume ideal conditions with no
losses. Estimate the SOC of the battery after 2 hours.
The Coulomb Counting Method estimates SOC as:
= Initial SOC (in percentage)
: Rated capacity of the battery (Ah).

• = 100%.
• Current I(t) = 2 A (constant current).
• Duration (t) = 2 hours.
• Battery Capacity = 10 Ah.
Calculate the Charge Withdrawn
The charge withdrawn is:
Charge Withdrawn=I(t)×t=2A×2 hours=4Ah
𝑆𝑂𝐶 𝑓𝑖𝑛𝑎𝑙=𝑆𝑂𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 −
∫𝐼 (𝑡)𝑑𝑡
𝑄𝑟𝑎𝑡𝑒𝑑
∗ 100
Calculate the Final SOC
𝑆𝑂𝐶 𝑓𝑖𝑛𝑎𝑙=100 −
4
10
∗100=60 %
The battery’s SOC after 2 hours of
discharge is 60%.

A 12V, 50 Ah battery is connected to a DC load. The load draws a constant current of 10 A.
• If the battery starts at 100% SOC, calculate the %SOC of the battery after 3 hours of
operation using the Coulomb Counting Method. Assume ideal conditions with no losses.
Coulombs used =
SoC (used )=
CoulombsUsed
Total coulombs
× 100

An expression of the present battery capacity as a percentage of maximum capacity. SOC is
generally calculated using current integration to determine the change in battery capacity over time.
12 Volt, 50 Ah Battery connected with a DC load . Load current is
10 ampere. Calculate the %SoC of the battery after 3hr .

12 Volt, 50 Ah Battery connected with a DC load . Load current is 10 ampere. Calculate the %SoC of
the battery after 3hr .
Coulombs used =
SoC (used )=
CoulombsUsed
Total coulombs
× 100

Charging time for a battery bank
you have a battery bank with a capacity of 200 Ah, and you want to charge it from
50% to 80% SoC using a charging rate of 20 amps
Charging time (in hours)=
(200 Ah x (80% − 50%))
20 Amp
Keep in mind that this calculation is an estimate, and the actual charging time may
vary depending on factors such as the battery chemistry, temperature, and
charging method.

SOC Estimations Techniques

Cell Load Current Profile, Voltage Behavior, SoC and Temperature Using 1RC

1RC EQUIVALENT CIRCUIT MODEL

1RC ECM MODEL PARAMETERS
SoC Breakpoints

Cell Behaviour
0 1 2 3 4
Time (s) 10
4
-40
-20
0
20
40
Amp
Battery Load Current
0 1 2 3 4
Time (s) 10
4
3
3.5
4
4.5
Volt
Battery voltage behaviour as per load current
0 1 2 3 4
Time (s) 10
4
0
25
50
75
100
SoC
%
Battery state of charge as per load current
0 1 2 3 4
Time (s) 10
4
20
25
30
35
(°C)
Battery temperature in (°C) as per load current

1RC ECM MODEL PARAMETERS
%% Thermal Properties
% Cell dimensions and sizes
cell_thickness = 0.0084; % m
(thickness of the cell)
cell_width = 0.215; % m (width of the
cell)
cell_height = 0.220; % m (height of
the cell)
% Cell surface area (m^2)
cell_area = 2 * (... % Total surface
area of the cell
cell_thickness * cell_width +... % Two
sides with thickness * width
cell_thickness * cell_height +... %
Two sides with thickness * height
cell_width * cell_height); % Two sides
with width * height
% Cell volume (m^3)
cell_volume = cell_thickness *
cell_width * cell_height;
% Cell mass (kg)
cell_mass = 1; % Assuming mass of the cell
is 1 kg
% Volumetric heat capacity (J/m^3/K) -
Assumed uniform throughout the cell
cell_rho_Cp = 2.04E6; % Volumetric heat
capacity
% Specific Heat (J/K)
% Calculating total heat capacity (Joules
per Kelvin) of the cell
cell_Cp_heat = cell_rho_Cp * cell_volume;
% Convective heat transfer coefficient
(W/m^2/K)
% For natural convection, values range from
5 to 25 W/m^2/K
h_conv = 5;
%% Initial Conditions
% Charge deficit (Ampere-hours)
Qe_init = 15.6845; % Initial charge in the
cell
% Ambient temperature (K)
T_init = 20 + 273.15; % Initial temperature

BATTERY MODELING METHODS
Models Expression Strength Weakness
Empirical Models  Simple Expression
 Good Computational
Efficiency
 Limited capability of
describing the terminal voltage
Electro-chemical
Models
 High accuracy of voltage
calculation
 Require prior knowledge of the
Battery
 Time consuming
Data- Driven
Models
 High accuracy of voltage
calculation
 do not need prier knowledge
of the battery
 Laborious training dataset
collection process
Electrical
Equivalent
Circuit Model
 Easily understand widely
used in SoC estimation
 High accuracy
 Complex parameter
identification process

