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In this paper, different methods are utilized to solve the coordination issue involving directional overcurrent relays (DOCRs) and distance relays. The proper coordination of DOCRs and distance relays is a critical issue for system security in electrical networks. Finding the DOCRs setting, pickup current(Ip) and timed dial setting (TDS), and operating time for zone-2 of distance relays is the primary objective of solving the coordination problem. The constant parameters A & B of the directional overcurrent relay that are responsible to control the form of the relay´s characteristics as well as the Ip and TDS have been regarded as variables in this problem. The optimal value for these four DOCR settings has been determined using different optimization techniques. The primary and backup relays must operate sequentially and without any violations, and this must be guaranteed by optimization techniques. In order to determine the operation time for zone-2 and DOCRs setting, optimization methods are examined utilizing the 8-bus and IEEE 30-bus networks. Different optimization algorithms, including recent and traditional techniques, are compared. The obtained results show the superiority of the genetic algorithm (GA) in solving the coordination problem of distance relays and DOCRs. Also, the obtained results prove the ability of the GA method compared to the particle swarm algorithm (PSO), grey wolf optimization (GWO), water cycle technique (WCA), equilibrium optimizer (EO), African vultures optimization algorithm (AVOA), flow direction algorithm (FDA), and gorilla troops optimizer (GTO) techniques. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient Gorilla troops-inspired algorithm to cope optimal power flow (OPF) problem considering uncertainty of renewable energy sources (RES). The problem is formulated as large-scale constrained optimization problem with non-linear characteristics. Its degree of complexity increases with incorporation of intermittent energy sources, making it harder to be solved using conventional optimization techniques. However, could be efficiently resolved by nature-inspired optimization algorithms and solvers. The objective function is the overall cost of system, including reserve cost for over-estimation and penalty cost for under-estimation of two types of PV-solar and wind energy. To demonstrate the consistency and robustness of the developed algorithm a case study on the modified IEEE 30-bus system and and Adrar's power network (isolated grid) is carried out. Simulation results show the capability of GTO to find high quality optimal feasible solutions and ranked first among the compared algorithms, and so, over different function landscapes. [ABSTRACT FROM AUTHOR]

The focus of this study is on solving the coordination problem between distance relays (DISRs) and directional overcurrent relays (DOCRs), which is a complex nonlinear problem with various constraints. Ensuring proper coordination between DOCRs and distance relays is critical for maintaining the security of electrical networks. The primary objective of employing optimization algorithms is to determine the optimal operating time for zone-2 of distance relays, as well as the DOCRs setting, time dial setting (TDS), and pickup current (Ipickup). The optimization techniques must also guarantee that the primary and backup relays operate in sequence without any violation. To this end, both recent and well-established optimization algorithms are evaluated using an 8-bus network, with the aim of determining the DOCRs setting and the optimal operating time for zone-2 of distance relays. Furthermore, a comparative analysis of different optimization algorithms, including both traditional and recent techniques, is conducted. [ABSTRACT FROM AUTHOR]

The aim of the optimization economic load dispatch (ELD) problem is to assign the optimal generated power of the thermal units for cost reduction with satisfying the loading of the operational constraints. The ELD is a high-dimensional and non-convex problem that became a more complex problem in the case of optimizing the output generated power of large-scale systems. In this regard, an enhanced version of the Beluga whale optimization (EBWO) is proposed to deal with the ELD of the large-scale systems. Beluga whale optimization (BWO) is an efficient new optimization technique that mimics the behavior of the Beluga whales (BWs) in preying, swimming, and whale fall. However, the BWO may suffer from stagnation in local optima and scarcity of population diversity like other metaheuristics. The proposed EBWO algorithm is presented to render the standard BWO more robust and powerful search by using two strategies including the cyclone foraging motion for boosting the exploitation phase of the optimization algorithm and the quasi-oppositional based learning (QOBL) for improving population diversity. Firstly, Simulations are carried out on seven benchmark functions to prove the validation of the proposed EBWO algorihm compared with five recent algorithms. Then, The performance of the EBWO is checked on 11-units, 40-units, and also 110-unit test systems, and the obtained results of EBWO are compared with other well-known techniques such as the classical BWO, FOX Optimization Algorithm (FOX), Skill Optimization Algorithm (SOA), and Sand Cat swarm optimization (SCSO) as well as the with existing algorithms from the literature including DE, TLBO, MPSO, NGWO, IGA, NPSO, CJAYA, SMA, PSO, PPSO, SSA, MPA, MGMPA, and HSSA. The Numerical results show that the proposed algorithm is very competitive compared with the other reported optimization algorithms in obtaining low fuel costs. [ABSTRACT FROM AUTHOR]

Sizing optimization and power smoothing methodology in highly fluctuating grid-connected renewable systems represent important challenges nowadays, the total cost and energy quality depend on the effective balance between source and load with certain restrictions to increase reliability and enhance the use of renewable sources at all scales. This article presents a novel power smoothing effect and sizing optimization methodology for a grid-connected photovoltaic-hydrokinetic system by pattern search method comparatively with three optimization algorithms encompassing a multi-objective optimization. In this context, the method considers the reduction of power fluctuations using supercapacitors, where the objective function considers technical and economic indexes. The main contribution of the research is that the objective function decreases the fluctuation suppression ratio to sizing optimization of renewable system through three pattern search size optimization algorithms. Experiments have shown that pattern search method can find the global optimum by reducing the computational effort; the Latin hypercube algorithm reduces the photovoltaic capacity by approximately 5 % and 2.3 % with respect to the Nelder Mead and genetic algorithm respectively. The influence of the supercapacitor successfully reduces power fluctuations and causes an increase in self-consumption of 32.32 %, this result represents an annual cost savings of 42 % on energy purchased from the grid. Furthermore, this paper goes further by calculating the optimal location of a hydrokinetic turbine in a river using the HEC-RAS software to determine with high precision the HKT power fluctuations as input signal to novel proposed method. [Display omitted] • Hybrid supercapacitor-integrated dispatch model with analysis of pattern search method. • Dispatch-coupled sizing renewable sources and energy storage with power smoothing, improving energy quality. • Numerical analysis on different size optimization methods comparatively considering experimental data. • An improved pattern search optimization that exceeds the standard one. • Validation of the effectiveness of the proposed framework in a laboratory microgrid test system. [ABSTRACT FROM AUTHOR]

