The worldwide energy revolution has accelerated the utilization of demand-side manageable energy systems such as wind turbines, photovoltaic panels, electric vehicles, and energy storage systems in order to deal with the growing energy crisis and greenhouse emissions. The control system of renewable energy units and energy storage systems has a high effect on their performance and absolutely on the efficiency of the total power network. Classical controllers are based on integer-order differentiation and integration, while the fractional-order controller has tremendous potential to change the order for better modeling and controlling the system. This paper presents a comprehensive review of the energy system of renewable energy units and energy storage devices. Various papers are evaluated, and their methods and results are presented. Moreover, the mathematical fundamentals of the fractional-order method are mentioned, and the various studies are categorized based on different parameters. Various definitions for fractional-order calculus are also explained using their mathematical formula. Different studies and numerical evaluations present appropriate efficiency and accuracy of the fractional-order techniques for estimating, controlling, and improving the performance of energy systems in various operational conditions so that the average error of the fractional-order methods is considerably lower than other ones.

The two-way communication of electricity and information in smart homes facilitates the optimal management of devices with the ability to charge and discharge, such as electric vehicles and electrical storage systems. These devices can be scheduled considering domestic renewable energy units, the energy consumption of householders, the electricity tariff of the grid, and other predetermined parameters in order to improve their efficiency and also the technical and economic indices of the smart home. In this paper, a novel framework based on decision vectors and the analytical hierarchy process method is investigated to find the optimal operation schedule of these devices for the day-ahead performance of smart homes. The initial data of the electric vehicle and the electrical storage system are modeled stochastically. The aim of this work is to minimize the electricity cost and the peak demand of the smart home by optimal operation of the electric vehicle and the electrical storage system. Firstly, the different decision vectors for charging and discharging these devices are introduced based on the market price, the produce power of the domestic photovoltaic panel, and the electricity demand of the smart home. Secondly, the analytical hierarchy process method is utilized to implement the various priorities of decision criteria and calculate the ultimate decision vectors. Finally, the operation schedule of the electric vehicle and the electrical storage system is selected based on the ultimate decision vectors considering the operational constraints of these devices and the constraints of charging and discharging priorities. The proposed method is applied to a sample smart home considering different priorities of decision criteria. Numerical results present that although the combination of decision criteria with a high rank of electricity demand has the highest improvement of technical and economic indices of the smart home by about 12 and 26%, the proposed method has appropriate performance in all scenarios for selecting the optimal operation schedule of the electric vehicles and the electrical storage system.