This project proposes to estimate SOC of the LIB from a reduced-order electrochemical model (ROEM) using an Extended Kalman Filter (EKF). To reduce the model complexity, the solid phase equations will be reconstructed by combining the Pade approximation and quadratic polynomial method. Volume averaging technique will be used for electrolyte physics simplification. Then an EKF will be used to estimate the SOC of the battery.

1. Electrochemical Model-Based Estimation Of SOC Using
Extended-Kalman Filter
PROJECT PRESENTATION
AENG 576 – MODELING AND CONTROL OF BATTERY SYSTEMS
Dr. Youngki Kim
Nipun Kumar – 31440148
Ratnesh Sharma – 38533793
Satya Patel – 85826429
Varma Jelli – 19000585

2. Topics Covered
⮚ Problem Description
⮚ Electrochemical Models of Battery
⮚ Improved Reduced Order Electrochemical Model (iROEM)
⮚ Solid Diffusion
⮚ Electrolyte Diffusion
⮚ Terminal Voltage – Pulse Cycle
⮚ Terminal Voltage – Dynamic Stress Test Cycle
⮚ SOC Estimation using EKF
⮚ SOC Estimation – Pulse Cycle
⮚ SOC Estimation – Dynamic Stress Test Cycle
⮚ Equivalent Circuit Model considering Electro Chemical Properties
⮚ Conclusion
⮚ References
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3. Problem Description
• This project proposes to estimate SOC of a LIB with LMO (LiyMn2O4) chemistry from an improved reduced-order
electrochemical model (iROEM) using an Extended Kalman Filter (EKF).
• The solid phase equations will be reconstructed by combining the Padé approximation and quadratic polynomial method.
• Volume averaging technique will be used for electrolyte physics simplification. Then an EKF has been used to estimate the
SOC of the battery.
• Using the transfer function from Padé approximation, we will attempt to obtain a relationship with the resistances and
capacitances of an equivalent circuit model.
• Terminal voltage of the iROEM model is then compared against the enhanced equivalent circuit model.
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4. Electrochemical Models of Battery
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P2D
SPM
SPMe
(iROEM)
The pseudo two-dimensional (P2D) model is one of the more popular electrochemical models
(EM), but it requires large amount of computation and a few limits in real-time application in
BMS.
To overcome these drawbacks, many researchers have proposed reduced-order
electrochemical models (ROEMs) such as single particle model (SPM). However, SPM
ignores the electrolyte physics including changes in electrolyte concentration and
potential, which may easily result in the bad accuracy at medium and high C-rate.
To improve on this, an SPM model with electrolyte dynamics has been proposed. The SPMe
can provide better accuracy in the terminal output voltage (TOV) even at high C-rates. This
model focuses on achieving the necessary balances between the model fidelity and
computational complexity

5. Improved Reduced Order Electro Chemical Model (iROEM)
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Padé approximation Quadratic PP
Improved Reduced Order Electro Chemical Model (iROEM) is proposed
• To improve the observability of SPMe with acceptable accuracy and computational cost
⮚ Solid Phase :- Padé Approach + Quadratic parabolic polynomial (PP)
⮚ Electrolyte Phase:- Volume Averaging Technique(VAT) + Quadratic approx.
Total ODEs: 6
Total AE: 7
Longxing et al.
Simulink model of iROEM for TOV calculation

6. Solid Diffusion
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Pade approach (ODE:3 & AE 2)
(Negative Electrode)
Plot of Surface concentration profile using third order Pade
approx. approach for pulse current input
Quadratic Polynomial approach (ODE:1 & AE 2)
(Positive Electrode)
Longxing et al.
Yinyin et al.

7. Electrolyte Diffusion
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V Senthil
Longxing et al.
Longxing et al.
Electrolyte Potential equation:

8. Terminal Voltage (TOV) Calculation – Pulse Cycle
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Input current profile for pulse cycle
TOV comparison between different models using pulse cycle
Longxing et al.
OCV at positive and negative electrode:

9. Input current profile for dynamic stress test (DST) cycle
TOV comparison between different models for dynamic stress test (DST) cycle
Terminal Voltage (TOV) Calculation – Dynamic Stress Test Cycle
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Longxing et al.

10. SOC Estimation using EKF
• P1 = (A*P0*(A)'+Qw);
• xbar_new = A*x0+B*I_input_pre
• Vt = h ( xbar_new, I_input)
(Nonlinear function)
• L1 = (P1*Ck')*inv(Ck*P1*Ck'+Rw)
• xhat_new = xbar_new+(L1*(Vmeas-Vt))
• P0new = (eye(3)-(L1*Ck))*P1
Ck =
⮚ Three states of Negative Electrode Pade approximation are considered for
observability.
⮚ Terminal voltage Vt = h (CsnSurf, Csn, I_Input )
⮚ Csp Surf = f ( Csn ) is used from SOC definition and Quadratic polynomial
approximation.
Longxing et al.
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Simulink model of EKF

11. Jacobian Matrix
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12. SOC Estimation (EKF) – Pulse Cycle
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13. SOC Estimation (EKF) – Dynamic Stress Test Cycle
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14. Equivalent Circuit Model considering Electro Chemical Properties
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Gao J et.al Zhang Xi et.al

15. Conclusion
1. Compared quadratic polynomial and Pade approximation methods for solid diffusion dynamics. 3rd order Pade
approximation provided best results for terminal voltage (TOV).
2. Adding electrolyte dynamics improved the terminal voltage (TOV) calculation at high charge/discharge rate
and successfully validated our results with the reference paper.
3. Performed observability analysis with Pade and polynomial approximation methods for solid dynamics and
volume averaged technique (VAT) for electrolyte dynamics.
4. Estimated state of charge (SOC) using Extended Kalman Filter (EKF) with iROEM.
5. Using electrochemical properties, estimated RC pair values for equivalent circuit model (ECM), which can be
used as an initial non-linear least square regression (LSR) method.
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Limitations
1. The iROEM does not include thermal behavior of the battery and needs to be incorporated for online BMS
applications.
2. Calculated RC values from ECM are dependent on electrochemical model parameters. Few parameters are not
time invariant. This affects the accuracy of ECM.

16. 1. Longxing Wu, Kai Liu and Hui Pang, "Evaluation And Observability Analysis Of An Improved Reduced-Order Electrochemical Model
For Lithium-Ion Battery", Electrochimica Acta 368 (2021): 137604, doi:10.1016/j.electacta.2020.137604.
2. Gao J, Zhang Y, He H. A Real-Time Joint Estimator for Model Parameters and State of Charge of Lithium-Ion Batteries in Electric
Vehicles. Energies. 2015; 8(8):8594-8612. https://doi.org/10.3390/en8088594
3. V. Senthil Kumar , Reduced order model for a lithium-ion cell with uniform reaction rate approximation, J. Power Sources 222
(2013) 426–441 .
4. Zhang, Xi & Lu, Jinling & Yuan, Shifei & Yang, Jun & Zhou, Xuan. (2017). A novel method for identification of lithium-ion battery
equivalent circuit model parameters considering electrochemical properties. Journal of Power Sources. 345. 21-29.
10.1016/j.jpowsour.2017.01.126.
5. Yinyin Zhao and Song-Yul Choe, "A Highly Efficient Reduced Order Electrochemical Model For A Large Format Limn2o4/Carbon
Polymer Battery For Real Time Applications", Electrochimica Acta 164 (2015): 97-107, doi:10.1016/j.electacta.2015.02.182.
References
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17. THANK
YOU
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18. Back Up Slide
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