An electric power supply system intended to be connected at the input to an electric power source and at the output to a load, comprising: - a main switching cell comprising a first main branch and a second main branch each including a main switch (T1, T2) which is controllable between an open state and a closed state, and - an auxiliary switching cell connected to the main switching cell and comprising a first secondary branch and a second secondary branch each including a secondary switch (T3, T4) controllable between an open state and a closed state on the one hand, and a connection branch for connecting the auxiliary switching cell to the main switching cell, the connection branch including a switching inductor, on the other hand, the main switching cell and the auxiliary switching cell being connected, cascaded from each other, the auxiliary switching cell further comprises at least two switching capacitors (C1, C2), a switching capacitor being positioned to parallel to one of the secondary switches (T3, T4) and another switching capacitor being positioned parallel to one of the main switches (T1, T2), the electric power supply system further comprising two input terminals (E1, E2), two output terminals (S2, S2), an output filter connected between the output terminals (S1, S2) and an inductor, the inductor being comprised in the output filter or else connected to one of the input terminals (E1, E2) and to the main switching cell, said inductor being capable of being passed through by an inductor current (i 2), the power supply system being capable of receiving an input voltage (Ve) and of providing at the output an output voltage (Vs), the power supply system further comprising control means able to control the opening and the closing of the main switches (T1, T2) and secondary main switches (T3, T4) for voltage-controlling the power supply system according to the input voltage (Ve) or to the output voltage (Vs), or else current-controlling the power supply system according to the inductor current (i 2), and the control means being configured to control the secondary switches (T3, T4) with opposite phases in relation to each other depending on an auxiliary switching current (i 1) passing through the switching inductor, to the state of the main switches (T1, T2) and to the voltage on the terminals of the secondary switch of the second secondary branch of the auxiliary switching cell, characterized in that that the control means are configured for controlling the closing of the secondary switch of the first secondary branch of the auxiliary switching cell: - if the main switch of the first main branch of the main switching cell is closed and the auxiliary switching current (i 1) is less than a second current threshold (I1_th_neg) of negative value, and - if the voltage on the terminals of the secondary switch of the second secondary branch of the auxiliary switching cell is greater than a first secondary threshold value (Vsw1_th_h), or else the main switch of the first main branch of the main switching cell is closed and the auxiliary switching current (i 1) is less than the second threshold current (I1_th_neg) for a predetermined time, and for controlling the opening of the secondary switch of the first secondary branch of the auxiliary switching cell if the main switch of the second main branch of the main switching cell is closed and the auxiliary switching current (i 1) is greater than a first current threshold (I1_th_pos) of positive value. - a main switching cell comprising a first main branch and a second main branch each including a main switch (T1, T2) which is controllable between an open state and a closed state, and - an auxiliary switching cell connected to the main switching cell and comprising a first secondary branch and a second secondary branch each including a secondary switch (T3, T4) controllable between an open state and a closed state on the one hand, and a connection branch for connecting the auxiliary switching cell to the main switching cell, the connection branch including a switching inductor, on the other hand, - if the main switch of the first main branch of the main switching cell is closed and the auxiliary switching current (i 1) is less than a second current threshold (I1_th_neg) of negative value, and - if the voltage on the terminals of the secondary switch of the second secondary branch of the auxiliary switching cell is greater than a first secondary threshold value (Vsw1_th_h), or else the main switch of the first main branch of the main switching cell is closed and the auxiliary switching current (i 1) is less than the second threshold current (I1_th_neg) for a predetermined time,