System and method for protecting a power converter. A system includes a threshold generator configured to generate a threshold signal, and a first comparator configured to receive the threshold signal and a first signal and to generate a comparison signal. The first signal is associated with an input current for a power converter. Additionally, the system includes a pulse-width-modulation generator configured to receive the comparison signal and generate a modulation signal in response to the comparison signal, and a switch configured to receive the modulation signal and adjust the input current for the power converter. The threshold signal is associated with a threshold magnitude as a function of time. The threshold magnitude increases with time at a first slope during a first period, and the threshold magnitude increases with time at a second slope during a second period. The first slope and the second slope are different.