Methods of operating a mobile device are provided. A method of operating a mobile device includes calculating a mean power consumption with respect to a time duration, using a measured power consumption or using an estimated power consumption. The method includes comparing a performance constraint standard with the mean power consumption. Moreover, the method includes constraining performance of the mobile device, using an application processor of the mobile device, in response to determining that the mean power consumption exceeds the performance constraint standard. Related mobile devices are also provided.