Uncertainty Of Renewable Energy Sources Research Articles

A cooperative transactive multi-carrier energy control mechanism with P2P energy + reserve trading using Nash bargaining game theory under renewables uncertainty

Transactive Energy Control (TEC) as a market-based control is a critical notion for scheduling Multi-Carrier Energy Systems (MCESs) in local networks and forming an Energy Hub (EH). Nevertheless, implementing TEC for scheduling and controlling MCESs is extremely difficult due to the lack of a cooperative TEC model that accounts for network constraints and the uncertainty of Renewable Energy Sources (RESs). This paper defines and formulates Prosumer-Based Multi-Carrier Energy Systems (PB-MCESs), which include electricity, heat, cooling, and gas hubs to enable internal coordination of resources and flexibility extraction for PB-MCESs. Subsequently, Nash Bargaining Game Theory is employed to construct a cooperative TEC that prioritizes P2P energy trade. In addition to P2P energy trading, PB-MCESs can trade their reserve in a P2P fashion to mitigate their uncertainty. PB-MCESs estimate the level of uncertainty using stochastic programming and allot a reserve capacity based on this estimation in order to manage their uncertainty via P2P reserve trading and internal reserves. PB-MCES can also control their risk by altering their risk-taking factor in accordance with the Conditional Value-at-Risk (CVAR) index. Implementations have demonstrated that the proposed cooperative TEC decreases total costs by 17.14% and that the proposed P2P reserve trading reduces total costs by 16.32%.

CoLinFlow: An Iterative Solution Approach for the Scenario-Based AC OPF in Active Meshed Distribution Grids With Batteries

Distribution grids are characterized by an increased installation of renewable energy sources (RESs) and of batteries. Both the uncertainty of RESs and the controllability of batteries should be considered when optimizing their operation. This leads to large-scale, non-convex Optimal Power Flow (OPF) problems. Existing solution approaches either refer to radial grids or do not work under uncertainty. However, many Distribution System Operators operate their grids in meshed topologies. In this paper, CoLinFlow, an efficient solution approach for a scenario-based AC OPF in meshed balanced three-phase distribution grids with intermittent RESs and controllable batteries is proposed. First, a particular power flow form in rectangular coordinates that is accurate for meshed grids is applied. Then, Generalized Linearized Power Flow (GLPF), a novel linearization of the power flow equations based on replacing non-linear terms with constants is developed. Based on GLPF, we design CoLinFlow, a heuristic iterative scheme that at each iteration solves a convex OPF and updates GLPF until convergence. The solution of CoLinFlow at convergence is proven to be feasible with respect to the original non-convex OPF and convergence is reached after very few iterations. Also, it is shown that CoLinFlow achieves almost the same optimal objective as Ipopt, while being faster.

A Two-Stage Flexibility-Oriented Stochastic Energy Management Strategy for Multi-Microgrids Considering Interaction With Gas Grid

Introduction of renewable energy sources (RESs) and independently operated multi-microgrid (MMG) systems have led to new issues in the management of power systems. In this context, uncertainty associated with RESs as well as intense ramps inflicted on the network called system flexibility constraints have raised new challenges in power systems. The new condition necessitates the implementation of novel frameworks that enable local system operators to efficiently manage the available resources to cope with the flexibility-ramp constraints. Moreover, the new framework should facilitate energy management in a system with an MMG structure considering uncertainty of RESs. Consequently, in this article, we aim to provide a novel framework that composes of a two-level stochastic optimization procedure to optimize the energy management in an MMG, considering uncertainty of RESs as well as grid flexibility constraints. In the proposed scheme, resource scheduling in microgrids (MGs) is conducted in the first level by their control units, while the second-level procedure focuses on the coordination of MGs, considering flexibility constraints. Furthermore, interaction with gas grid as a potential flexible resource is optimized in the second-level procedure. Finally, the provided flexibility-oriented management scheme is implemented to schedule the local resources in a three-MG test system, considering flexibility constraints.

