# How accurate is state of charge as a predictor of remaining useful work? (ICLSB 2019)

Presentation given at ICLSB 2019. Abstract follows:

It is well known that lithium sulfur cells have a distinctive open-circuit voltage profile: at high states of charge there is a ‘high plateau’, starting at around 2.35 V, and at low states of charge there is a flatter ‘low plateau’ at near constant voltage. This presentation will discuss the implications this profile might have for the prediction of the work that cell is capable of doing before it is fully discharged, which is vital for real-world applications.

This presentation will introduce a family of techniques that has been developed for the creation of low-complexity dynamic models [1,2] and their application in state estimation algorithms embedded within real-life battery management systems using extended Kalman filters, unscented Kalman filters and particle filters [3,4] or adaptive neuro-fuzzy inference systems (ANFIS) [5]. So far, algorithms for management of lithium-sulfur have all been based on state of charge, rather than ‘remaining energy’. In a practical application, the real information the end user needs is an answer to the question ‘how much work can I still do?’ The work done by a cell is the product of the terminal voltage and the current delivered to the load, and a Coulomb-based metric, dependent on current alone, is only a proxy for this. In this presentation, we explore the question ‘how accurate is state of charge as a predictor of remaining useful work?’

In this presentation, the title question is addressed, both using theoretical and simulation studies comparing a lithium-ion cell [6] from the literature with a model of development-grade industrial lithium sulfur cell [1] and through the analysis of experimental data collected from the same lithium-sulfur cell. In the theoretical studies, it is observed that with low currents, state of charge is a good predictor of remaining useful work in both the lithium-ion cell and the lithium-sulfur one, but that where the remaining useful work predictions for the lithium-ion cell are least accurate at the mid-discharge point, the remaining useful work predictions for the lithium-sulfur cell were least accurate near to the transition between the high and low plateau. The results of the theoretical analysis were supported by an analysis of the experimental data. From these results, no significant motivation was been identified for refactoring estimation algorithms in terms of state of energy.

At the time this abstract is prepared, work to consider the accuracy of prediction of remaining useful work at higher loads is underway, and the results of this will also be presented at the conference.

[1] Propp K, Marinescu M, Auger DJ, O'Neill L, Fotouhi A, Somasundaram K, Offer GJ, Minton G, Longo S, Wild M & Knap V (2016) Multi-temperature state-dependent equivalent circuit discharge model for lithium-sulfur batteries, Journal of Power Sources, 328 (October) 289-299. Dataset/s: 10.17862/cranfield.rd.c.3292031

[2] Fotouhi A, Auger DJ, Propp K, Longo S, Purkayastha R, O'Neill L & Walus S (2017) Lithium-Sulfur cell equivalent circuit network model parameterization and sensitivity analysis, IEEE Transactions on Vehicular Technology, 66 (9) 7711-7721.

[3] Propp K, Auger DJ, Fotouhi A, Longo S & Knap V (2017) Kalman-variant estimators for state of charge in lithium-sulfur batteries, Journal of Power Sources, 343 (March) 254-267. Dataset/s: 10.17862/cranfield.rd.3834057

[4] Knap V, Auger DJ, Propp K, Fotouhi A & Stroe D-I (2018) Concurrent real-time estimation of state of health and maximum available power in lithium-sulfur batteries, Energies, 11 (2133) 1-23.

[5] Fotouhi A, Auger D, Propp K & Longo S (2018) Lithium-sulfur battery state-of-charge observability analysis and estimation, IEEE Transactions on Power Electronics, 33 (7) 5847-5859.

[6] Antaloae C, Marco J & Assadian F (2012) A novel method for the parameterization of a Li-ion cell model for EV/HEV control applications. IEEE Transactions on Vehicular Technology, 61(9), 3881–3892. https://doi.org/10.1109/TVT.2012.2212474