Robust Fail-Safe Iteration Free Solvers for Battery Models

Mathematical models of batteries^{1, 3, 4} are dynamic systems. which are typically solved by using a finite difference or other discretization technique in the spatial direction and solving the resulting system of nonlinear differential algebraic equations (DAEs) in time².

The resulting DAEs are stiff, often times ill-conditioned and many standard solvers fail to solve them. The complications in solving the system of DAEs also include the inability of the solvers to find consistent initial conditions for the algebraic variables^5,6.  Most stiff solvers include a Newton-Raphson type iterative methods to solve these stiff equations. (DASKR, RADAU, IDA⁷).

In this work, we propose a single-step iteration free approach to system initialization and simulation allowing for systems of DAEs to be solved using explicit ODE solvers without exact knowledge of the initial conditions for the algebraic variables. We will present this new solver which is guaranteed to not fail for any meaningful physical situations.

 Acknowledgements

The work presented herein was funded in part by the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

References

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