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In this paper, Improved Moth Flame Optimization (IMFO) algorithm is implemented to restore power flow solvability by transferring of adequate amount of load shedding (LS) through the power system. Shunt Flexible Alternating Current Transmission System (FACTS) devices including Static VAR Compensator (SVC) and Static Synchronous Compensator (STATCOM) are incorporated with the system for obtaining better reactive power support. Maximum power system loadability is obtained using Continuation Power Flow (CPF). Both of normal operation and contingency conditions for generator and bus outages are considered for the fruition of the validity of the suggested method to operate under various conditions. The proposed approach is validated using IEEE-30 bus standard test system. The obtained results manifest the capability of the suggested method to reduce the LS values leading to continuous service to the customers and the capability of preventing voltage collapse and restore the bus voltages to the permissible limits. The emulation results reveal the effectiveness of the suggested method for enhancement of the power system loadability. [ABSTRACT FROM AUTHOR]

In power systems protection, the optimal coordination of directional overcurrent relays (DOCRs) is of paramount importance. The coordination of DOCRs in a multi-loop power system is formulated as an optimization problem. The main objective of this paper is to develop the whale optimization algorithm (WOA) for the optimal coordination of DOCRs and minimize the sum of the operating times of all primary relays. The WOA is inspired by the bubble-net hunting strategy of humpback whales which leads toward global minima. The proposed algorithm has been applied to six IEEE test systems including the IEEE three-bus, eight-bus, nine-bus, 14-bus, 15-bus, and 30-bus test systems. Furthermore, the results obtained using the proposed WOA are compared with those obtained by other up-to-date algorithms. The obtained results show the effectiveness of the proposed WOA to minimize the relay operating time for the optimal coordination of DOCRs. [ABSTRACT FROM AUTHOR]