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•Open circuit voltage, Z-modulus and the phase angle are indicators of state of charge.•Different frequencies reflect the different phenomena in the lead-acid battery.•Combination of indicators leads to a higher accuracy of state of charge estimation.

•As additives were used carbon CR-2996 and various types of organic expanders − Vanisperse A, Vanillex HW and Vanillex N.•Cells with higher amount of added organic expander well tolerates deep cycling.•Cells with high amount of additives regenerate better during the conditioning cycles between PSoC runs.•The cell capacities increase with higher amount of organic expanders.•The cell without additional organic additives (Indulina AT) shows only slight degradation during the three PSoC runs.

•This work deals with the study of influence of additives added to the negative active mass of the lead-acid battery electrode. Specifically, it’s studied the influence of acrylic fibers (1.5wt%) and different amounts of carbon CR 2996 on the final properties. Carbon was added in an amount of 0.15; 0.46; 0.78; 1.4; 2.65 and 5.15wt.%. It was performed formation, depth of discharge cycles (DoD) and partial state of charge cycling (PSoC).

•Glass fiber on lead is one of the additives studied.•Graphite and titanium dioxide additives enhance the lead electrode performance.•AFM study contributes to development of better lead-acid batteries/

•Values of the impedance components are changing with ageing of the cell.•Impedance modulus and phase angle are changing during discharging.•Impedance modulus and phase angle are changing during charging.•Used frequency reveals different impedance components of the battery.

•Glass fibers in the negative electrode improve its performance.•Expander Indulin AT suppresses formation of a passivation layer.•Expander Indulin AT causes higher polarization resistance of the lead electrode.•Atomic Force Microscopy gives direct insight on surface during charging/discharging.