In electrical engineering problems, bio- and nature-inspired optimization techniques are valuable ways to minimize or maximize an objective function. We use the root tree algorithm (RTO), inspired by the random movement of roots, to search for the global optimum, in order to best solve the problem of overcurrent relays (OCRs). It is a complex and highly linear constrained optimization problem. In this problem, we have one type of design variable, time multiplier settings (TMSs), for each relay in the circuit. The objective function is to minimize the total operating time of all the primary relays to avoid excessive interruptions. In this paper, three case studies have been considered. From the simulation results, it has been observed that the RTO with certain parameter settings operates better compared to the other up-to-date algorithms.

The model of directional over current relays (DOCRs) coordination is considered as an optimization problem. It is generally formulated as linear programming (LP), non-linear programming (NLP) and mixed integer non-linear programming (MINLP), according to the nature of the design variables. For each kind of formulation, the main goal is to minimize the summation of operating times of primary relays, by setting optimal values for decision variables as time dial setting (TDS) and pickup current setting (IP) or plug setting (PS). In this paper, we proposed an oppositional Jaya (OJaya) algorithm with distance-adaptive coefficient (DAC), to effectively solve the DOCRs coordination problem. Firstly, by oppositional learning (OL), the searching space of Jaya is expanded and the diversity of its population is strengthened; secondly, by DAC, the population's trends of running towards the best position and escaping from the worst position is accelerated. The performance of OJaya is evaluated by 3-bus, 8-bus, 9-bus and 15-bus testing systems, in aspects of convergence rate, objective function value, robustness and computation efficiency. The results indicate the effectiveness and superiority of OJaya in solving DOCRs coordination problems compared with standard Jaya.

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The directional overcurrent relays (DOCRs) coordination is a useful tool in guaranteeing the safe protection of the power system by the proper coordination of primary and backup protection systems. The optimization model of this problem is non-linear and highly constrained. The main objective of this paper is to develop a hybridized version of the Whale optimization algorithm referred to as HWOA for the optimal coordination of the DOCRs. The hybridization is done by deploying the simulated annealing (SA) in the WOA algorithm in order to improve the best solution found after each iteration and enhance the exploitation by searching the most promising regions located by the WOA algorithm, which leads toward a globally optimum solution. The proposed algorithm has been applied to five test systems, including the IEEE 3-bus, 8-bus, 9-bus, 15-bus, and 30-bus test systems. Furthermore, the results obtained using the proposed HWOA are compared with those obtained using the traditional WOA and a number of up-to-date algorithms. The obtained results show the effectiveness of the proposed HWOA in minimizing the relay operating time for the optimal coordination of the DOCRs.INDEX TERMS Hybrid WOA, WOA, SA, directional overcurrent relay (DOCR), plug setting (PS), time dial setting (TDS), protection coordination. the Department of Electrical Engineering, Yeungnam University, South Korea. His areas of interest include power system protection, power system analysis, and design and power system deregulation.

In this paper, a recently proposed Jaya algorithm is implemented on the economic load dispatch problems (ELDPs). Different from most of the other meta-heuristics, Jaya algorithm needs no algorithm-specific parameters, and only two common parameters are required for effective execution, which makes the implementation simple and effective. Simultaneously, considering the non-convex, non-linear, and non-smooth characteristics of the ELDPs, the multi-population (MP) method is introduced to improve the population diversity. However, the introduction of the MP method adds extra parameters to the Jaya algorithm, hence a self-adaptive strategy is used to cope with the tuning problem for extra parameters. Moreover, to avoid being trapped by local optima, Lévy flights distribution is incorporated into the population iteration phase. Finally, Jaya algorithm with self-adaptive multi-population and Lévy flights (Jaya-SML) is proposed, it is evaluated by ELDPs with different constraints including power balance constraints, generating capacity limits, ramp rate limits, prohibited operating zones, valve-point effects, and multi-fuel options. The comparisons with state-of-the-art methods indicate that Jaya-SML can generate more competitive results for solving the ELDPs. INDEX TERMS Economic load dispatch problems, Jaya, self-adaptive, multi-population, Lévy flights.