A Mathematical Modelling of Discharge and Charge Phenomena of A Lead-Acid Battery

A mathematical model has been formulated and verified with experimental data to describe a lead acid battery’s discharging and charging characteristics here. First, an overview of the empirical formula and the corresponding circuit model for discharging has been explained in this work. Then a set of 25 battery samples has been discharged at different C-rate to obtain discharge data (voltages vs SOC) to evaluate all the parameters in the model. Next, simulation has been performed with the model from the existing formula and the results have been compared with each of the battery samples. Finally, the parameters have been set from that particular battery for which the simulated value gives a minimum error with all the other battery discharge data from the set. Conclusively the discharge model with all of its parameters has been verified with battery sets of different capacities. For charging, the existing formula has been modified to represent the over-charging phenomenon at higher SOC. Then all of the parameters have been selected by analyzing all of the experimental data from a set of few battery samples. The final value of the parameters has been chosen for which the error is minimum. Battery temperature, average DOD, and battery lifetime are all of these variables that have been considered to be constant for the obtained experimental data here.