Integrating distributed generations (DGs) into the radial distribution system (RDS) are becoming more crucial to capture the benefits of these DGs. However, the non-optimal integration of renewable DGs and shunt capacitors may lead to several operational challenges in distribution systems, including high energy losses, poor voltage quality, reverse power flow, and lower voltage stability. Therefore, in this paper, the multi-objective optimization problem is expressed with precisely selected three conflicting goals, incorporating the reduction in both power loss and voltage deviation and improvement of voltage stability. A new index for voltage deviation called root mean square voltage is suggested. The proposed multi-objective problems are addressed using two freshly metaheuristic techniques for optimal sitting and sizing multiple SCs and renewable DGs with unity and optimally power factors into RDS, presuming several voltage-dependent load models. These optimization techniques are the multi-objective thermal exchange optimization (MOTEO) and the multi-objective Lichtenberg algorithm (MOLA), which are regarded as being physics-inspired techniques. The MOLA is inspired by the physical phenomena of lightning storms and Lichtenberg figures (LF), while the MOTEO is developed based on the concept of Newtonian cooling law. The MOLA as a hybrid algorithm differs from many in the literature since it combines the population and trajectory-based search approaches. Further, the developed methodology is implemented on the IEEE 69-bus distribution network during several optimization scenarios, such as bi- and tri-objective problems. The fetched simulation outcomes confirmed the superiority of the MOTEO algorithm in achieving accurate non-dominated solutions with fewer outliers and standard deviation among all studied metrics. [ABSTRACT FROM AUTHOR]

The present work develops a novel gorilla troops optimization algorithm (GTO) for optimal control of an autonomous microgrid. The proposed proportional‐integral controller parameters are properly designed by the GTO algorithm. It is based on the integral squared error to minimize the system objective function. The suggested islanded microgrid system operates with several decentralized, electronically interfaced energy resources and their local loads. The new optimal controller is applied to regulate its voltage at the different points of common coupling and its frequency despite the load variation. The performance of the new proposal is compared with the PI controller that was designed by a particle swarm optimization algorithm. It is observed that the microgrid functioning operation is improved even more by applying a GTO‐based than the other. The control strategy is thoroughly tested using a Matlab/Simulink simpower‐system environment under various microgrid operating situations. It is also implemented with OPAL 4510 real‐time hardware in the loop and a rapid control prototyping module. The different benchmark experiments serve to show the superiority of the new optimizer. [ABSTRACT FROM AUTHOR]

In this paper, the main objective is the simulation of the electric supply for homes in remote areas located in Morocco (Oujda and Ouarzazate), Spain (Granada), and Algeria (Bechar). This simulation study is divided into two ideas, the first one is to optimize the hybrid system under a varied number of houses and the second part is to fix it in chosen values. This work relied on the particle swarm optimization (PSO) method to optimize and analyze the proposed stand-alone photovoltaic/wind/diesel/battery hybrid system. MATLAB software is used to run the simulations and to carry out the optimal solutions of the optimized system using a developed PSO algorithm. The PSO approach contains five principal operator axes, which are problem definition, PSO initial parameters, initialization, PSO main loop, and then run of the algorithm. Optimizing the system component sizes and reaching the minimum cost of energy (COE) were the function objectives of this optimization study. Moreover, calculation of the hydrogen production from the generated energy by PV and wind systems is performed. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hybrid optimization technique based on a machine learning (ML) approach and transient search optimization (TSO) to solve the optimal power flow problem. First, the study aims at developing and evaluating the proposed hybrid ML-TSO algorithm. To do so, the optimization technique is implemented to solve the classical optimal power flow problem (OPF), with an objective function formulated to minimize the total generation costs. Second, the hybrid ML-TSO is adapted to solve the probabilistic OPF problem by studying the impact of the unavoidable uncertainty of renewable energy sources (solar photovoltaic and wind turbines) and time-varying load profiles on the generation costs. The evaluation of the proposed solution method is examined and validated on IEEE 57-bus and 118-bus standard systems. The simulation results and comparisons confirmed the robustness and applicability of the proposed hybrid ML-TSO algorithm in solving the classical and probabilistic OPF problems. Meanwhile, a significant reduction in the generation costs is attained upon the integration of the solar and wind sources into the investigated power systems. [ABSTRACT FROM AUTHOR]

Zafarana Wind Park is considered the largest wind farm in Middle East. By the year 2022, Zafarana wind farm will inject 545 MW to Egypt national electric network (ENEN). This wind farm has been connecting to ENEN in stages (eight stages) from ten years ago. Each stage represents a project of wind farm. Hence, the impact of the emergency condition of ENEN on the performance of the installed stage of Zafarana Wind Park should be studied. Moreover, determining the possible method to reduce the side effects of the emergency condition of ENEN on the installed stage of Zafarana Wind Park becomes an important issue. In this paper, a combination between Static Synchronous Series Compensator (SSSC) and crowbar (Cro-SSSC) is used to enhance the performance of the one installed stage of Zafarana Wind Park. The studied stage of Zafarana Wind Park is Zafarana Z1 wind farm (Z1). Zafarana Z1 wind farm represents that first stage of Zafarana Wind Park that was connected to ENEN. Hence, the paper takes Zafarana Z1 wind farm as the studied case to examine the impact of Cro-SSSC. The crowbar is used to protect the power components of the SSSC from the high current during grid fault condition. Also, in this paper multi-objective lightning attachment procedure optimization algorithm (LAPO) and the sine cosine algorithm (SCA) are used to evaluate and tune the control gains of SSSC and the value of crowbar's resistance. This step is important in order to determine the values of the control's gains of SSSC and the value of crowbar resistance which suit the studied system (one installed stage of Zafarana Wind Park). The sliding mode control (SMC) is used as an example of nonlinear control of SSSC. Also, a hybrid of LAPO and SMC is used to improve the performance of Zafarana Z1 during faults. The results of LAPO, SCA and SMC are compared during three-phase fault and single line to ground fault applied to the studied system. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA's robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of efficiently solving well- and ill-conditioned Power-Flow cases in a modern power-system paradigm. While the well-conditioned cases are easily solvable using standard methods, the ill-conditioned ones suppose a challenge for such solvers. In this regard, methods based on the Continuous Newton's principle have demonstrated their ability to address ill-conditioned cases with acceptable efficiency. This paper demonstrates that the approaches proposed so far do not extract the best numerical properties of such solvers. To fill this gap, an optimization framework is proposed by which the parameters involved in the two-stage Runge–Kutta-based solvers are appropriately set, so that the stability and convergence order of the numerical mapping are maximized. By using the developed optimization technique, three solvers with quadratic, cubic, and 4th order of convergence are developed. The new proposals are tested on a variety of large-scale ill-conditioned cases. Results obtained were promising, outperforming other conventional and robust approaches. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic transmission expansion planning (TEP) in the presence of wind farms under uncertain load and wind source conditions when reliability and N-1 contingency is taken into consideration is proposed. The main aim of the suggested TEP is to minimize the total planning cost while satisfying techno-economic constraints. In this paper, reliability cost is also incorporated as the loss of load cost (LOLC) into the objective function in addition to the investment cost. In order to provide more accurate and real results, the N-1 contingency is also considered as a constraint in the TEP problem. Uncertainties for the wind source and loads in the TEP problem are modeled using a scenario-based approach and Monte Carlo simulation. Grey wolf optimization (GWO) is applied to solve the TEP problem, and it is compared to other optimization techniques. The simulation results are provided in various scenarios to confirm the efficiency of the suggested stochastic TEP. [ABSTRACT FROM AUTHOR]

