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.

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.

Abstract:In an electrical power system, the coordination of the overcurrent relays plays an important role in protecting the electrical system by providing primary as well as backup protection. To reduce power outages, the coordination between these relays should be kept at the optimum value to minimize the total operating time and ensure that the least damage occurs under fault conditions. It is also imperative to ensure that the relay setting does not create an unintentional operation and consecutive sympathy trips. In a power system protection coordination problem, the objective function to be optimized is the sum of the total operating time of all main relays. In this paper, the coordination of overcurrent relays in a ring fed distribution system is formulated as an optimization problem. Coordination is performed using proposed continuous particle swarm optimization. In order to enhance and improve the quality of this solution a local search algorithm (LSA) is implanted into the original particle swarm algorithm (PSO) and, in addition to the constraints, these are amalgamated into the fitness function via the penalty method. The results achieved from the continuous particle swarm optimization algorithm (CPSO) are compared with other evolutionary optimization algorithms (EA) and this comparison showed that the proposed scheme is competent in dealing with the relevant problems. From further analyzing the obtained results, it was found that the continuous particle swarm approach provides the most globally optimum solution.

Abstract: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.

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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 paper 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 DOCR problems. The main aim of this paper 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 experiencebased 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 9bus system for numerical DOCRs and the results had been compared with results of Whale optimization algorithm to validate the performance of IFA in case of numerical DOCR. 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. INDEX TERMS Improved firefly algorithm (IFA), directional overcurrent relay coordination (DOCR), time dial setting (TDS), power system protection.

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 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.