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The use of energy storage systems (ESS) and distributed generators (DGs) to improve reliability is one of the solutions that has received much attention from researchers today. In this study, we utilize a multi-objective optimization method for optimal planning of distributed generators in electric distribution networks from the perspective of multi-objective optimization. The objective is to improve the reliability of the network while reducing the annual cost and network losses. A modified version of the multi-objective sine–cosine algorithm is used to determine the optimal size, location, and type of DGs and the optimal capacity, location, and operation strategy of the ESS. Three case studies of IEEE 33-bus, 69-bus and 141-bus test systems with Turkish DG and load data were conducted to validate the effectiveness of the proposed approach. The distribution of the Pareto front solutions and the optimal objective functions are compared with the other known algorithms. The simulation results show that the average energy not supplied and annual energy losses for the test systems are reduced by up to 68% and 64%, respectively. Moreover, the Pareto fronts of the proposed method show a better distribution and dominate those obtained by MOGWO, MOSMA, NSGA-II, MOPSO and MOEA-D according to three different Pareto optimization metrics. Finally, the computational effort result shows faster convergence of MOSCA compared to MOGWO, MOSMA, NSGA-II, MOPSO and MOEAD. • Optimal DER planning and ESS management in EDNs using a three-dimensional multiobjective optimization framework • DN Reliability improvement together with power losses and annual cost minimization. • 72 h optimization period to account the seasonal characteristics of the load and the DGs. • Real load curve and wind and solar radiation data of Turkish territory. • Multi objective sine–cosine algorithm providing better Pareto fronts according to two performance indices. [ABSTRACT FROM AUTHOR]

• A new formulation comprising energy exchange between off-peak and peak load hours. • MOGOA comprising an additional stopping criteria. • Reduced Pareto solution space due to cost analysis at peak load hours. • Better performance than the other heuristic optimization algorithms. • Real load and DG data with site-specific constraints and incentives of Turkey. The penetration of small-scale generators (DGs) and battery energy storage systems (BESSs) into the distribution grid is growing rapidly and reaching a high percentage of installed generation capacity. These units can play a significant role in achieving various objectives if installed at suitable locations with appropriate sizes. In this paper, we present a new multi-objective optimization model to improve voltage profiles, minimize DG and BESS costs, and maximize energy transfer between off-peak and peak hours. We allocate and size DG and BESS units to achieve the first two objectives, while optimizing the operation strategy of BESS units for the last objective. The Multi-Objective Grasshopper Optimization Algorithm (MOGOA) is used to solve the formulated constrained optimization problem. The proposed formulation and solution algorithm are tested on 33-bus and 69-bus radial distribution networks. The advantages of the Pareto solutions are discussed from various aspects, and the Pareto solutions are subjected to cost analysis to identify the best solutions in the context of the worst voltage profiles at peak load times. Finally, the performance of the MOGOA algorithm is compared with the other heuristic optimization algorithms using two Pareto optimality indices. [ABSTRACT FROM AUTHOR]