An electrical power supply system is provided comprising a number of rechargeable cells, a number of control electronics circuits and a charger which consists of apparatus for producing electricity from a renewable energy source, the electrochemical cells being divided into separate branches connected in parallel to the charger. Each control electronics circuit controls the charging of one branch by measuring a current being applied to the branch, integrating the current measured in the branch, determining a state of charge of the cell or cells of the branch, comparing the integrated current value with a set value set as a function of the determined state of charge, and interrupting the passage of current being applied to the branch when the integrated current reaches the set value. This system makes it possible to optimize the sharing out of charging current between parallel branches of battery cells while being adaptable as regards the number of cells used in parallel in the system.