With emergence of automated environments, energy demand increased with unexpected ratio, especially total electricity consumed in the residential sector. This unexpected increase in demand in energy brings a challenging task of maintaining the balance between supply and demand. In this work, a robust artificial ecosystem-inspired optimizer based on demand-side management is proposed to provide the optimal scheduling pattern of smart homes. More precisely, the main objectives of the developed framework are: i) Shifting load from on-peak hours to off-peak hours while fulfilling the consumer intends to reduce electricity-bills. ii) Protect users comfort by improving the appliances waiting time. Artificial ecosystem optimizer (AEO) algorithm is a novel optimization technique inspired by the energy flocking between all living organisms in the ecosystem on earth. Demand side management (DSM) program is modeled as an optimization problem with constraints of starting and ending of appliances. The proposed optimization technique based DSM program is evaluated on two different pricing schemes with considering two operational time intervals (OTI). Extensive simulation cases are carried out to validate the effectiveness of the proposed optimizer based energy management scheme. AEO minimizes total electricity-bills while keeping the user comfort by producing optimum appliances scheduling pattern. Simulation results revealed that the proposed AEO achieved a minimization electricity-bill up to 10.95, 10.2% for RTP and 37.05% for CPP for the 12 and 60 min operational time interval (OTI), respectively, in comparison to other results achieved by other optimizers. On the other hand peak to average ratio (PAR) is reduced to 32.9% using RTP and 31.25% using CPP tariff. [ABSTRACT FROM AUTHOR]

This paper presents an analysis and optimization of an isolated hybrid renewable power system to operate in the Alrashda village in the Dakhla Oasis, which is situated in the New Valley Governorate in Egypt. The proposed hybrid system is designed to integrate a biomass system with a photovoltaic (PV), wind turbine (WT) and battery storage system (Bat). Four different cases are proposed and compared for analyzing and optimizing. The first case is a configuration of PV and WT with a biomass system and battery bank. The second case is the integration of PV with a biomass system and battery bank. The third case is WT integrated with biomass and a battery bank, and the fourth case is a conventional PV, WT, and battery bank as the main storage unit. The optimization is designed to reduce component oversizing and ensure the dependable control of power supplies with the objective function of reducing the levelized cost of energy and loss of power supply probability. Four optimization algorithms, namely Heap-based optimizer (HBO), Franklin's and Coulomb's algorithm (CFA), the Sooty Tern Optimization Algorithm (STOA), and Grey Wolf Optimizer (GWO) are utilized and compared with each other to ensure that all load demand is met at the lowest energy cost (COE) for the proposed hybrid system. The obtained results revealed that the HBO has achieved the best optimal solution for the suggested hybrid system for case one and two, with the minimum COE 0.121171 and 0.1311804 $/kWh, respectively, and with net present cost ( NPC ) of $3,559,143 and $3,853,160, respectively. Conversely, STOA has achieved the best optimal solution for case three and four, with a COE of 0.105673 and 0.332497 $/kWh, and an NPC of $3,103,938 and $9,766,441, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes a modified version of a well-known optimization technique called Farmland Fertility Optimization algorithm (FFA). The modified FFA (MFFA) is developed in order to improve the performance of conventional FFA. It is mainly based on two stages. Firstly, the Levy flights are used to enhance the local searching capability in the exploitation phase and the global searching capability in the exploration phase. Secondly sine–cosine functions are used to create different solutions which fluctuate outwards or towards the best possible solution. The developed algorithm has been validated using ten benchmark functions and three mechanical engineering benchmark optimization problems. After that, the newly developed algorithm MFFA is used for extracting the effective unknown parameters of Proton Exchange Membrane Fuel Cells (PEMFCs) models. The optimal extraction of these parameters is essential to determine an accurate semi-empirical mathematical model for PEMFC. The sum of squared errors between the experimental data and the corresponding calculated ones is adopted as the objective function. Four different commercial PEMFC stacks are used to validate the effectiveness of the developed algorithm. The results obtained by MFFA are compared with those obtained by the conventional FFA and other well-known optimization techniques. Moreover, a comprehensive statistical analysis is performed to determine the accuracy and efficiency of the developed algorithm. The results prove the reliability and superiority of the developed algorithm compared with the conventional FFA and other state-of-the-art optimizers. [ABSTRACT FROM AUTHOR]

