Numerical Analysis of the Single Particle Model for 50Ah NMC Batteries Using the Runge-Kutta Method with Experimental Validation

This study introduces an efficient numerical analysis with an iterative volumetric source for the Single Particle Model (SPM) of lithium-ion batteries with Nickel Manganese Cobalt (NMC) chemistry. We employ the fourth-order Runge-Kutta (RK4) method, a widely recognized and robust technique for solving differential equations, to derive the ordinary differential equations (ODEs) of the SPM. By using volume averaging and polynomial approximations, we convert the governing partial differential equations (PDEs) for solid-phase diffusion into linear ODEs. The results highlight the accuracy of the RK4 method in modeling the charge, discharge, and rest periods of lithium-ion batteries. The method is validated through simulations of charge and discharge curves under different operating conditions, comparing the results with Pybamm simulations against time and capacity domain. The error rate fluctuates between 7 mV to 24 mV at low to high C-rates, with the smallest deviations observed during the middle and end stages of charge and discharge curves. The RK4-based approach is further evaluated by simulating a widely used 50 Ah NMC commercial battery, where simulation errors remain less than 1% corresponding to terminal voltage. These findings demonstrate the reliability and efficiency of the RK method in simulating lithium-ion battery behaviors, providing a computationally efficient tool for analyzing charge and discharge curves. The results affirm the models capability to accurately predict battery performance across varying C-rates.