In recent years, demand response programs (DRPs) have become an effective method of encouraging users to participate in energy system operations. The problem of optimal energy flow (OEF) is a complex challenge in multiple power systems. Accordingly, this study aims to propose a novel evolving framework for optimal OEF operation of an electricity, heat, and gas integrating system, taking into account flexible heat and electricity demands. To this end, a switching idea between input energy carriers has been introduced to combine the traditional DRP with demand-side energy supply management. Switching between the feeding energy carriers could change how power is supplied to the end users and thus would affect the total cost of the grid. Operators of integrated systems minimize the operational costs associated with supplying flexible power to users in this study. Considering the high nonlinearity of the problem, a novel optimization algorithm is presented for solving the complex OEF based on the improved teaching–learning-based optimization algorithm (ITLBOA). According to the outcomes, flexible DRP reduces operational prices and smooths power demand curves for power and heating networks.

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