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Summary Penetration of distributed generations in distribution networks (active distribution networks) has resulted in some problems such as change in short circuit level and direction of fault current flow. Such conditions may cause some relays to malfunction. In this paper, a method for coordinating directional overcurrent relays in active distribution networks taking uncertainties into consideration is proposed. These uncertainties include changes in operation conditions, changes in fault conditions, error in measuring equipment, and outage of distributed generations. Therefore, an optimization frame with new variables is presented, which can be used to create different characteristic curves. Taking uncertainties into account causes the number of constraints to increase and the problem of coordination of directional overcurrent relays to become more complicated. Thus, a two‐step approach is used to solve this problem. In the first step, an algorithm is used to form the constraints of the problem, then, in the second step, a hybrid optimization algorithm consisting of the cuckoo search algorithm and linear programming is proposed. The simulation results for active radial and meshed distribution networks are presented to demonstrate the effectiveness of the proposed approach.

One of the important issues in the planning stage of active distribution networks (ADNs) is the optimal design of microgrids (MGs). The design, as a multi-MG system, is comprehensively investigated in this study. In this way, the allocation of energy storage systems (ESSs) and partitioning of ADN are simultaneously performed in order to minimise the cost and maximise the self-adequacy and the reliability considering the uncertainty of load and renewable energy resources. In this study, two approaches are considered. In approach I, the cost, reliability and self-adequacy objectives are taken into account whereas, in approach II, a new probabilistic index representing the ratio of load to storage capacity is also added to mentioned objectives. The proposed multi-objective problem is solved with non-dominated sorting genetic algorithm-II (NSGA-II) as a well-known algorithm based on a probabilistic approach using the Monte-Carlo simulation method (MCSM) and in each approach, several Pareto optimal solutions are evaluated. To simulate and validate the effectiveness of the proposed method, two benchmark distribution networks (the 33-bus and the 119-bus) are used.

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