An accumulator battery system has stages, a power connection, a controller, and circuits. The stages are series-connected. Each has an electrochemical accumulator and a switch. A power connection connects a load to the stages. Each the circuit is associated with a stage. Each circuit generates a voltage variation at terminals of its associated stage, and applies, to a switch of the associated stage, a binary sequence at a frequency. The sequence differs from those of other stages, thus allowing distinguishing between stages based on the sequence. The controller, which is connected to the stages by the power connection, measures a voltage variation across terminals of the stage in response to application of the binary sequence to the stage, identifies a stage from which the variation originates by searching for its associate sequence, and determines, from the variation, an impedance of the identified stage for that frequency.