PARAMETERS ESTIMATION OF CELLS
Parameter Estimation
Method Advantages Disadvantages
Least squares fitting
Simple and widely used method, can estimate
multiple parameters simultaneously
Sensitive to initial guess values, may
not converge to global minimum,
cannot handle non-linear relationships
Non-linear least
squares
Can handle non-linear relationships, can
estimate uncertainty in parameters
Requires accurate battery model,
computationally intensive, may not
converge to global minimum
Genetic algorithm
Can handle non-linear relationships, can handle
noise and uncertainty in measurements
converge to global minimum
Particle swarm
optimization
Can handle non-linear relationships, can handle
converge to global minimum,
sensitive to initial guess values

PARAMETERS ESTIMATION OF CELLS
Parameter Estimation
Method Advantages Disadvantages
Bayesian inference
Can estimate uncertainty in parameters, can handle
Requires accurate battery model and
prior knowledge, computationally
intensive
Markov chain Monte
Carlo
Can estimate uncertainty in parameters, can handle
Requires accurate battery model and
prior knowledge, computationally
intensive
Artificial neural
networks
Can handle non-linear relationships between
parameters, can learn from historical data, can be
used for real-time estimation
Requires large amounts of data for
training, black-box model, difficult to
interpret

CELL MODELING

PARAMETER ESTIMATION FLOWCHART

BATTERY EQUIVALENT CIRCUIT MODELING
T :- inside cell temperature ( o
C)
-ambient temperature ( o
C)
:- convection resistance ( )
:-Power dissipated (W)
:-heat capacitance ( J )
: -Actual Value
:- Predicted Value
Ambient Temperature Equations

EXPERIMENTAL WORKBENCH

=(SOC, T ) = (SOC,T) =(SOC, T) = (SOC,T)
= (SOC, T) = (SOC,T) = (SOC, T) = (SOC,T)
= (SOC, T) = (SOC,T) = (SOC,T) = (SOC,T)
T :- inside cell temperature ( o
C)
-ambient temperature ( o
C)
:- convection resistance ( )
:-Power dissipated (W)
:-heat capacitance ( J )
: -Actual Value
:- Predicted Value
2. Temperature Equations

Error Analysis
MAD: Mean Absolute Deviation
RMSE: Root Mean Squared Error
MSE : Mean Squared Error
MAPE: Mean Absolute Percentage Error
%
: -Actual Value :- Predicted Value

Initial Equations for Battery Modeling
+
-
𝐶1(SOC ,T)
𝑅1(SOC ,T)
𝑅0(SOC ,T )
𝑉 1
-
+
𝑉 𝑇 1
𝐼 𝐿
-
+
𝑉 𝑜𝑐𝑣

Various Equivalent Circuit Models

Parameters Estimation

ESTIMATED PAREMETERS

Source:
https://www.forbes.com/sites/qai/2022/09/24/growth-sector-electric
-vehicles-sales-and-the-new-electric-economy/?sh=4271b1a6143a
Source:
https://in.mathworks.com/help/simscape/ug/lithium-battery-cell-
one-rc-branch-equivalent-circuit.html

DRIVE CYCLES
0 200 400 600 800 1 000 1 200 1 400
-2.1
0.0
2.1
0 1 80 360 540 720 900
-2.2
0.0
2.2
0 1 80 360 540 720 900
-2
-1
0
1
0 1 00 200 300 400 500 600
-4
-2
0
2
Current
(A)
FUDS
Current
(A)
DST
Current
(A)
BJDST
Current
(A)
Time (s)
US06
This test consists of different dynamic current profiles like
1. FUDS :- Federal Urban Driving Schedule;
2. DST :- Dynamic stress test;
3. BJDST :- Beijing Dynamic Stress Test;
4. US06 :- Highway Driving Schedule;
Source:
https://www.forbes.com/sites/qai/2022/09/24/growth-sector-electric-vehicles-sales-and-the-new-electric-economy/
?sh=4271b1a6143a

HARDWARE RESULTS COMPARED WITH SIMULATION RESULTS
0 1000 2000 3000 4000 5000 6000 7000
3.0
3.2
3.4
3.6
3.8
4.0
4.2
Voltage
(V)
Time (s)
Experiment
Simulation
(a). 1RC DST T = 0C
0 200 400 600 800 1000
3.3
3.4
3.5
3.6
3.7
3.8
3.9
(b). 1RC FUDS T = 25C Experiment
Simulation
Time (s)
Voltage
(V)
0 500 1000 1500 2000 2500 3000 3500 4000
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
Time (s)
Voltage
(V)
(b). 1RC BJDST T = 25C Experiment
Simulation
0 1000 2000 3000 4000 5000 6000 7000
3.0
3.2
3.4
3.6
3.8
4.0
4.2
Voltage
(V)
Time (s)
(a). 2RC DST T = 0C Experiment
Simulation
0 1000 2000 3000 4000 5000 6000 7000
3.0
3.2
3.4
3.6
3.8
4.0
4.2
Voltage
(V)
Time (s)
Experiment
Simulation
(a). 3RC DST T = 0C
0 100 200 300 400 500 600 700 800
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
Voltage
(V)
Time (s)
(a). 3RC US06 T = 0C Experiment
Simulation

1b. Battery Basics and Equivalent Circuit Model.pptx

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1b. Battery Basics and Equivalent Circuit Model.pptx