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Integrating renewable energy sources (RESs) into modern electric power systems offers various techno-economic benefits. However, the inconsistent power profile of RES influences the power flow of the entire distribution network, so it is crucial to optimize the power flow in order to achieve stable and reliable operation. Therefore, this paper proposes a newly developed circle search algorithm (CSA) for the optimal solution of the probabilistic optimal power flow (OPF). Our research began with the development and evaluation of the proposed CSA. Firstly, we solved the OPF problem to achieve minimum generation fuel costs; this used the classical OPF. Then, the newly developed CSA method was used to deal with the probabilistic power flow problem effectively. The impact of the intermittency of solar and wind energy sources on the total generation costs was investigated. Variations in the system's demands are also considered in the probabilistic OPF problem scenarios. The proposed method was verified by applying it to the IEEE 57-bus and the 118-bus test systems. This study's main contributions are to test the newly developed CSA on the OPF problem to consider stochastic models of the RESs, providing probabilistic modes to represent the RESs. The robustness and efficiency of the proposed CSA in solving the probabilistic OPF problem are evaluated by comparing it with other methods, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and the hybrid machine learning and transient search algorithm (ML-TSO) under the same parameters. The comparative results showed that the proposed CSA is robust and applicable; as evidence, an observable decrease was obtained in the costs of the conventional generators' operation, due to the penetration of renewable energy sources into the studied networks. [ABSTRACT FROM AUTHOR]

The fuel cell is vital in electrical distribution networks as a distributed generation in today's world. A precise model of a fuel cell is extensively required as it rigorously affects the simulation studies' transient and dynamic analyses of the fuel cell. This appears in several microgrids and smart grid systems. This paper introduces a novel attempt to optimally determine all unknown factors of the polymer exchange membrane (PEM) fuel cell model using a meta-heuristic algorithm termed the Lightning search algorithm (LSA). In this model, the current–voltage relationship is heavily nonlinear, including several unknown factors because of the shortage of fuel cell data from the manufacturer's side. This issue can be treated as an optimization problem, and LSA is applied to detect its ability to solve this problem accurately. The objective function is the sum of the squared error between the estimated output voltage and the measured output voltage of the fuel cell. The constraints of the optimization problem involve the factors range (lower and upper limit). The LSA is utilized in minimizing the objective function. The effectiveness of the LSA-PEM fuel cell model is extensively verified using the simulation results performed under different operating conditions. The simulation results of the proposed model are compared with the measured results of three commercial fuel cells, such as Ballard Mark V 5 kW, BCS 500 W and Nedstack PS6 6 kW, to obtain a realistic study. The results of the proposed algorithm are also compared with different optimized models to validate the model and, further, to determine where LSA stands in terms of precision. In this regard, the proposed model can yield a lower SSE by more than 5% in some cases and high performance of the LSA-PEMFC model. With the results obtained, it can be concluded that LSA prevails as a potential optimization algorithm to develop a precise PEM fuel cell model. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a novel Circle Search Algorithm (CSA) with the purpose of obtaining a precise electrical model of a proton exchange membrane fuel cell (PEMFC). Current-voltage and current-power curves are used to characterize the performance of PEMFCs. A nonlinear model with seven unknown parameters is used to describe these polarization curves. Estimating these unknown parameters is a critical issue because they influence the dynamic analysis of fuel cells in a variety of applications such as transportation and smart grids. The suggested method is based on minimizing the fitness function (the sum of the squared errors (SSE)) between estimated and measured voltage values. The CSA is compared to the neural network algorithm (NNA), grey wolf optimization (GWO), and the sine cosine algorithm (SCA). The optimization results reveal that the simulation times of the CSA, NNA, GWO, and SCA are 5.2, 6, 5.8, and 5.75 s, respectively. Moreover, the CSA converges to the best minimum within the first 100 iterations, which is faster than the other algorithms. The robustness of the CSA is verified using 20 independent runs, where the CSA achieves the smallest average and standard deviation. In addition, the t-test proves the superiority of the CSA compared to the other algorithms, where all p-values are less than 5%. The simulated I-V and I-P curves of the CSA-PEMFC model match the measured curves very closely. Moreover, the efficacy of the CSA-PEMFC model is evaluated under a variety of temperature and pressure conditions. Therefore, the suggested CSA-PEMFC model has the potential to be an accurate and efficient model. [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]

Mathematical design of a new fourth-order harmonic passive filter is presented and its optimal strategy is proposed with regards to various design scenarios. The considered objective function is total demand distortion minimization of the supply current. The crow spiral-based search algorithm (CSSA) is applied to solve the design problem formulated. This CSSA relies on a spiral search mechanism that improves the convergence and balances the exploration and exploitation abilities of the conventional crow search algorithm. Various power quality indices are taken into consideration like the individual and total harmonic voltage distortion values, individual and total current harmonic distortion values, active power loss, actual and displacement power factor percentages, and resonance damping capabilities. These indices were handled as non-linear constraints in the design. Additionally, a comparative investigation of the different damped filters is presented to assess the planned filter performance. The results obtained confirm the success of the filter design proposed in this paper. [ABSTRACT FROM AUTHOR]

Three-diode model (TDM) of photovoltaic (PV) cells is more accurate model that includes most of the optical and electrical losses of PV module. However, the nonlinearity and parameters of this TDM are higher, which make it complex and challengeable model. This article utilizes an efficient algorithm called the Circle Search Algorithm (CSA) for accurate electrical modeling of PV modules. The CSA is inspired by the circle's well-known geometrical properties and the perpendicular relationship between its radius and tangent line. The CSA and other four algorithms are applied to determine the nine parameters of the TDM of three commercial PV modules. The objective function is the root mean square error (RMSE) between the estimated and measured output currents. The statistical optimization results and convergence curves proved the robustness and speed of CSA in determining the optimum TDM among the other methods. The predicted I - V curves are plotted against observed I - V curves at various temperatures and solar irradiance to demonstrate the CSA's superiority under various scenarios. The absolute current error of the CSA-TDM at maximum voltage is less than that of other algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a novel minimum seeking algorithm referred to as the Hunger Games Search (HGS) algorithm. The HGS is used to obtain optimal values in the model describing proton exchange membrane fuel cells (PEMFCs). The PEMFC model has many parameters that are linked in a nonlinear manner, as well as a set of constraints. The HGS was used with the aforementioned model to test its performance against nonlinear models. The main aim of the optimization problem was to obtain accurate values of PEMFC parameters. The proposed heuristic algorithm was used with two commercial PEMFCs: the Ballard Mark V and the BCS 500 W. The simulation results obtained using the HGS-based model were compared to the experimental results. The effectiveness of the proposed model was verified under various temperature and partial pressure conditions. The numerical output results of the HGS-based fuel cell model were compared with other optimization algorithm-based models with respect to their efficiency. Moreover, the parametric t-test and other statistical analysis methods were employed to check the robustness of the proposed algorithm under various independent runs. Using the proposed HGS-based PEMFC model, a model with very high precision could be obtained, affecting the operation and control of the fuel cells in the simulation analyses. [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]