A switching power converter includes an inductor coupled to a terminal operably supplied with an input voltage. A semiconductor switch is coupled to the inductor and configured to enable and disable an input current passing through the inductor in accordance with a drive signal. A current sense circuit is coupled to the inductor or the semiconductor switch and is configured to generate a current sense signal representing the input current passing through the inductor or the semiconductor switch. A control circuit receives the current sense signal and is configured to: close the semiconductor switch regularly in accordance with a clock frequency, to integrate the current sense signal thus providing an integrated current sense signal to compare the integrated current sense signal with a threshold that is a function of the input voltage.