**4. Discussion**

This research work has been beneficial for us, as our research experience was considerably improved, and we learned some useful lessons for the future. The preliminary results obtained so far in the design, modelling, implementation and validation of Li-ion batteries, development and implementation of real-time SOC estimation algorithms are enriched continuously and supplemented based on a new experience and a considerable routine in using one of the most powerful pieces of software for real-time design and implementation, such as MATLAB and Simulink. In the following are summarized some of the most relevant aspects that have attracted our attention and enriched our research experience in the field so far. In the next five subsections, the performance analysis of each SOC estimator, in terms of SOC convergence speed, real-time implementation, accuracy and robustness performance analysis, is based on the data shown in Tables 1 and 2 and Figures A12, A15, A18 and A21 from Appendix A.1, corresponding to the scenario R0, for an SOC initial value, SOCini = 70%.


**Table 2.** The response speed convergence of AEKF SOC, UAKF SOC and PFE SOC (in seconds). Qnom =4.2 Ah (30% degradation of battery due to ageing e ffects) VarY = 0.001.
