Background and Objectives: Distributed generations (DGs) based on renewable energy, such as PV units, are becoming more prevalent in distribution networks due to technical and environmental benefits. However, the intermittency and uncertainty of these sources lead to technical and operational challenges. Energy storage application, uncertainty analysis, and network reconfiguration are apt therapies to resist these challenges. Methods: Energy management of modern, smart, and renewable-penetrated distribution networks is tailored here considering the uncertainties correlations. Network operation costs including switching operations, the expected energy not served (EENS) index as the reliability objective, and the node voltage deviation suppression as the technical objective are mathematically modeled. Multi-objective particle swarm optimization (MOPSO) is considered as the optimization engine. Scenario generation method and Nataf transformation are used in Probabilistic evaluations of the problem. Moreover, the technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) is deployed to make a final balance between different objectives to yield a unified solution.Results: To show the effectiveness of the proposed approach, the IEEE 33-node distribution network is put under extensive simulations. Different cases are simulated and interrogated to assess the performance of the proposed model.Conclusion: For different objectives dealing with different aspects of the network, remarkable achievements are attained. In brief, the final solution shows 4.50% decrease in operation cost, 13.07% improvement in reliability index, and 18.85% reduction in voltage deviation compared to the initial conditions.