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Washington University in Saint Louis team disseminating code to identify optimal charging protocols for new advanced Li-ion battery materials

Researchers at Washington University in Saint Louis led by Dr. Venkat Subramanian are offering the open download of application code which, in conjunction with their paper published in the RSC journal Physical Chemistry Chemical Physics, can help the developers of new materials or electrodes for Li-ion batteries to determine how optimally to charge their batteries based on the properties of the new materials.

The code can be downloaded here and run on any Windows PC. “As far I know,” said Dr. Subramanian, “this is the first code disseminated in the literature to show how to charge to minimize capacity fade caused by stress caused by intercalation.

This paper illustrates the application of dynamic optimization in obtaining the optimal current profile for charging a lithium-ion battery using a single-particle model while incorporating intercalation-induced stress generation. In this paper, we focus on the problem of maximizing the charge stored in a given time while restricting the development of stresses inside the particle. Conventional charging profiles for lithium-ion batteries (e.g., constant current followed by constant voltage) were not derived by considering capacity fade mechanisms. These charging profiles are not only inefficient in terms of lifetime usage of the batteries but are also slower since they do not exploit the changing dynamics of the system. Dynamic optimization based approaches have been used to derive optimal charging and discharging profiles with different objective functions. The progress made in understanding the capacity fade mechanisms has paved the way for inclusion of that knowledge in deriving optimal controls.

While past efforts included thermal constraints, this paper for the first time presents strategies for optimally charging batteries by guaranteeing minimal mechanical damage to the electrode particles during intercalation. In addition, an executable form of the code has been developed and provided. This code can be used to identify optimal charging profiles for any material and design parameters.

—Suthar et al.

While novel materials with high gravimetric and volumetric capacities such as silicon are being pursued as potential candidates to replace traditional graphite anodes in lithium ion batteries, these materials exhibit well-known significant volume changes and stress development during charge and discharge, which leads to mechanical degradation and capacity fade. This is spurring a great amount of research activity into novel materials to solve that set of problems.

Model-based control strategies can be utilized to address such issues and to to ensure safe operation of batteries. Several research groups (such as Professor Newman’s group at UC Berkeley; Professor Sastry’s group at the University of Michigan; Professor White’s group at the University of South Carolina; and Dr. Mark Verbrugge’s group at General Motors) have developed physics-based models to simulate pressure induced diffusion, stress development, volume changes, and so on, Subramanian notes.

In the paper in Phys. Chem. Chem. Phys., Subramanian’s group showed how stress generation during charging can be minimized by optimizing the charging protocol, thereby reducing capacity fade.

The Washington University in Saint Louis team is providing the code in executable form, with material properties editable in the text file. The code given can be used for any material. List of all the parameters that needs to be provided for specific material can be found in “parameters.txt” (included in the package).

List of parameters for WUSTL code
Parameter Default value
Temperature 298
Maximum concentration in anode C[nmax] 31833
Diffusion coefficient 3.9e-14 (3.9 x 10-14)
Particle Radius (m) 1.25e-05 (1.25 x 10-5)
Surface Area of Anode 0.7824
tau (sec) scaling constants use for better numerical solvability 3600
Young’s Modulus (Pa) 15000000000
Poisson’s ratio 0.3
Omega m3/mol 4.081545566e-06 (4.081545566 x 10-6)
Final time (1 = 1tau) 1

The code, hosted in the WUSTL website, derives a charging profile to maximize the amount of charge in a given time while restricting the peak stresses generated at center and surface of the particle. The code given should be viewed as providing an initial estimate for an optimal charging profile, Subramanian said.

Other important phenomena, such as volume changes, require more detailed models, simulated in efficient form. Although not addressed by either the code or the Phys. Chem. Chem. Phys. paper, a recent paper from the group published in the Journal of The Electrochemical Society discusses a computationally efficient representation for solid-phase diffusion. That paper introduces efficient methods for solid phase reformulation: (1) parabolic profile approach; and (2) a mixed order finite difference method for approximating/representing solid-phase concentration variations within the active materials of porous electrodes for macroscopic models for lithium-ion batteries.


  • Bharatkumar Suthar, Venkatasailanathan Ramadesigan, Sumitava De, Richard D. Braatz and Venkat R. Subramanian (2014) “Optimal charging profiles for mechanically constrained lithium-ion batteries,” Phys. Chem. Chem. Phys., 16, 277-287doi: 10.1039/C3CP52806E

  • Sumitava De, Bharatkumar Suthar, Derek Rife, Godfrey Sikha, and Venkat R. Subramanian (2013) “Efficient Reformulation of Solid Phase Diffusion in Electrochemical-Mechanical Coupled Models for Lithium-Ion Batteries: Effect of Intercalation Induced Stresses,” Journal of The Electrochemical Society, 160 (10) A1675-A1683 doi: 10.1149/2.024310jes



Future ultra quick chargers will have to closely respect specific battery parameters and adjust charging variables accordingly.

This could be done automatically with the charger sensing the battery specific parameters before sending the energy. Continued sensing would also adjust and stop charging at the proper time etc.


The pack communicates with the charger, it declares its chemistry and charge history. If a certain chemistry has been repeatedly quick charged and heavily discharged, this would be taken into consideration. The owner can override this in favor of a massive quick charge, but they pay for a new pack sooner.


A dynamic optimum charging profile may provide the fastest recharge before any significant loss of recharging cycles for given battery chemistries.

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