New conservative numerical schemes in mass conservation in solid particles ofLithium-ion battery for efficient simulation

Lithium-ion batteries have been used prevalently as an energy storage system in electric and hybridelectric vehicles (HEVs) due to no memory effect, low self-discharge and high energy/powerdensity. To design a more reliable battery with higher power/energy density, in depthunderstanding of phenomena occurred inside the battery is required. By using modeling andsimulation, these can be handled in a low cost with less restriction against experimental methods.But simulation time is one of the most barriers to use it in applications which require huge amountof data and in battery management systems. Common methods used to solve mass transfer problemin Li-ion battery particles often require significant computational effort which makes the P2Dmodel [1] too slow for optimization, uncertainty quantification and control purposes. Variousmethods have been employed to overcome these difficulties such as approximate methodsincluding diffusion length method [2], Duhamel’s superposition integral [3], polynomialapproximation [4], PSS method [5], finite element method [6], finite difference method [7], andfinite volume method. Some methods lose their validity under some situation such as non-constantdiffusion coefficient and high rate charge/discharge. These methods show less accuracy respect tofull order model and sometimes they provide nonphysical results. Since the value of Liconcentration at the surface of particle determines the electrochemical reaction rate, accuracy ofsimulation results highly depend on its accurate value. Moreover, at the surface of particle,concentration gradient is high, so to decrease computational nodes in whole domain, non-uniformmesh spacing scheme is more convenient. To this end, the vertex based finite volume method ischosen to directly involve concentration gradient at the particle surface with variable mesh spacing.With this motivation, a new numerical discretization method is derived for spherical diffusionequation. First original PDE is integrated along spherical radius to obtain a coupled system of51ODEs, then the integrand is interpolated by second degree Lagrange polynomial which provides3rd-order approximation of integral. Despite of high order accuracy of the method, it is remainedtri-diagonal. For solving system of ordinary differential equations the Crank-Nicolson method isused which is A-stable finite-difference scheme with the second order accuracy. This newnumerical scheme is proposed to solve P2D mathematical model of a Li-ion battery. As shown infollowing figure, the results indicate good agreement as compared to Khaleghi et al. study [8] withsignificant time reduction.

کلیدواژه ها:

Li battery ، Simulation ، Solid concentration ، Finite volume method