Salp swarm algorithm (SSA) is a recent optimization technique inspired by behavior of the salp chains in deep oceans. However, the SSA is efficient, simple and easy to implement, it is susceptible to stagnation at local optima for some cases. The main contribution of this paper is proposing an improved salp swarm algorithm algorithm (ISSA) for enhancing the search capabilities of the original SSA to solve the optimal power flow (OPF) problem. In the proposed ISSA, both of exploration and the exploitation processes are enhanced. The exploration process is achieved by applying a random mutation to find new searching areas while an adaptive process is developed to enhance the exploitation process by focusing on the most promising search area. This strategy will balance the transformation between exploration and exploitation. The ISSA is employed to achieve OPF with non-smooth and non-convex generator fuel cost functions such as; minimizing quadratic fuel cost, piecewise quadratic cost, quadratic fuel cost considering the valve-point effect and prohibited zones. The main advantages of the ISSA are avoiding stagnation at local optima and can solve nonlinear and non-smooth optimization problems where its adaptive operators balance between the exploration and exploitation phases of this algorithm. However, the parameters of ISSA need to be carefully defined before application of algorithm. The proposed algorithm is validated using the standard IEEE 30-bus, IEEE 57-bus and IEEE 118-bus test systems. The performance of proposed algorithm is comprehensively compared with moth-flame optimization algorithm, improved harmony search algorithm, genetic algorithm and other reported optimization techniques. The results prove the effectiveness and superiority of the proposed algorithm compared with other optimization techniques. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hybrid (MFO-SCA) method based on Moth Flame Optimization (MFO) algorithm and Sine Cosine Algorithm (SCA). MFO is utilized for the exploitation phase while SCA is used for the exploration phase. In addition, the hybrid MFO-SCA method is used with combined power loss sensitivity (CPLS) to determine the optimal allocation of single and multiple of distributed generations (DGs) and capacitors in distribution system. In this paper, the total active power loss is used as a single objective function for incorporating DGs and capacitors in RDS. Also, this paper studies the system performance when integrating DGs or capacitors alone and DGs with capacitors simultaneously in RDS. The proposed method is validated using the standard IEEE 69-bus and IEEE 33-bus radial distribution system (RDS). From comparative study, the novel hybrid MFO-SCA proved its effectiveness in obtaining the best global optimum results of the objective function compared with other recent optimization techniques, especially SCA and MFO algorithms. [ABSTRACT FROM AUTHOR]

This article proposes a hybrid analytical and metaheuristic optimization technique for optimal allocation of multiple types of distributed generator (DG) in radial distribution networks. DG integration aims to minimize the total power losses and enhance the voltage stability of the distribution system. The proposed technique is formulated using the analytical technique which utilizes the exact loss formula to calculate the initial DG size at a certain bus. However, the analytical technique may not be proper to allocate multiple DGs types due to the mass of calculations, hence, a metaheuristic optimization technique named Tree Growth Algorithm (TGA) is combined with the analytical technique to find the final solution of optimal DG locations and sizes. The hybridization between the analytical and metaheuristic optimization techniques combines the advantages of both techniques and eliminates the disadvantages. The proposed hybrid Analytical TGA (ATGA) is validated using the stranded radial distribution feeders, IEEE 33‐bus and 69‐bus and practical 94‐bus Portuguese system. A comprehensive comparison between the proposed technique and other competitive optimization techniques is carried out to prove its effectiveness. The result shows that the proposed hybrid ATGA is efficient to allocate the multiple DGs types with minimum power loss and a high convergence rate. [ABSTRACT FROM AUTHOR]

Recently, fast uptake of renewable energy sources (RES) in the world has introduced new difficulties and challenges; one of the most important challenges is providing economic energy with high efficiency and good quality. To reach this goal, many traditional and smart algorithms have been proposed and demonstrated their feasibility in obtaining the optimal solution. Therefore, this paper introduces an improved version of Bonobo Optimizer (BO) based on a quasi-oppositional method to solve the problem of designing a hybrid microgrid system including RES (photovoltaic (PV) panels, wind turbines (WT), and batteries) with diesel generators. A comparison between traditional BO, the Quasi-Oppositional BO (QOBO), and other optimization techniques called Harris Hawks Optimization (HHO), Artificial Electric Field Algorithm (AEFA) and Invasive Weed Optimization (IWO) is carried out to check the efficiency of the proposed QOBO. The QOBO is applied to a stand-alone hybrid microgrid system located in Aswan, Egypt. The results show the effectiveness of the QOBO algorithm to solve the optimal economic design problem for hybrid microgrid power systems. [ABSTRACT FROM AUTHOR]

This paper deals with the simultaneous tuning of proportional integral controller of static synchronous compensator (STATCOM) associated with lead-lag controller (LL) in order to improve the stability performance of combined wind farm (CWF). This type of farms has been developed to summarize the main benefits of Squirrel-Cage Induction Generator (SCIG) and doubly fed induction generators (DFIG). The performance of CWF with the tuned STATCOM is studied during line-to-line and three-phase faults. Multi-objective Lightning Attachment Procedure Optimization Algorithm (LAPO) is used as an intelligent optimization technique to determine the control parameters which can achieve the specified objective functions; minimizing the error signal and maximizing the output signal. The multi-objective LAPO is used to obtain the optimized values of AC voltage regulator, DC voltage regulator, current regulator, gains and time constant of LL. The ability of STATCOM tuned by multi-objective LAPO is examined by studying the performance of three wind farms. The first one is CWF and two other wind farms; one of them is based only on SCIG (SCIG-WF) and the other based only on DFIG (DFIG-WF) when they associated with the tuned STATCOM LAPO during grid fault. The results show that CWF associated with the tuned STATCOM LAPO has the best performance during grid faults compared with the other wind farms. [ABSTRACT FROM AUTHOR]

Recently, integration of distributed generations (DGs) and shunt capacitors in radial distribution network are becoming popular to withstand the rapidly increasing in electricity demands. In this article, a hybrid method is proposed to obtain the best locations and sizes of capacitors and DGs in radial distribution network. This hybrid method is based on chaotic whale optimization algorithm (CWOA) and loss sensitivity factor (LSF). The proposed method is tested on IEEE 69-bus system to enhance the buses voltages, increase the distribution system capacity, and decrease the total power loss. The obtained results prove that the proposed method based on CWOA and LSF can be highly effective in determining the locations and sizes of capacitors and DGs in RDS compared with other optimization techniques. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced version of grey wolf optimizer (EGWO) to solve the coordination problem of directional overcurrent relays (DOCRs). The EGWO is proposed to improve the convergence characteristics and computation time of the conventional grey wolf optimizer (GWO) by selecting a suitable balance between exploration and exploitation phases. This balance is achieved by exponential decreasing of the control parameter during the iterative process. The EGWO is explored in all search space during predetermined iterations, and then it fast converges to the best optimal solution by local exploitation around the optimal solutions. The proposed optimization technique is applied to solve the coordination problem of DOCRs. The main objective of optimal coordination of DOCRs is to minimize total operating time of all primary relays with sustaining the selectivity between relay pairs. The feasibility and performance of the proposed technique for solving the coordination problem of DOCRs are investigated using four different systems, compared with several well-known techniques. The obtained results prove the effectiveness and superiority of the proposed technique compared with these techniques. The proposed technique is able to find the optimal relay settings and minimize the total operating time of relays (with a reduction ratio about 19.3995% relative to the conventional GWO) without any miscoordination. In addition, DIgSILENT PowerFactory is used to validate the proposed technique. [ABSTRACT FROM AUTHOR]

