Bursa Technical University
Department of Mechanical Engineering
Battery State of Charge (SoC) Analysis Using Equivalent Circuit Model
Calculating battery charge status
Selim Efe KAYA
Furkan TAŞKIN
23332647037
23332647035
Oğuz ÖZKAN
23332647036
Furkan KÜÇÜKBIYIK
23332647034
Süleyman Can DUMAN
23332647038
MECH0103, FALL SEMESTER, 2025
Table of Contents
1 İntroduction ........................................................................ Error! Bookmark not defined.
2 Methodology.........................................................................................................................1
2. 1 ECM BATTERY MODELİNG.........................................................................................1
2.2 Relationships between current, voltage and SoC value ..........................................1
3 iterative calculation with codes..................................................................................1
3.1 SoC-Voc...........................................................................................................1
4 Result and Conclusion..........................................................................................................2
4.1 Constant Current Scenario...........................................................................................2
4.2 Variable Current Scenario.......................................................................................3
4.3 Conclusion............................................................................................................3
Work Cides.................................................................................................................................3
Appendix……………………………………………………………………………………….4
List of Figures
Figure1 – The graph of SoC to time with costant current..........................................................2
Figure2 – The graph of SoC to time with variable current.........................................................3
Foreword
This report aims to explore the State of Charge (SoC) estimation of batteries using Equivalent
Circuit Models (ECM). As part of this project, we simulated battery behavior under constant
and variable current scenarios to better understand the relationships between current, voltage,
and SoC. Through this study, we hope to contribute to the understanding and development of
reliable battery management systems, which are essential for advancing modern electric
vehicle technologies and sustainable energy solutions.
1. Introduction
The increasing global emphasis on eco-friendly infrastructure has led to significant
advancements in electric vehicle (EV) technologies. Central to these advancements is the
development of reliable battery management systems (BMS), which play a vital role in
monitoring key parameters such as the state of charge (SoC). Accurate SoC estimation
ensures optimal battery performance, safety, and reliability, addressing challenges such as
range anxiety and efficient energy utilization.
This study focuses on the Equivalent Circuit Model (ECM)-based approach for SoC
estimation. ECMs are widely preferred due to their simplicity and practical applicability, as
they approximate battery behavior using electrical components like resistors and capacitors.
This report evaluates battery dynamics under both constant and variable current scenarios,
employing computational simulations to model and analyze SoC and voltage behaviors.
2. Methodology
2.1 ECM Battery Modeling
The ECM framework models the battery as a combination of key electrical elements:
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Open-Circuit Voltage (VoC): Dependent on SoC.
Internal Resistance (R_int): Represents instantaneous voltage drops.
RC Branch (R_p and C_p): Models transient voltage behavior under load.
The voltage response of the battery is calculated as: V_battery(t) = V_oc(t) - I(t) *
R_int - V_RC(t)
The RC branch voltage is expressed as: V_RC(t) = I(t) * R_p * (1 - exp(-Δt / (R_p *
C_p))) + V_RC(t-1) * exp(-Δt / (R_p * C_p))
2.2 Relationships Between Current, Voltage, and SoC Value
The SoC is updated iteratively based on the following equation: SoC(t) = SoC(t-1) – I(t-1)*∆t/Q
A polynomial relationship between SoC and VoC is defined as: Voc(t)=a+b*SoC(t)+c*SoC(t)^2
3. Iterative Calculation with Codes
3.1 SoC-Voc
MATLAB scripts were utilized to iteratively calculate SoC and VoC values by simulating the
battery's behavior under constant and variable current scenarios.
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• Initialization of Parameters: Battery capacity (Q), internal resistance (Rint), RC branch
parameters (Rp,Cp), and initial SoC were defined.
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Constant Current: A fixed current of 0.2 A was applied.
Variable Current Case: A sinusoidal current with a constant component
(I(t)=A⋅sin⁡(2πft)+AI(t) = A \cdot \sin(2\pi f t) + AI(t)=A⋅sin(2πft)+A) was defined.
The iterative process updates the voltage and SoC values at each time step. Results were
plotted to visualize battery performance.
4. Results and Conclusion
4.1 Constant Current Scenario
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Initial SoC: 100%.
Final SoC: Decreased linearly over time due to the fixed current load.
figure 1 –The graph of SoC to time with costant current.
Page 2 of 5
4.2 Variable Current Scenario
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The sinusoidal current caused periodic fluctuations in SoC and voltage.
Voltage dynamics showed transient effects due to the RC branch.
figure 2 –The graph of SoC to time with variable current.
4.3 Conclusion
The results demonstrate the ECM's capability to accurately model both steady-state and
transient behaviors of the battery. In the constant current case, SoC decreased predictably,
while in the variable current case, the effects of transient load conditions were evident in both
SoC and voltage dynamics.
Work Cites
(Onur Kadem,Real-Time State of Charge Estimation Algorithm for Electrical Batteries, 2022)
(Farshid Naseri, n Enhanced Equivalent Circuit Model With Real-Time Parameter
Identification for Battery State-of-Charge Estimation,2022)
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Appendix
Constant Current Scenario’s code
Page 4 of 5
Varieble Current Scenario’s code
Page 5 of 5