This article addresses the application of real-time scheduling to the reduction of the peak load of power consumption generated by electric loads in Cyber-Physical Energy Systems (CPES). The goal is to reduce the peak load while achieving a desired Quality of Service of the physical system under control. The considered physical processes are characterized by integrator dynamics and modelled as sporadic real-time activities. Timing constraints are obtained from physical parameters and are used to manage the activation of electric loads by a real-time scheduling algorithm. As a main contribution, an algorithm derived from the multi-processor real-time scheduling domain is proposed to efficiently deal with a high number of physical processes (i.e., electric loads), making its scalability suitable for large CPES, such as smart energy grids. The cyber-physical nature of the proposed method arises from the tight interaction between the physical processes operated by the electric loads, and the applied scheduling. To allow the use of the proposed approach in practical applications, modelling approximations and uncertainties on physical parameters are explicitly included in the model. An adaptive control strategy is proposed to guarantee the requirements on physical values under control in presence of modelling and measurement uncertainties. The compensation for such uncertainties is done by dynamically adapting the values of timing parameters used by the scheduler. Formal results have been derived to put into relationship the values of quantities describing the physical process with real-time parameters used to model and to schedule the activation of loads. The performance of the method is evaluated by means of physically accurate simulations of thermal systems, showing a remarkable reduction of the peak load and a robust enforcement of the desired physical requirements.