Flexible AC transmission systems (FACTS) technology is widely adopted and utilized to maintain the performance of power systems. However, the improvements of power system performance achieved by FACTS devices depend on the right sizing and allocation of such devices. For technical and economic considerations, a FACTS device's location and size should be selected very carefully in order to maximize its benefits to the power system. In this paper, the sizing and location of a static VAR compensator (SVC) are optimally determined using a new optimization technique called lightning attachment procedure optimization (LAPO). The optimal allocation of the SVC is determined regarding the improvement of voltage deviation index and the reduction of total active power losses. The system is optimized in two cases: once without SVC installation in order to find out the optimal settings of the system that achieve the objective functions, and another time with SVC installation to determine its optimum sizes and locations by which the required objective functions are achieved. Then the system performance is analyzed after optimization with and without SVC devices to show the impact of the optimum sizing and location of the SVC on the system. The study is validated using the standard IEEE 30-bus system, while the developed LAPO is performed by MATLAB M-Files and the system performance analysis in different cases is performed by NEPLAN software. [ABSTRACT FROM AUTHOR]

Assessment of power systems voltage stability is considered an important assignment for the operation and planning of power system. In this paper, a voltage stability study using Continuous Power Flow (CPF) is introduced to evaluate the impact of Distribution Generator (DG) on radial distribution systems. On the way to allocate the DG, a hybrid between the Voltage Stability Index (VSI) and Whale Optimization Algorithm (WOA) is developed. The main purpose of using VSI is to find the most sensitive buses for allocating the DG in the system. Hence, Fuzzy logic control with the Normalized VSI (NVSI) and the voltage magnitude at each bus are used to determine the candidate buses. However, the best DG size is calculated using WOA. Four standard radial distribution systems are used in this paper; 12, 33, 69, and 85-bus. The developed hybrid optimization method is compared with other existing analytical and metaheuristic optimization techniques to prove its efficiency. The results prove the ability of the developed method in the allocation of DG. In addition, the influence of the DG integration on enhancing the voltage stability through injecting the proper active and reactive powers is studied. [ABSTRACT FROM AUTHOR]

Solution of optimal power flow (OPF) problem is very important for power system operation, planning and energy management. OPF analysis aims to find the optimal solution of system nonlinear algebraic equations with satisfying operational constraints. In this paper, a new and efficient technique called Jaya optimizer is comprehensively applied to solve the OPF problem in power systems. Jaya optimization algorithm is characterized with the movement toward the best solution and avoiding the trapping into local optima. Different frameworks are developed for solving the single- and multi-objective (two- to five-objective functions) OPF problems. These frameworks are developed to achieve the following objective functions: fuel cost minimization, voltage deviation minimization, voltage stability enhancement, power loss minimization and emission minimization. In the developed multi-objective OPF framework, Pareto concept is combined with Jaya optimization algorithm to obtain a set of non-dominated solutions, and then the best compromise solution is extracted using fuzzy set theory. The developed OPF frameworks are validate using two standard IEEE test systems with 23 studied cases. The results prove the effectiveness and superiority of the developed OPF frameworks compared with other well-known optimization algorithms. [ABSTRACT FROM AUTHOR]

Communication latency which inherently occurs in wide area measurement system greatly degrades small-signal stability (SSS) and is stochastic in nature, and thus, the current power oscillation damping controllers (PODCs) designed to improve SSS must consider this crucial factor. This paper proposes a probabilistic method to tune the parameters of PODCs incorporated in renewable farms to improve SSS under stochastic time delay and under other power system uncertainties arising due to renewable energy resources and loads. The proposed method is composed of two stages: The first stage quantifies the effect of time delay and other power system uncertainties on SSS, and the second stage uses this information to formulate an optimization problem. This optimization problem is solved with the help of four swarm intelligence-based optimization algorithms which are: bat algorithm, cuckoo search algorithm, firefly algorithm, and particle swarm optimization algorithm. The solutions from all these four optimization algorithms are compared, and the best result is used to optimize the parameters of the PODCs. All the analyses were conducted on a modified IEEE 68 bus system. The results show that the PODCs tuned using the proposed method greatly enhances the SSS margin under different scenarios and are probabilistically robust to the varying time delay and other power system uncertainties. [ABSTRACT FROM AUTHOR]

High penetration of photovoltaic and wind turbine-based distributed generators (DGs) can help reduce carbon emissions which is an important goal for the whole world. DG can be used to improve the voltage stability, present generation reserve/emergency, and consequently, the system power quality can be improved. However, it is very important to select the right size and location of a DG so that the power system can increase the gained benefits of such an installation to the maximum. In this paper, a hybrid optimization technique is proposed to determine the optimal allocation of DG in the standard IEEE 33-bus radial distribution system in order to improve the voltage stability and minimize the total power loss. The proposed hyprid technique is based on the gray wolf optimizer algorithm with loss sensitivity factor. The performance of the system is analyzed without DG installation, then it is compared with the performance of the system when DGs are installed with the predefined optimal sizes and locations. The study is performed by MATLAB M-Files and NEPLAN software. [ABSTRACT FROM AUTHOR]

This paper proposes a modified grasshopper optimization algorithm (MGOA) to solve the optimal power flow (OPF) problem. The conventional GOA is a recent optimization technique that is conceptualized from the natural lifestyle of grasshopper including their movement and migration. The MGOA is based on modifying the mutation process in the conventional GOA in order to avoid trapping into local optima. Different single- and multi-objective functions are solved using the proposed optimization technique. These objective functions consist of quadratic fuel cost minimization, emission cost minimization, active power loss minimization, quadratic fuel cost and active power loss minimization, quadratic fuel cost minimization and voltage profile improvement, quadratic fuel cost minimization and voltage stability improvement, quadratic fuel cost minimization and emission minimization, quadratic fuel cost and power loss minimization, voltage profile and voltage stability improvement. The proposed technique is validated using standard IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus test systems with thirteen case studies. Simulation results reveal the better performance and superiority of the proposed technique to solve various OPF problems compared with well-recognized evolutionary optimization techniques stated in the literature review. [ABSTRACT FROM AUTHOR]

