Unveiling Impedance Response of Commercial Coin-type Lithium-ion

Batteries Exposed to Overcharge and Over-discharge through

Equivalent Circuit Modeling

SALIM EROL

Department of Chemical Engineering,

Eskisehir Osmangazi University,

Meselik Campus, 26040 Eskisehir,

TURKEY

Abstract: - This study investigates the impedance spectroscopy response of commercial coin-type lithium-ion

cells under overcharge and over-discharge conditions through equivalent circuit modeling. Electrochemical

tests were conducted on battery cells, employing impedance spectroscopy to track variations across various

charge states, including overcharge and over-discharge conditions. The impedance data highlighted distinct

patterns during normal operation, prompting the application of an anomalous diffusion impedance model.

Regression analysis of the model parameters offered valuable insights into the cells' electrochemical

performance before and after exposure to overcharge and over-discharge.

Key-Words: - Electrochemical impedance spectroscopy, lithium-ion battery, overcharge, over-discharge,

equivalent circuit modeling, regression.

Received: May 7, 2024. Revised: November 19, 2024. Accepted: December 6, 2024. Published: December 31, 2024.

1 Introduction

A Li-ion battery, an electrochemical energy storage

device, is a broadly used rechargeable battery. Like

other batteries, the Li-ion battery consists of

electrochemical reactions on electrodes and a

diffusion mechanism to convert this energy to

electricity. Due to the electrochemical reactions and

the diffusion, the battery model includes nonlinear

terms and uncertainties with some additive

disturbances (e.g., unmodelled effects), [1].

State of Charge (SoC) could be defined as the

available capacity and formulated as a percentage of

its fixed capacity. State of Health (SoH) is described

as a measure of the battery’s capability to store and

release electrical energy, compared with a new one,

[2]. These two quantities are key parameters to

predict the battery's life and performance; however,

the estimation of SoC and SoH is problematic since

the battery model includes nonlinearities and

uncertainties depending on time, [3]. In recent years,

researchers have shown an increased interest in

estimating SoC and SoH of Li-ion batteries, [4].

Three primary approaches have provided a basis; i)

simple capacity measurement, [5], ii) Voigt

elements in series (RC networks), [6], iii)

Impedance-based (equivalent circuit) model, [7].

The conventional capacity measurement method is a

straightforward technique based on a simple

coulomb counting procedure, [5]. RC networks are

used to represent battery dynamics [6]. The

implementation of these two techniques is not

complicated, and they are commonly used, [8].

However, they lack expressing kinetics and mass

transfer mechanisms adequately; therefore, they

might represent nonrealistic models. On the other

hand, the impedance-based model successfully

defines electrochemical reactions and diffusion

occurring in Li-ion batteries, which is more realistic

and physically based, [9].

The objective of this study is to use the

impedance-based model to estimate SoC and SoH

accurately under non-stationary circumstances. The

uncertain terms in the battery dynamics will be

estimated by using a novel adaptive-based observer.

The estimated terms will be used to determine the

SoC and SoH of the battery. Unlike other associated

methods, the proposed technique will not assume

battery voltage and the current which are

persistently excited throughout the estimation of

SoC and SoH process. This proposed model is valid

for different states of charge and abuse conditions

like overcharge and over-discharge. Therefore, it

will be a realistic model for engineering applications

using batteries, i.e., electric vehicles, and storage-

based smart grids.

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2 Experimental Method

Electrochemical experiments were conducted on

commercially available Li-ion coin cells. Impedance

spectroscopy was employed to observe variations

linked to diverse SoC, as well as instances of

overcharge and over-discharge.

2.1 Battery Cells

Secondary 2032 coin (or button) cells obtained

commercially were utilized for the electrochemical

experiments. These cells featured lithium cobalt

oxide (LiCoO2) cathodes, graphitic carbon (C6)

anodes, and an electrolyte comprising lithium

hexafluorophosphate (LiPF6) salt dissolved in a

mixture of organic solvents, including ethylene

carbonate (EC), propylene carbonate (PC), dimethyl

carbonate (DMC), and diethyl carbonate (DEC).

The cells exhibited a normal potential range

between 3.00 and 4.20 volts. The nominal

capacity and nominal potential of the batteries were

30 mAh and 3.6 V, respectively.

2.2 Instrumentation

Experiments were conducted using a Gamry

Reference 3000 Potentiostat /Galvanostat connected

to a desktop computer. Gamry Framework and

Electrochemical (EChem) Analyst software

packages were employed for data acquisition and

analysis.

2.3 Protocol

The impedance response and capacity of the battery

cells were analyzed under various SOC profiles,

encompassing different potential ranges.

Additionally, the impedance response was studied

under overcharge and over-discharge profiles.

The battery cells were initially charged to 4.20

V under galvanostatic control, with a current of 2

mA. Subsequently, each cell underwent discharge to

3 V at a 1C rate, followed by charging back to 4.20

V with the same bias, i.e., at a constant 30 mA

current. The cells were then held potentiostatically

at a constant cell potential until the current dropped

below 20 μA, [10]. Following this constant-

potential rest period, impedance measurements were

conducted using a 10 mV alternating current

perturbation within a frequency range of 10 kHz to

10 mHz. To study the influence of overcharge, the

cell was initially charged under a constant current of

4.2 V. Impedance measurements were performed at

each 80mV step up to and including 5 V. A similar

protocol was followed for the over-discharge.

