In the energy management of a network, it is expected that by extracting the optimal performance for the power sources, storage equipment, and responsive demand, a favorable economic and technology situation is achievable for the network and the mentioned elements. Virtual power plants, as a unit aggregating resources, storage, and responsive loads, can create more favorable conditions in network energy management. So, it is expected that the positive effect of the virtual power plant format on the economic and technical situation of the distribution system is far more than those of managing individual elements mentioned in the network. Consequently, the distribution network operator's economic, environmental, and technical goals are met through the concurrent administration of reactive and active power in the smart distribution network that is equipped with a flexible-sustainable virtual power plant. The system operator is accountable for reducing the weighted sum of the voltage security index, energy loss, and energy cost of the distribution network. This problem is associated with the optimal power flow formulation, which considers the environmental limits and security of voltage in the distribution network, the renewable resource operation model and flexibility in the form of a virtual power plant, and the system's flexibility constraints. Flexibility resources considered in the present study are price-based demand response and electric vehicle parking lots. Stochastic optimization relying on the Unscented Transform assists in providing a suitable model for uncertain quantities resulting from the amount of load, electric vehicles, renewable power, and price of energy and eventually shortens the computing time and accurately computes the flexibility index. The optimal compromise solution amongst various objective functions can be found through fuzzy decision-making. Some innovations of this research include concurrent administration of active and reactive power in virtual power plant, concurrent modeling of economic, operational, environmental, voltage security, and flexibility indicators in the distribution network, utilization of electric vehicles, and demand response as a source of flexibility, use of Unscented transform for modeling the uncertainties corresponding to the exact calculation of flexibility. The suggested method was simulated in the IEEE 69-bus radial smart distribution system. Regarding the numerical report obtained, the optimal performance of each of the renewable generation, demand response, and parking of electric vehicles can significantly impact the economic and technical condition of the distribution network. However, the best condition was obtained when the mentioned elements were placed in the form of a virtual power plant. So, in such a situation, the energy cost is around $1862 for the said network. The lowest value for the worst security index in this network is around 0.933 p.u. Energy loss, maximum voltage drop, and peak load carrying capability are equal to 1.902 MWh, 0.047 p.u., and 5.624 MW, respectively. As a result, and based on numerical findings, the method can attain sustainable social welfare. The optimal power scheduling of sustainable systems can enhance the economic, security of voltage, and operational, conditions of the network by roughly 43 %, 26.9 %, and 47 %-62 %, respectively, compared to power flow studies. Furthermore, the ideal administration of virtual power plants enables the proposed plan to achieve 100 % flexibility. Additionally, it can substantially diminish the degree of contamination within the distribution network.
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