In this article, a new hybrid metaheuristic optimization algorithm is proposed to solve the coordination problem of directional overcurrent relays (DOCRs). The proposed algorithm is constructed using hybrid whale optimization algorithm and gray wolf optimizer (HWGO) that enhance the performance and reliability of the traditional whale optimization algorithm (WOA). The proposed method enhances the exploitative phase of the WOA using a leadership hierarchy of the gray wolf optimizer (GWO) to find the best optimum solution. The coordination problem of DOCRs is subject to numerous constraints. The goal function for optimal coordination of DOCRs aims to minimize total operation time for all primary relay without violation in constraints to maintain reliability and security of the electric power system. The effectiveness of the proposed algorithm has been investigated on four different interconnected networks. The results using HWGO algorithm are compared with the original WOA, GWO, and earlier reported results of other optimization techniques. The results prove the viability of the proposed algorithm to solve the DOCR coordination problem and the ability of the proposed algorithm to overcomes the drawbacks and cover the weakness of the conventional WOA. [ABSTRACT FROM AUTHOR]

Abstract The optimization model of Directional Over Current Relays (DOCRs) coordination is considered non-linear optimization problem with a large number of operating constraints. This paper proposes a modified version for Water Cycle Algorithm (WCA), referred to as MWCA to effectively solve the optimal coordination problem of DOCRs. The main goal is to minimize the summation of operating times of all relays when they act as primary protective devices. The operating time of a relay depends on time dial setting and pickup current setting or plug setting, which they are considered as decision variables. In the proposed technique, the search space has been reduced by increasing the C-value of traditional WCA, which effects on the balance between explorative and exploitative phases, gradually during the iterative process in order to find the global minimum. The performance of proposed algorithm is assessed using standard test systems; 8-bus, 9-bus, 15-bus, and 30-bus. The obtained results by the proposed algorithm are compared with those obtained by other well-known optimization techniques. In addition, the proposed algorithm has been validated using benchmark DIgSILENT PowerFactory. The results show the effectiveness and superiority of the proposed algorithm to solve DOCRs coordination problem, compared with traditional WCA and other optimization techniques. Graphical abstract Highlights • Optimization model of directional ov-er current relays coordination. • Modified version for Water Cycle Algorithm. • The main objective is to minimize the operating times of all relays. • Time dial setting and pickup current setting or plug setting. • Balance between explorative and exploitative phases. [ABSTRACT FROM AUTHOR]

In the last few decades, interest in the integration of Distributed Generators (DGs) into distribution networks has been increased due to their benefits such as enhance power system reliability, reduce the power losses and improve the voltage profile. These benefits can be increased by determining the optimal DGs allocation (location and size) into distribution networks. This paper proposes an efficient optimization technique to optimally allocate the multiple DG units in distribution networks. This technique is based on Sine Cosine Algorithm (SCA) and chaos map theory. As any random search-based optimization algorithm, SCA faces some issues such as low convergence rate and trapping in local solutions during the exploration and exploitation phases. This issue can be addressed by developing Chaotic SCA (CSCA). CSCA is mainly based on the iterative chaotic map which used to update the random parameters of SCA instead of using the random probability distribution. The iterative chaotic map is applied for single and multi-objective SCA. The proposed technique is validated using two stranded IEEE radial distribution feeders; 33 and 69-nodes. Comprehensive comparison among the proposed technique, the original SCA, and other competitive optimization techniques are carried out to prove the effectiveness of CSCA. Finally, a complete study is performed to address the impact of the intermittent nature of renewable energy resource on the distribution system. Hence, typical loads and generation (represented in PV power) profiles are applied. The result proves that the CSCA is more efficient to solve the optimal multiple DGs allocation with minimum power loss and high convergence rate. • Integration of distributed generators into distribution networks. • Efficient optimization for allocation of multiple distributed generators. • Sine cosine algorithm and chaos map theory. • Stranded IEEE radial distribution feeders. • The result shows that the proposed optimization technique is efficient. [ABSTRACT FROM AUTHOR]

• Effects of different storage technologies on a hybrid renewable energy system. • Photovoltaic system, hydrokinetic system and diesel generator. • Five types of storage are considered. • The study is done in the HOMER Pro software. • Sensitivity analysis and variation of the minimum state of charge. This study analyzes the effects of different storage technologies on a hybrid renewable energy system composed of photovoltaic, hydrokinetic and diesel generator. Five types of storage are considered: lead acid, lithium ion, vanadium redox flow, hydrogen and hydrogen-vanadium redox flow. The analysis is mainly based on indicators such as Net Present Cost, Cost of Energy, unmet load and CO 2 emissions. HOMER software has been used in this paper with time-sampling models and sensitivity studies to determine the effects of each storage system. The results show that the vanadium redox flow batteries system presents a lower net present cost and cost of energy. The sensitivity analysis shows that the vanadium redox flow system presents a greater variation of the minimum state of charge (SOC) in relation to the net present cost. However, the system composed of hydrogen and fuel cell present the lowest variation. The two proposed strategies for energy control show the same performance. However, when using the Load Tracking Control, the variation of the minimum state of charge with respect to the net cost is greater than the variation obtained when applying the Load Cycle Control. [ABSTRACT FROM AUTHOR]

Summary: Unified power flow controller (UPFC) is utilized to regulate the bus voltage as well as the power flow through a power system. A solution of optimal power flow (OPF) problems with UPFC is a crucial and complex task due to the required modifications for considering the parameters of UPFC. This work proposes a simplified UPFC modeling into an OPF code in order to avoid the programming complexity. Moreover, the solution of an OPF problem with a UPFC model is obtained by a recent physical‐based optimization technique called lightning attachment procedure optimization (LAPO). Different objective functions including minimizing fuel cost and fuel cost with valve point effect (VPE), reduction of emission, improvement of voltage profile, and improving the voltage stability index are considered. The proposed algorithm is tested using the standard IEEE 30‐bus system. The results obtained by the proposed algorithm are compared with those obtained by other optimization techniques. However, the obtained results verify the applicability of the simplified UPFC model in OPF. [ABSTRACT FROM AUTHOR]

The optimal power flow (OPF) problem is a non-linear and non-smooth optimization problem. OPF problem is a complicated optimization problem, especially when considering the system constraints. This paper proposes a new enhanced version for the grey wolf optimization technique called Developed Grey Wolf Optimizer (DGWO) to solve the optimal power flow (OPF) problem by an efficient way. Although the GWO is an efficient technique, it may be prone to stagnate at local optima for some cases due to the insufficient diversity of wolves, hence the DGWO algorithm is proposed for improving the search capabilities of this optimizer. The DGWO is based on enhancing the exploration process by applying a random mutation to increase the diversity of population, while an exploitation process is enhanced by updating the position of populations in spiral path around the best solution. An adaptive operator is employed in DGWO to find a balance between the exploration and exploitation phases during the iterative process. The considered objective functions are quadratic fuel cost minimization, piecewise quadratic cost minimization, and quadratic fuel cost minimization considering the valve point effect. The DGWO is validated using the standard IEEE 30-bus test system. The obtained results showed the effectiveness and superiority of DGWO for solving the OPF problem compared with the other well-known meta-heuristic techniques. [ABSTRACT FROM AUTHOR]

