In an electrical power network linear and non-linear models are used for directional overcurrent relay (DOCR) coordination issue by applying different heuristic techniques. Nature inspired algorithms (NIA) have found great interest in power system optimization issues. This article proposes the recently developed meta-heuristic technique known as Firefly Algorithm (FA) that mimics the flashing behavior of fireflies. The implementation of the proposed algorithm has been utilized to solve the coordination of Directional Over-current Relay (DOCR) problems. The main aim of this work is to find out the optimum values of the Time Dial Setting (TDS) to minimize the relay operating time. The modifications to original FA has been implemented in this paper to solve the DOCR coordination issues. Self-adaptive weight and experience-based learning strategy are added in the original FA, named as improved firefly algorithm (IFA). In IFA, a self-adaptive weight is presented to change the propensity of moving the best solution and ignoring the worst solution. In addition, an experience-based learning system is created and utilized arbitrarily to keep up the populace-assorted variety and improve the exploration capacity. The IFA has been tested on IEEE 6 and 30-bus systems and tested on IEEE 9-bus system for numerical DOCRs and the results had been verified by a comparative study with other optimization techniques. The obtained results show that the IFA provides efficient and promising results compared to other meta-heuristic techniques mentioned in the literature. The IFA has been successfully implemented on MATLAB software programming.

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.

In this study, recently proposed JAYA algorithm is implemented on the economic load dispatch problmes (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, multi-population (MP) method is introduced to improve the population diversity. However, the introduction of MP method adds extra parameters to JAYA algorithm, hence a self-adaptive strategy (SAS) is used to cope with the tuning problem for extra parameters. Moreover, to avoid being trapped by local optima, Lévy flight distribution is incorporated into the population iteration phase. Finally, a self-adaptive multi-population JAYA algorithm with Lévy flights (AML-JAYA) is proposed, it is evaluated by ELDPs with different constraints including power balance constraints, generating capacity limits, ramp rate limits, prohibited operating zones (POZs), valve-point effects and multi-fuel options. The comparisons with state-of-the-art methods indicate that AML-JAYA algorithm can generate more competitive results for solving the ELDPs.

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.

The economic load dispatch (ELD) problem is an optimization problem of minimizing the total fuel cost of generators while satisfying power balance constraints, operating capacity limits, ramp-rate limits and prohibited operating zones. In this paper, a novel multi-population based chaotic JAYA algorithm (MP-CJAYA) is proposed to solve the ELD problem by applying the multi-population method (MP) and chaotic optimization algorithm (COA) on the original JAYA algorithm to guarantee the best solution of the problem. MP-CJAYA is a modified version where the total population is divided into a certain number of sub-populations to control the exploration and exploitation rates, at the same time a chaos perturbation is implemented on each sub-population during every iteration to keep on searching for the global optima. The proposed MP-CJAYA has been adopted to ELD cases and the results obtained have been compared with other well-known algorithms reported in the literature. The comparisons have indicated that MP-CJAYA outperforms all the other algorithms, achieving the best performance in all the cases, which indicates that MP-CJAYA is a promising alternative approach for solving ELD problems.