An uninterruptible power supply system, UPS system, comprising a plurality of uninterruptible power supply, UPS, sources (2a to 2e) coupled in parallel between a main input configured to be coupled to a power supply source and receive an input power, and a main output configured to be coupled to a load and provide output power to the load derived from at least the input power, each UPS (2a to 2e) comprising: - an input coupled to the main input, - an output coupled to the main output, and - a bypass line coupled between the input and the output via a bypass switch configured to be closed in a first operating mode, coupling said input to said output via the bypass line, and to be opened in a second operating mode, decoupling said input from said output, characterized in that, each UPS (2a to 2e) of the UPS system comprises a control unit, each of the control units is configured to be in communication with all the other control units of the UPS system, the control unit of each UPS (2a to 2e) comprising: - a first block comprising a first unit configured to monitor a current signal flowing in the bypass line of its UPS and determine a root mean square value, RMS, that is to say an effective value, of the current strength of said current signal, a second unit configured to collect the RMS values of its UPS and other UPSs of the UPS system for which the bypass switch is closed, and to set an RMS reference value corresponding to the lowest collected RMS value, and a third unit configured to determine an activation delay for closing the bypass switch of its UPS, the activation delay being equal to zero if the RMS value of its UPS is equal to the reference RMS value and the activation delay being different from zero otherwise, and - a second block comprising a fourth unit configured to control the bypass switch of its UPS according to the activation delay emitted by the third unit, the bypass switch is configured to be kept closed if the activation delay is at zero, otherwise the bypass switch is configured to be opened for a certain time corresponding to the activation delay and then closed. - an input coupled to the main input, - an output coupled to the main output, and - a bypass line coupled between the input and the output via a bypass switch configured to be closed in a first operating mode, coupling said input to said output via the bypass line, and to be opened in a second operating mode, decoupling said input from said output, characterized in that, each UPS (2a to 2e) of the UPS system comprises a control unit, each of the control units is configured to be in communication with all the other control units of the UPS system, the control unit of each UPS (2a to 2e) comprising: - a first block comprising a first unit configured to monitor a current signal flowing in the bypass line of its UPS and determine a root mean square value, RMS, that is to say an effective value, of the current strength of said current signal, a second unit configured to collect the RMS values of its UPS and other UPSs of the UPS system for which the bypass switch is closed, and to set an RMS reference value corresponding to the lowest collected RMS value, and a third unit configured to determine an activation delay for closing the bypass switch of its UPS, the activation delay being equal to zero if the RMS value of its UPS is equal to the reference RMS value and the activation delay being different from zero otherwise, and - a second block comprising a fourth unit configured to control the bypass switch of its UPS according to the activation delay emitted by the third unit, the bypass switch is configured to be kept closed if the activation delay is at zero, otherwise the bypass switch is configured to be opened for a certain time corresponding to the activation delay and then closed.