The development of hybrid systems that combine different energy sources has become increasingly important to meet the growing demand for clean and sustainable energy. These systems can offer a reliable and efficient solution to reduce dependence on conventional energy sources and address the issues of climate change and environmental degradation. This study focuses on two types of hybrid systems, namely PV/biomass and PV/diesel, which are commonly used in off-grid areas or places with limited access to electricity. The proposed optimization framework aims to determine the optimal sizing of each component in the system, including PV panels, batteries, and backup sources, to maximize the performance and efficiency of the hybrid system. The Gradient Pelican Optimization Algorithm (GPOA), which is an advanced optimization technique, is proposed to solve the optimization problem. The algorithm is modified to include a local escaping operator, which allows the algorithm to escape local optima and achieve better solutions. The outcomes of the simulation show that the GPOA algorithm outperforms other well-known algorithms in terms of accuracy and computational efficiency. The simulation results also demonstrate that the PV/biomass hybrid system outperforms the PV/diesel hybrid system in terms of cost and environmental impact. The proposed framework and optimization methodology can be useful for designing and optimizing other hybrid systems and can be applied to various applications, including off-grid and remote areas, distributed power systems, and microgrids. The findings of this study can also contribute to the development and promotion of renewable energy and sustainable development. [ABSTRACT FROM AUTHOR]

• This paper presents a novel application of AHA to tune the controllers parameters. • The super twisting sliding mode controller is applied to microgrids. • The results of proposed model are compared with other recent models. • The proposed model is verified by comparing its results with the measured results. It is essential to improve optimal control for an autonomous microgrid operation. This paper presents a novel application of an artificial hummingbird algorithm for achieving optimal control of an autonomous microgrid. It also suggests a comparative analysis for the optimal super-twisting sliding mode control with both optimal fuzzy logic control and optimal proportional-integral control. The proposed super-twisting sliding mode controller parameters are adequately designed by using the AHA optimization method; meanwhile, the FLC and PI controllers are designed by using the African vultures and the Gorilla troops optimization algorithms, respectively. A MATLAB/Simulink environment is used to verify the effectiveness of the suggested microgrid control methods. The overall system detailed approaches for modeling, designing, and controlling are introduced. The investigation of the ST-SMC approach is also tested in a real-time setting. OPAL-RT 4510 rapid control prototyping and OPAL-RT 8660 data acquisition are used to implement the suggested controller. The verification results prove the superiority of the ST-SMC based on the AHA optimization technique compared with other optimal control techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a sizing method and different control strategies for the suitable energy management of a stand-alone hybrid system based on photovoltaic (PV) solar panels, hydrogen subsystem and battery. The battery and hydrogen subsystem, which is composed of fuel cell (FC), electrolyzer and hydrogen storage tank, act as energy storage and support system. In order to efficiently utilize the energy sources integrated in the hybrid system, an appropriate sizing is necessary. In this paper, a new sizing method based on Simulink Design Optimization (SDO) of MATLAB was used to perform a technical optimization of the hybrid system components. An analysis cost has been also performed, in that the configuration under study has been compared with those integrating only batteries and only hydrogen system. The dynamic model of the designed hybrid system is detailed in this paper. The models, implemented in MATLAB-Simulink environment, have been designed from commercially available components. Three control strategies based on operating modes and combining technical-economic aspects are considered for the energy management of the hybrid system. They have been designed, primarily, to satisfy the load power demand and, secondarily, to maintain a certain level at the hydrogen tank (hydrogen energy reserve), and at the state of charge (SOC) of the battery bank to extend its life, taking into account also technical-economic analysis. Dynamic simulations were performed to evaluate the configuration, sizing and control strategies for the energy management of the hybrid system under study in this work. Simulation results show that the proposed hybrid system with the presented controls is able to provide the energy demanded by the loads, while maintaining a certain energy reserve in the storage sources. [Copyright &y& Elsevier]

In this paper, a hybrid optimization technique based on analytical and two heuristic methods is developed and applied to determine the optimal allocation of shunt capacitors into distribution systems, aiming to minimize the total power loss and energy cost. The developed technique is a combination of analytical technique based on Loss Sensitivity Factor (LSF) and two recent metaheuristic optimization techniques called Salp Swarm Algorithm (SSA) and Sine Cosine Algorithm (SCA). LSF with a fuzzy logic controller is utilized to determine the candidate buses while the hybrid approach based on SSA and SCA (SSA_SCA) is used to find the optimal capacitor size. The performance of developed technique is investigated using 15-bus, 69-bus, 85-bus, and East Delta Network EDN 30-bus distribution systems. The results of developed technique are compared with those obtained by other comparative optimization methods. The results show the superior of developed technique in determining the optimal allocation of capacitor. [ABSTRACT FROM AUTHOR]

Optimal reactive power dispatch (ORPD) in electrical networks is essential for the secure and stable operation of the entire power system; it also significantly impacts the economic situation. However, the solution of ORPD is highly complex while considering the multiple variables, time-varying characteristics, dynamic loads such as electric vehicles, and operational constraints. The ORPD problem is classified as a non-linear, non-convex complex problem. Thus, a robust optimization technique should be utilized to solve the ORPD. This paper presents a novel Enhanced Transient Search Optimization (ETSO) technique for the optimal solution of the ORPD problem by integrating electric vehicles (EVs). The proposed ETSO implemented for the optimal solution of ORPD consequently minimize the active power loss and voltage deviation at the load buses. The proposed method is tested and verified on the IEEE 30-bus, the IEEE-57 bus, and IEEE 118-bus systems. The simulation results show the robustness and efficiency of the proposed ETSO optimization in solving the ORPD problem by evaluating and comparing it with other well-established metaheuristic optimization methods under the same system data, control variables, and constraints. Statistical features of the proposed ETSO algorithm and the results obtained led to an improvement in the performance of the power systems. • Optimal energy management and reactive power dispatch is presented. • The model is solved using a novel enhanced TSO algorithm. • The impact of electric vehicles on the system performance is studied. • Real data of electric vehicles are implemented for obtaining realistic responses. • The results of the proposed method are compared with other models. [ABSTRACT FROM AUTHOR]

