This document presents a five-parameter analytical curvefit model for modeling the open-circuit voltage (OCV) variation with state-of-charge (SOC) of a rechargeable battery. The model uses different functions (logarithmic and polynomial) to model the nonlinear OCV-SOC relationship in the low and high SOC regions. It is shown that the model can accurately fit empirical discharge curve data for a lithium-ion cell using only five adjustable parameters. The proposed simple and flexible OCV model is well-suited for incorporation into equivalent circuit battery models used for simulation and analysis. Future work includes accounting for temperature effects through temperature-dependent parameter tuning.

1. A Five-Parameter Analytical Curvefit Model
for Open-Circuit Voltage Variation with State-
of-Charge of a Rechargeable Battery
Dr. Lalit Patnaik
European Organization for Nuclear Research (CERN)
Geneva, Switzerland
Prof. Sheldon Williamson
University of Ontario Institute of Technology (UOIT)
Oshawa, Canada
Presentation at
Power Electronics Drives and Energy Systems (PEDES)
19 Dec 2018
Chennai, India

2. Models for secondary batteries
• Electrochemical models
➢ Accurate
➢ Complex: Need to solve large systems of coupled non-linear PDEs!
• Equivalent circuit models (ECMs)
➢ Less accurate
➢ Less complex
ECMs are the preferred modelling technique for ease of computation

3. Equivalent circuit models for secondary batteries
Thevenin
Model
One Time-Constant
(OTC) Model or
First-Order RC Model
Two Time-Constant
(TTC) Model or
Second-Order RC
Model
[1] J. Issac, “Modeling and state of charge estimation of Li-ion batteries for vehicular applications,” Master’s thesis,
Purdue University, Masters Thesis, 2013.

4. Terminal voltage and OCV vs depth of discharge
• Terminal voltage = OCV + series impedance drop
• OCV typically has
➢ Strong non-linearity in low-SOC region
➢ Weak non-linearity in high-SOC region
DOD
i.e. 100-SOC
OCV
100%
0%
Gradual
Sharp “knee”
[2] B. Lawson, Battery performance characteristics," 2005. [Online].
Available: http://www.mpoweruk.com/performance.htm.

5. OCV modeling approaches
• Look-up table (LUT)
➢ Accurate
➢ Not flexible
➢ Data intensive
• Analytical curvefit, in accordance with empirical data
➢ Less accurate
➢ More flexible: Parametric approach
➢ Less data intensive
OCV models comparison
Reference Number of
parameters
Correction
term required?
Weng 2014 12 No
Lam 2011 6 No
Zhang 2016 6 No
Gao 2002 2 Yes
Proposed model 5 No

6. Proposed model
• Use different functions to model the two non-linearities
➢ Low-SOC region: Logarithmic
➢ High-SOC regions: Polynomial
OCV
100%
0%
Polynomial
Logarithmic
DOD
i.e. 100-SOC
Vmax
dVmax

7. Cut-off voltage factor
𝑑 =
𝑉𝑐𝑢𝑡𝑜𝑓𝑓
𝑉
𝑚𝑎𝑥

8. Comparison: Model vs Experiment
𝑥 = Normalized SOC
𝑥0 = Normalized SOC at the start of the discharge/charge session
𝑘 = Reciprocal of cell capacity [A-1h-1]
𝑓(𝑥) = Proposed OCV model

9. Results: Discharge curves for Li-ion cell
(a) At various discharge currents. (b) For various values of a.
Lower the value of a greater the
OCV bend in the low-SOC region.

10. Results: Discharge curves for Li-ion cell
(c) For various values of c. (d) For various values of n.
Higher the value of c greater the
OCV bend in the high-SOC region.
Higher the value of n greater the OCV
bend in the high-SOC region.

11. Conclusion
• Proposed an analytical curvefit model for OCV variation with respect to SOC of a secondary battery
• Proposed model comprises a sum of logarithmic and polynomial terms and uses only 5 parameters
• Effect of various parameters on OCV curve shape demonstrates that
➢ Two of the parameters are uniquely determined: b, d
➢ Three remaining parameters can be tuned to fit the empirical data: a, c, n
• This model can be
➢ Incorporated in Thevenin, OTC, and TTC models
➢ Used for evaluating various charging techniques and discharge scenarios
• Need to incorporate the effect of temperature variation: Temperature-dependent parameter tuning

12. Thank You!