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The fuzzy graph theory uses a substantial and important role in modelling and structuring many optimization problems. DIfferent type of uncertainties exist in most of the optimization problems in real lIfe scenarios due to indeterminate and incomplete information and it is a challenging task for the expert to design those optimization problems applying fuzzy graph. To design the incomplete, uncertainty and vagueness in graphical optimization problems, several extensions of graph theoretical ideas are proposed. The idea of neutrosophic graph plays an important role to manage the uncertainty, linked with the indeterminate and incomplete data/information of any optimization problem. In this manuscript, we present the idea of regular neutrosophic graph, strong neutrosophic graph, bipartite neutrosophic graph, regular neutrosophic graph, and regular strong neutrosophic graph. We also introduce six different operations on neutrosophic graph, viz., cartesian product, composition, join, direct product, lexicographic and strong product. [ABSTRACT FROM AUTHOR]

This study proposes a dual‐stage cascaded operational control to attain a seamless transition of a standalone microgrid to a grid‐connected microgrid system. In order to safeguard the microgrid's stability, the strategy incorporates a bi‐directional converter. A dynamic reference frequency loop‐based resynchronisation controller is proposed to control the operation of the bi‐directional converter. The stage‐I operates to maintain the converter end system parameters equal to the utility. This creates a pseudo‐equalisation between the converter connected microgrid parameters and the utility. As a result, the simultaneously operating synchroniser controller switches the resynchronisation switch. The stage‐II of the proposed strategy addresses the transition controller, which switches the microgrid's mode of operation from standalone mode to grid‐connected mode. The grid connected bi‐directional converter‐based microgrid builds up its parameter equal to the utility. When microgrid builds up to a level that it satisfies the set values of the bypassing controller, it signals the bypassing switch (BS) to operate. In this study, the BS plays an essential role in bypassing the bi‐directional converter. The test system designed to study the proposed strategy is simulated on the podium of Matlab 2015b/Simulink. [ABSTRACT FROM AUTHOR]

Control over the voltage and the frequency instabilities in a grid‐forming microgrid due to the power mismatch conditions become the point of concern. Therefore, the study implements a self‐tuned proportional–integral integrated active power–voltage drooping and reactive power–frequency boosting control strategy for the precise power sharing among the distributed generators. Furthermore, to handle the power deficit scenarios and protect the system from the blackout, a system independent and priority‐based adaptive three‐stage load shedding strategy is proposed. The sensitivity of the strategy depends on the system inertia and is computed according to the varying absolute rate‐of‐change‐of‐frequency. The strategy incorporates the operation of a hybrid storage system comprised of battery and supercapacitor present in the microgrid, to provide a reliable power supply to the customers for a considerable time rather than a sudden load shedding. The effectiveness of the proposed strategies is investigated on a modified IEEE 13‐bus system. The study is simulated in the time domain, on the podium of MATLAB 2015b. [ABSTRACT FROM AUTHOR]