A multi-stage interval optimization approach for operation of the smart multi-carries energy system considering energy prices uncertainty

This study presents a approach to optimize the operation of the smart multi-carrier energy system (SMCES) in residential consumers taking into account the uncertain nature of gas and electrical prices. The optimal operation of the SMCES is implemented using a multi-stage interval optimization approach with a multifunctional hydrogen storage system and demand-side management. Modeling optimization approach as three-stage is done for minimizing operation costs of the SMCES under energy prices uncertainty. The demand-side management based on load-shifting and load-interruption approaches for electrical demand in the residential buildings for the first and second stages is considered, respectively. The load-shifting for electrical demand is modeled subject to optimal consumption at day-ahead. Also, load-interruption approach is implemented for peak clipping of electrical demand subject to bidding prices from energy operator to residential consumers. In the third stage optimization, uncertainty of the electricity and gas prices in the operation cost with multi-criteria problem such as deviation and average rates by interval optimization approach is modeled. The modified electrical demand in the first and second stages is linked in the third stage for managing uncertainties. Moreover, multifunctional hydrogen storage system based on gas and electrical generation alongside demand-side management in third stage optimization for covering uncertainties is taken into account. The improved sunflower optimization algorithm is used to solve all stages, and the TOPSIS method is proposed for choosing the best trade-off of the multiple-criteria problem in the third stage. Finally, the suggested optimization modeling is represented in the several case studies to validate the achieved results with participation of the demand-side management and hydrogen storage system in day-ahead optimal operation of the SMCES. The participation of the demand-side management and the hydrogen storage systems leads to minimizing the deviation and average rates by 2.14% and 2.64% in comparison with non-participation.