Systems and methods are provided for regulating a power converter. An example system controller includes: a driver configured to output a drive signal to a switch to affect a current flowing through an inductive winding of a power converter, the drive signal being associated with a switching period including an on-time period and an off-time period. The switch is closed in response to the drive signal during the on-time period. The switch is opened in response to the drive signal during the off-time period. A duty cycle is equal to a duration of the on-time period divided by a duration of the switching period. One minus the duty cycle is equal to a parameter. The system controller is configured to keep a multiplication product of the duty cycle, the parameter and the duration of the on-time period approximately constant.