Managing energy in electrical systems that encounter uncertainties is one of the prevalent challenges in power systems. This problem arises from the variations in real-time fossil fuel prices in global markets and power plants. Consequently, the unpredictability of energy prices in the markets presents a considerable obstacle to accurately modeling the economic factors of power consumption and generation. This research concentrates on power optimization within the smart electrical grid (SEG), taking into account the uncertainty of power prices with the involvement of consumers. The power optimization under uncertainty is done by two-level interval and multi-objective approach. At the first level, multi-demand side management (DSM) strategies such as load demand reduction and shifting, are formulated as a multi-objective approach for optimizing power consumption. The optimization of energy consumption at this level through load demand reduction and shifting strategies is achieved by providing a price to consumers and establishing an optimal consumption rate, respectively. It is important to note that the optimization of energy consumption at the first level is modeled independently of power prices. The second level employs an interval approach to model the uncertainty of power prices while aiming to minimize power generation costs. The operational cost of power is modeled using a multi-objective approach that includes both the average and deviation amounts of the power generation cost. The optimization of power consumption at the first level is integrated into the second level to alleviate the impacts of uncertainty in power prices. The grasshopper optimization algorithm (GOA) and Shannon entropy method are utilized to solve the two-level interval and multi-objective approach. A 69-node test grid is used as the SEG for implementing the two-level interval and multi-objective approach alongside various DSM strategies. The proposed optimization method is presented as a numerical model in several case studies to validate the results obtained in deterministic and interval approaches.
Moradi et al. (Mon,) studied this question.