In this research, a hybrid algorithm called a Gradient Artificial Hummingbird Algorithm (GAHA) is developed for reducing energy cost (EC) of microgrid system; this hybrid approach is based on the combination between Gradient based optimizer (GBO) and Artificial Hummingbird Algorithm (AHA). This proposed GAHA is firstly tested on a group of 23 benchmark test functions, and its obtained results are compared with five well-known algorithms including supply-demand-based optimization (SDO), wild horse optimizer (WHO), grey wolf optimizer (GWO), tunicate swarm algorithm (TSA) and original AHA algorithm. The obtained results using the GAHA algorithm show better performance in most cases and comparative results in other cases. Moreover, the developed GAHA algorithm is applied to obtain the optimal configuration of an isolated hybrid system, which is consists of photovoltaic (PV) modules, wind turbine (WT), biomass system, and battery storage system. The proposed standalone hybrid system is implemented for feeding loads in the new Tiba city, in northeast of Luxor in southern Egypt. GAHA technology is applied to four different system configurations to obtain the optimal system design. The GAHA optimization findings are compared with the findings from other optimization algorithms namely the original AHA, Sine Cosine Algorithm (SCA), and whale optimization algorithm (WOA) methods. The GAHA method achieved the best results for all the suggested configuration scenarios compared to the rest of the algorithms used. • Hybrid algorithm called a Gradient Artificial Hummingbird Algorithm. • For reducing energy cost of microgrid system. • Optimal configuration of an isolated hybrid system. • The proposed method achieved the best results. [ABSTRACT FROM AUTHOR]

This paper introduces a novel enhancement to the Transient Search Optimization (TSO) algorithm to estimate an accurate electrical model of the proton exchange membrane fuel cell (PEMFC). The PEMEFC model is a non-linear model that includes seven unknown variables which cannot be calculated analytically. The TSO is enhanced by inserting two new factors, the Levy function and the Weibull distribution function. The proposed enhanced Transient Search Optimization (ETSO) and TSO algorithms are applied to estimate the seven variables by minimizing the sum of the squared errors (SSEs) between the measured and calculated voltages. The error is defined as the difference between the measured and the calculated output voltage of the PEMFC. Three different commercial types of PEMFCs are modeled: i) Ballard, Mark V 5 kW, ii) Horizon H-12, and iii) 6 kW Nedstack PS6 stacks PEMFC. The estimated seven variables and the minimum SSE of electrical PEMFCs using ETSO and TSO algorithms are compared with the results obtained by using other optimization algorithms like whale optimization algorithm, genetic algorithm, neural network algorithm and others. The results obtained by the ETSO are better than that obtained by TSO by more than 10% and this percentage increases with other algorithms. The accuracy of the proposed PEMFC model is verified by comparing the estimated V – I and P – I characteristics with the measured data. The effectiveness of the proposed ETSO based model is verified by an investigation of sensitivity analysis for design variables and the robustness of the ETSO algorithm via the statistical analysis and the parametric t -test. • This paper presents a novel improved TSO algorithm to extract PEMFC model parameters. • Three commercial PEMFC models are implemented in this paper. • The parameters of proposed model are compared with other recent models. • The proposed model is verified by comparing its results with the measured results. • The sensitivity and robustness analyses of the proposed method are tested. [ABSTRACT FROM AUTHOR]

• An isolated hybrid power system is simulated and analysed. • Optimal sizing and electricity demand with cost improvement. • Photovoltaic panels, biomass gasifier, and batteries units. • A Quantum model of a RUNge Kutta optimization algorithm. In this paper, an isolated hybrid power system (HPS) is simulated and analyzed to obtain the optimal sizing and meet the electricity demand with cost improvement for servicing Alrashda village, which is a small village of the Dakhla Oasis villages in the New Valley, Egypt. The major configuration of this HPS is Photovoltaic panels (PV), Biomass gasifier, and Batteries units. A Quantum model of a RUNge Kutta optimization algorithm called QRUN algorithm is applied to guarantee that all load needs are covered with high reliability with the minimum cost of energy (COE) of the proposed system. To ensure the superiority of the QRUN technique, its results are compared with those obtained by the original optimization algorithm RUNge Kutta optimization algorithm (RUN), and a well-known optimization algorithm, Aquila optimizer algorithm (AO) and Gray Wolf algorithm (GWO). The simulation results show that the modification QRUN algorithm gives the best Fitness Function with 0.080076 $/kWh of the COE, net present cost (NPC) with 3,352,062 $, and loss of power supply probability (LPSP) with 0.490866. [ABSTRACT FROM AUTHOR]

• Conventional evaporation rate water cycle algorithm (ERWCA). • The proposed MERWCA improves the performance of ERWCA. • To find the optimal solutions for the coordination problem of directional overcurrent relays. • The proposed MERWCA is verified on the CEC'2017 test suite. • MERWCA is assessed using benchmark DIgSILENT PowerFactory. An optimization algorithm called modified evaporation rate water cycle algorithm (MERWCA) is proposed in this paper to find the optimal solutions for the coordination problem of directional overcurrent relays (DOCRs). The proposed MERWCA improves the performance of a conventional evaporation rate water cycle algorithm (ERWCA) by enhancing the balance between exploitation (search locally) and exploration (search globally) phases to find the best optimum solution. MERWCA includes the Opposition Based Learning (OBL) and Levy Flight (LF) component to address the shortcomings that the original ERWCA may exhibit, to avoid falling on the local optimal and improve the convergence rate. The proposed MERWCA is verified on the CEC'2017 test suite and its performance are compared with those of ten common metaheuristic algorithms (MAs). Both MERWCA and ERWCA are evaluated in the case of non-conventional and conventional relay curves. The feasibility of MERWCA technique is assessed using the conventional IEEE 39-bus meshed distribution test system. The results prove the viability of the MERWCA in solving DOCRs coordination problems in both cases (conventional and non-conventional characteristic relay curve) without any miscoordination between DOCRs pair. Moreover, the reduction ratio in minimizing the total operating using MERWCA reaches 46% with respect to the ERWCA and about 66% using the non-conventional relay characteristic. Finally, the MERWCA is assessed using benchmark DIgSILENT PowerFactory. [ABSTRACT FROM AUTHOR]