Impedance measurements were performed at each

80 mV step down to and including 2.20 V. After

overcharging to a potential of 5 V, the battery was

allowed to relax for four days at the open-circuit

condition. When held at open-circuit, the

overcharged battery rapidly reached a cell potential

within the nominal operating range. After over-

discharging to a potential of 2.20 V, the battery was

allowed to relax for four days in the open-circuit

condition. When held at open-circuit, the over-

discharged battery also reached a cell potential

within the nominal operating range, but this process

was slower. The impedance response showed a

persistent change to the electrochemical

characteristics of a coin cell subjected to overcharge

and returned to normal cell potentials; whereas, the

electrochemical characteristics returned quickly to

normal for a coin cell subject to over-discharge and

returned to normal cell potentials.

All experiments were performed at room

temperature (around 20 oC), and they were repeated

a few times with the same type of battery cells to

ensure that the results were both consistent and

reproducible.

3 Results

The impedance measurements obtained during

normal operating conditions, specifically at 4.2 V,

displayed a distinctive pattern: a depressed

capacitive loop at high and intermediate

frequencies, along with a linear trend at low

frequencies characterized by a slope exceeding 45°

as shown in Figure 1.

Fig. 1: Impedance response for a battery held at 4.2

V. The line represents the fit of equation (1) to the

data

The equivalent circuit model represented in

Figure 2 was constructed based on the proposed

reactions occurring at both the cathode and anode.

This resulting model can be formulated as:

eca

Z R Z Z  

(1)

where

 

t,c d,c

d,c c

t,c

ZR Z Q









(2)

and

0.5 1.0 1.5 2.0 2.5

0.00

0.25

0.50

-Zj / ohm cm2

Zr / ohm cm2

Data

Model

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 

t,a

ZRQ







(3)

Fig. 2: Equivalent circuit representation of the Li-

ion battery cell

The impedance data deviated significantly from

what would be expected with a Warburg impedance

model, primarily due to the low-frequency

impedance slope in a Nyquist plot measuring

approximately 56°, well beyond the typical 45°

characteristic of a Warburg impedance. Instead, an

anomalous diffusion impedance model was adopted,

which is applicable to systems experiencing

diffusion hindered by intermittent adsorption of

diffusing species onto a stationary substrate. This

impedance response, incorporating a reflecting

boundary condition, was initially elucidated in the

literature, [11]. However, since the frequency range

in our measurements did not reveal the sharp rise

associated with the reflecting boundary condition,

we resorted to employing an asymptotic form of

their expression. Consequently, the resulting

diffusion impedance is expressed as follows:

     

/2 1

d,c

d,c /2















(4)

where

 

d,c 0/Z





represents a lumped parameter

encompassing both the diffusion time constant (τ)

and the zero-frequency asymptote for the real part of

the diffusion impedance.

(a)

(b)

Fig. 3: Impedance response and their fit of a coin

cell at a potential of 4 V before and after the cell

was: (a) overcharged and (b) over-discharged

Figure 3 illustrates the impedance response of a

coin cell at a potential of 4 V before and after

undergoing specific treatments: overcharging and

over-discharging. Panel (a) presents the impedance

response before and after overcharging, while panel

(b) depicts the response before and after over-

discharging. The impedance data is represented

graphically along with their respective fits.

Table 1 displays the parameter results obtained

through the Levenberg-Marquardt method for

regression analysis, [12]. Subsections (a) and (b) of

the table respectively present the parameters before

and after the cell was subjected to overcharging and

over-discharging treatments. These parameters

provide valuable insights into the changes occurring

within the cell's electrochemical system as a

consequence of the applied treatments.

Table 1. Parameter results obtained by Levenberg-

Marquardt method for regression: (a) before and

after the cell was overcharged and (b) before and

after the cell was over-discharged

(a)

(b)

4 Conclusion

This study conducted a comprehensive investigation

into the impedance spectroscopy response of

commercial coin-type lithium-ion cells subjected to

extreme conditions, including overcharge and over-

discharge. Through a combination of

electrochemical experiments and equivalent circuit

modeling, distinct impedance patterns

corresponding to various states of charge conditions

were identified. The anomalous diffusion impedance

Zd,c

Rt,c

t,a

CPE

Anode SEI Cathode

Electrolyte

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model provided a more accurate representation of

the experimental data, indicating that diffusion

within the cell was hindered by sporadic adsorption

of diffusing species onto a fixed substrate. This

insight significantly enhances the understanding of

the underlying mechanisms governing lithium-ion

battery behavior under such extreme conditions.

The parameter analysis, performed using the

Levenberg-Marquardt optimization method,

provided crucial information about the changes

occurring within the cell’s electrochemical system.

The results of this study contribute to an

improved understanding of battery degradation

mechanisms under overcharge and over-discharge

conditions, which can facilitate the development of

more effective battery management systems aimed

at prolonging battery life and improving

performance reliability. This knowledge is essential

for various industries, where demand for high-

performing and long-lasting lithium-ion batteries

continues to rise. As such, the findings presented

here are expected to play a significant role in

advancing battery diagnostics and maintenance

strategies.

Further research is recommended to broaden the

scope of this study. Expanding the range of

experimental conditions, such as exploring different

cell chemistries and cycling profiles, would help

generalize the applicability of these findings.

Additionally, the validation of the proposed models

through practical case studies in real-world

applications will be necessary. Continuous efforts in

combining electrochemical analysis, impedance

modeling, and advanced mathematical methods are

expected to lead to further optimization of battery

performance and reliability.

Declaration of Generative AI and AI-assisted

Technologies in the Writing Process

During the preparation of this work the author used

Gemini (Google AI platform) for grammar and

language editing reasons. After using this service,

the author reviewed and edited the content as

needed and take full responsibility for the content of

the publication.

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69 (Accessed Date: December 10, 2025).

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Creation of a Scientific Article (Ghostwriting

Policy)

The author performed the experiments, analyzed the

results, wrote and reviewed the manuscript.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflicts of interest to declare.

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