Suitability of physicochemical models for embedded systems regarding a nickel-rich, silicon-graphite lithium-ion battery

Local inhomogeneous electrode utilization in recent lithium-ion batteries tends to increase due to larger sizes and/or higher densification, which poses a challenge for accurate, model-based monitoring. Pseudo-two dimensional (p2D) physicochemical models (PCM) can offer such locality via calculating local potentials and concentrations through the thickness of the electrode stack and are numerically reduced for implementation in a microcontroller in this work. Finite difference method combined with solid-diffusion approximations and orthogonal collocation reformulation are applied to generate three MATLAB- and three microcontroller-suitable C-code p2D-PCMs, which are experimentally validated towards constant current charge/discharge and driving cycle loads on a high-energy NMC-811/SiC-18650 lithium-ion battery. Benchmarking to an equivalent circuit model reveals similar mean cell voltage errors below 20 mV for the driving cycle. Reducing spatial elements reveals errors below 1% for local (i.e. concentrations/potentials) and global states (i.e. cell voltage/temperature) and is applied to speed-up the C-code p2D-PCMs in the microcontroller (max. 168 MHz with 192 kB RAM) to calculate at least 37% faster than real-time. Real-time computability is investigated via varying processor frequencies and using hardware acceleration schemes. The memory allocation to solve and store the p2D-PCMs on the microcontroller require 115 kB and 213 kB at a maximum, respectively.