M.A.P.L.E. Lab

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Does your solver fail for battery models?

A major difficulty solvers have with battery models is the unknown values for certain battery states (such as SOC, SOH or individual electrode potential) at the start of a simulation. When trying to solve a system of differential algebraic equations (DAEs), which are present in most electrochemically based battery models, normal solvers will fail if the initial conditions for all the state variables are inconsistent. This causes issues in Battery management system. In addition, a nonlinear solver is typically used for battery models. We have developed an approach that helps solve battery models without knowing the exact initial conditions and without having to use a Newton Raphson iteration or a nonlinear solver.  
The approach corrects all of the algebraic variables to a set of consistent conditions. Additionally, once the consistent values are found the proposed approach uses the same solver for the simulation of the model. This means there is only one solver call for both initialization and simulation.The approach was applied successfully to a Nickel electrode model, single particle model, porous electrode model for lithium-ion batteries and many other DAE systems.


Direct initialization and simulation of index 1 DAEs. The algebraic variables (z) are initialized to consistent condition and the system is solved after that.

Claims: We confidently claim that the proposed approach is the most robust approach for solving index -1 DAEs as of today. If there is a better approach for robustness and efficiency, we would like to know of the same. In addition, if the proposed approach fails for any index-1DAE or battery model, we would like to be alerted about the same.

Link for the paper published.

Link for the appendix that includes 4 examples solved in Maple.

Link for the appendix that solves the same example in Maple, MATLAB and FORTRAN.

Link for a past discussion about this approach in Mapleprimes.

The proposed approach enables solving lithium-ion and other battery/electrochemical storage models accurately in a robust manner in a cheap microcontroller with minimum memory requirements. A disclosure has been filed with the University of Washington to apply for a provisional patent for battery models and Battery Management System for transportation, storage and other applications because of the current commercial interest in this topic (for batteries). In particular, use of this single step avoids intialization issues/(no need to initialize separately) for parameter estimation, state estimation or optimal control of battery models.

D. N. Sonawane, M. T. Lawder, M. Pathak and Venkat R. Subramanian, "Robust fail-safe iteration free approach for solving Index-1 DAEs arising from battery models", US Patent application #62/194,678.


Please feel free to contact Dr. Venkat Subramanian for any comments.