Deterministic observability calculations for zero-dimensional models of lithium–sulfur batteries

Among the various energy storage technologies under development, the lithium‑sulfur (Li–S) battery has considerable promise due to its higher theoretical energy density, small environmental footprint, and low projected costs. One of the main challenges posed by Li–S is the need for a battery management system (BMS) that can accommodate the system's complex multi-step redox behaviours; conventional approaches for lithium-ion batteries do not transfer. Most existing approaches rely on equivalent circuit network models, but there is growing interest in ‘zero-dimensional’ electrochemical models which can potentially give insights into the relative polysulfide species concentrations present at any given time. To be useful for state estimation, a model must be ‘observable’: it must be possible to uniquely determine the internal state through observation of the system's behaviour over time. Previous studies have assessed observability using numerical methods, which is an approximation. This study derives an analytic expression for the observability criterion, which allows greater confidence in the results. The analytic observability criterion is then validated against a numerical comparator. A zero-dimensional model from the literature is translated into an ordinary differential equation (ODE) form to define the state variables matrix A, the output matrix C, and subsequently the observability matrix O. These are compared to simulated numerical equivalents. In addition, the sensitivity of the numerical process has been demonstrated. The results have the potential to offer greater confidence in conclusions around observability, which in turn gives greater confidence in the effects of any algorithms based on them.