Entropy driven integrated fractional particle swarm optimization - gravitational search algorithm optimization expedition for optimal coordination of directional over current relays

The protective system is an essential part of all power network subsystems, including the protection systems of generation, transmission, and distribution networks, in order to ensure the integrity of the power system components, such as generators, bus bars, transformers, and feeder lines thus, a combination of different types of protection relays is utilized in the protection system, i.e., the prevention of the overcurrent, line to ground, line to line, double line to ground, faults in the associated system. In the current study, the performance of legacy power system protection is enhanced by means of reducing the total time of operation, including the directional over current relay (DOCR) operating time and coordination time among primary and backup DOCRs, while keeping the coordination time of interval (CTI), pickup tap setting (PTS), and time dial setting (TDS) within acceptable limits, during the protection of standard power system. In order to reduce the fitness evaluation function in IEEE 3-bus, 8-bus, and 15-bus systems, a new approach called fractional particle swarm optimization gravitational search algorithm entropy metric (FPSOGSA-EM) is designed for determining the optimal settings of the CTI, PTS, and TDS. The FPSOGSA-EM incorporates the underlying theories of fractional derivatives inside the mathematical framework of canonical particle swarm optimization aided with gravitational search algorithm along with entropy metric to improve its convergence rate and avoid sub optimality. The yielded results from FPSOGSA-EM are compared to those from other cutting-edge counterpart algorithms such as modified particle swarm optimization, modified water cycle technique, modified electromagnetic field optimization, enhanced grey wolf optimization, seeker algorithm, teaching learning-based optimization, harmony search algorithm and FPSOGSA. By sharply reducing the period of operation of DOCRs in traditional IEEE 3-bus, 8-bus, and 15-bus test systems, the FPSOGSA-EM has outperformed these previously described methods. While the consistency, robustness, optimization brilliance, reliability and stability of the proposed scheme are ascertained by means of statistical interpretations such as minimum fitness evolution, cumulative distribution function (CDF), Boxplot representations, histograms plots and quantile–quantile plot demonstrations as a measure of center tendency and diversity.