## 5 Conclusions  
The study evaluates LABs performance for TVs in terms of storage capacity and lifespan without changing the current chemical composition of the batteries. The results show that the proposed integrated fuzzy-logic and Triple-loop PI-based control battery management strategy for lead-acid and lithium-ion hybrid battery energy storage systems; improves the batteries' performance in terms of storage capacity and lifespan. The fuzzy  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case No.** & **Battery Type** & **Capacity (Ah)** & **CCC (A)** & **Load Share (\%)** \\ \hline \multirow{4}{*}{Two} & \multirow{2}{*}{a} & HESS & 70.4 & 599.1 & 100 \\ \cline{3-5}  & & LAB & 60 & 326.9 & 53 \\ \cline{3-5}  & & LIB & 7.8 & 290.3 & 47 \\ \cline{3-5}  & & HESS & 69.8 & 596.2 & 100 \\ \cline{3-5}  & & LAB & 62 & 378.5 & 62.9 \\ \cline{3-5}  & & LIB & 10.4 & 222.9 & 37.1 \\ \hline \multirow{4}{*}{Three} & \multirow{2}{*}{a} & HESS & 90.4 & 653.2 & - \\ \cline{3-5}  & & LAB & 80 & 386.7 & 59.7 \\ \cline{3-5}  & & LIB & 10.4 & 260.5 & 40.3 \\ \cline{3-5}  & & HESS & 90 & 665.5 & 100 \\ \cline{3-5}  & & LAB & 77 & 379.1 & 56.1 \\ \cline{3-5}  & & LIB & 13 & 293.4 & 43.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: A summary of the HESS case results.  
Figure 25: The estimated lifespan of case three (a) versus Case three (b).  
logic control is used to allocate the reference current within the hybridised batteries and to ensure the state of charge of hybridised batteries is within the permissible maximum and minimum limits. The results show that the FLC is capable of allocating the required reference current within a margin of \(\pm\)2%. The bidirectional DC-DC buck-boost converter with a triple-loop PI-based controller is used to control the voltage and current flow of the hybridised batteries during charging and discharging modes based on the reference voltage and current. The results show an enhancement of storage capacity and lifespan of the proposed 12 V-70 Ah HESS of 10.18% and 3.49 years, respectively, in comparison with single a 12 V-70 Ah LAB. The results of case three show an enhancement of storage capacity and lifespan for the proposed 12 V-90 Ah HESS is 3.3% and 3.5 years, respectively, in comparison with a single 12 V-90 Ah LAB.  
Conceptualization, M.J.L., S.P.D.C. and T.O.O.; methodology, M.J.L., A.T.P.Z., S.P.D.C. and T.O.O.; software, M.J.L., A.T.P.Z., S.P.D.C. and T.O.O.; validation, M.J.L., S.P.D.C. and T.O.O.; formal analysis, M.J.L., S.P.D.C. and T.O.O.; investigation, M.J.L., A.T.P.Z., S.P.D.C. and T.O.O.; resources, M.J.L.; data curation, M.J.L., A.T.P.Z., S.P.D.C. and T.O.O.; writing--original draft preparation, M.J.L.; writing--review and editing, M.J.L., S.P.D.C. and T.O.O.; visualization, M.J.L., A.T.P.Z., S.P.D.C. and T.O.O.; supervision, S.P.D.C. and T.O.O.; project administration, M.J.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors would like to thank the S5 Enterprises, Tshwane University of Technology, Au-toX (Pty) Ltd., South Africa for providing the necessary infrastructure, resources and support tosuccessfully conduct this research study.  
The authors declare no conflict of interest.