Perspective modelling and measuring discharge voltage on truncated data of long-term stored Li-ion batteries based on functional state space model

The subject of battery sources and electrical energy accumulators is currently very topical. Moreover, the possibilities of reusing already discarded sources are being explored as so-called “second-life batteries”. This article is concerned with studying and modelling the behaviour of a battery in an electric aircraft in operation — the voltage during discharge. Outcomes from extensive experiments on real long-term stored batteries have provided statistically robust sets of data on both long-term stored and new batteries; some of the data, however, are truncated. A modern approach that neglects the truncated issues and is based on functional data analysis and modified with a specific time series is used to model the process. This suggested model is much more accurate than the model used previously as it can effectively process truncated data. It also allows a certain degree of generalization. The aim is to determine the probability density of the time when the battery reaches the critical value, including the numerical statistics, for both stored and new batteries. The results are compared using the specific statistical Kullback–Leibler divergence approach to determine the degree of difference. The proposed model applies to similar issues where battery voltage is modelled in a time domain while the data form is truncated. It is proved, however, that further use of the stored batteries does not disrupt the safe and reliable operation of an electric airplane in terms of their functionality.