A charge balancing device of an electrical energy power storage device including a plurality of series-connected electrical energy storage elements (201, 202, 203), it including: - a DC/AC converter, including: - an inverter comprising an input intended to be connected to a direct-voltage source; - a plurality of AC/DC converters (301, 302, 303) each comprising an input and an output connected to one of said respective energy storage elements (201, 202, 203), each AC/DC converter selectively supplying its output with power, and being connected to a respective output of the secondary of a transformer via first and second conducting connections having respective inductances Lai and Lri for an AC/DC converter with an index i, the leakage inductance of the secondary of the transformer for its output connected to the converter with an index i having a value Lti; - a transformer; - a control circuit configured to control each AC/DC converter (301, 302, 303) for the selective power supply of its output, and configured to control the DC/AC converter in such a way that it supplies a power Pcc=act*Pinc to the primary of the transformer when the number of outputs act supplied with power by their AC/DC converter is less than or equal to a threshold, where Pinc is a constant, and configured to control the DC/AC converter in such a way that it supplies the same constant power Pout when the number of outputs act supplied with power by their AC/DC converter is greater than said threshold, characterized in that: - the charge balancing device further includes a series resonant circuit connected to the output of the inverter; - the primary of the transformer is connected to the series resonant circuit and the secondary of the transformer has secondary windings and outputs connected to the terminals of respective secondary windings, each of these outputs being connected to an input of a respective AC/DC converter; - each of said AC/DC converters includes a full-wave rectifier circuit, - the first and second conducting connections of said converters are dimensioned in such a way that the values of Lti, Lai and Lri verify the following relationship for each value of the index i: Lti+Lai+Lri=K, where K is a constant. - a DC/AC converter, including: - an inverter comprising an input intended to be connected to a direct-voltage source; - an inverter comprising an input intended to be connected to a direct-voltage source; - a plurality of AC/DC converters (301, 302, 303) each comprising an input and an output connected to one of said respective energy storage elements (201, 202, 203), each AC/DC converter selectively supplying its output with power, and being connected to a respective output of the secondary of a transformer via first and second conducting connections having respective inductances Lai and Lri for an AC/DC converter with an index i, the leakage inductance of the secondary of the transformer for its output connected to the converter with an index i having a value Lti; - a transformer; - a control circuit configured to control each AC/DC converter (301, 302, 303) for the selective power supply of its output, and configured to control the DC/AC converter in such a way that it supplies a power Pcc=act*Pinc to the primary of the transformer when the number of outputs act supplied with power by their AC/DC converter is less than or equal to a threshold, where Pinc is a constant, and configured to control the DC/AC converter in such a way that it supplies the same constant power Pout when the number of outputs act supplied with power by their AC/DC converter is greater than said threshold, - the charge balancing device further includes a series resonant circuit connected to the output of the inverter; - the primary of the transformer is connected to the series resonant circuit and the secondary of the transformer has secondary windings and outputs connected to the terminals of respective secondary windings, each of these outputs being connected to an input of a respective AC/DC converter; - each of said AC/DC converters includes a full-wave rectifier circuit, - the first and second conducting connections of said converters are dimensioned in such a way that the values of Lti, Lai and Lri verify the following relationship for each value of the index i: Lti+Lai+Lri=K, where K is a constant.