Robust Constraints-Based Supply-Demand Coordination With Storage Systems of Enterprise Microgrid

Renewable energy sources and electric vehicles provide an effective way to reduce the energy cost of an enterprise microgrid. However, the uncertainties of renewable energy sources and the time coupling characteristic of electric vehicles bring great challenges of non-anticipativity and feasibility for supply-demand coordination. To satisfy the non-anticipativity, we develop a supply-demand coordination optimal model using pre-scheduling method with virtual re-scheduling. In this model, the current decision only depends on the current and past realizations of random variables. Furthermore, we enhance the model with time-coupled robust constraints to guarantee the feasibility of the strategy under all possible realizations of the random variables. These time-coupled robust constraints bring high computational complexity to solve this model. So, we develop the method of combining forward recursion and backward recursion to decouple these time-coupled robust constraints in time. In this way, the coordination model is transformed to a mixed integer linear programming (MILP) model which can be efficiently solved. Finally, numerical test based on a real case is analysed and the results show that the energy cost of the enterprise is about 136129&#x0024; if the flexible load is about 20% and load shifting and generators rescheduling can reduce the energy cost more than 6%. <i>Note to Practitioners</i>&#x2014;This study is encouraged by the challenging problem caused by the multi-distributed energy introduced into an enterprise microgrid. In enterprises, as the large-area flat workshop roof assists in convenience for photovoltaics&#x2019; development and the EVs are widely used, the issue to best utilize renewable energy and EVs shows vital significance in reducing the energy cost. However, there exist the following three main challenges: (eq1) the non-anticipativity of the model, (eq2) the solution&#x2019;s feasibility under all possible realizations, and (eq3) the effectiveness of the solution method. For the concerns of non-anticipativity, we develop the model using a pre-scheduling model with virtual re-scheduling in which the current decision only depends on the current and past realizations of random variables. To handle the second challenge, an ideal of scenario model with robust constraints is developed considering both feasibility and economy. In order to solve the model with robust constraints, the all-scenario-feasible method and a combination of the forward recursion and backward recursion method are used to deal with time-independent and the time-coupled robust constraints, respectively. The numeric results demonstrate that load shifting and generators rescheduling can reduce the energy cost more than 6%, and using the method with the forward and backward recursion process can reduce the energy cost more than 9%.

Bi-objective optimal design of desalination plants considering the uncertainty of renewable energy sources

Desalination systems are commonly used in isolated areas to supply drinking water. However, they usually rely on fossil fuels, which emit greenhouse gases. Renewable energy sources can be used to power desalination systems, but they are intermittent. To address this, the power generation or the capacity of energy and/or water storage can be increased, but this increases the cost. In this paper, we present a bi-objective optimization methodology for designing a desalination system that is powered by renewable energy sources. The methodology aims to maximize reliability while minimizing the levelized cost of water (LCOW) by including the inherent uncertainty in renewable energy generation. We applied this methodology in the Guajira Peninsula, a region of Colombia with serious problems of drinking water scarcity, to evaluate photovoltaic (PV), wind, and PV/wind hybrid systems, determining the optimal combination of wind turbines, photovoltaic (PV) modules, desalination unit characteristics, water storage capacity, and batteries. We also introduced a new indicator, the Reliability - LCOW ratio (RLR), to assist in selecting the optimal configuration. Our results indicate that the renewable systems are feasible, achieving reliability levels between 92% and 95% and LCOW values between 0.82-0.84 USD/m3, when compared to fossil fuel configurations. Despite this, the PV-only system exhibited a significantly higher installed capacity when compared to wind and hybrid systems, while the latter two showed relatively similar characteristics. An analysis about the use of the water tank as a natural battery compared with electricity storage proved that the battery bank was more effective for the PV-only system, while the water tank was more suitable in systems where the use of wind power is predominant. Furthermore, an analysis of the direct CO2 emissions of the fossil fuel configurations shows that the renewable solutions reduce emissions by over 150 tons-eq/y.

Investigating effect of various time varying load models in grid connected microgrid system integrated with renewables and cogeneration units

ABSTRACT The optimal allocation of sources considering voltage-dependent load models is essential as the power consumption of the loads is sensitive to voltage magnitude. In this paper, optimal allocation of microgrid system with cogeneration units, renewable energy sources (RES), shunt capacitors and heat boiler are determined for constant, residential, industrial, commercial and mixed load models. The cost, emission, energy loss, voltage deviation and voltage stability values for each load model is determined using particle swarm optimisation (PSO) integrated fuzzy max–min approach while the uncertainties in RES are taken into account. Results demonstrate that the cost, energy loss and voltage deviation values are maximum for constant power (CP) load model compared with other load models. Furthermore, the system with constant impedance (CZ) load achieves maximum loading capability than with other types of constant loads. The proposed method is validated on 33-bus grid-connected microgrid system with all the load models.

Zero-Carbon AC/DC Microgrid Planning by Leveraging Vehicle-to-Grid Technologies

This paper explores the strategic planning required for a zero-carbon-emission AC/DC microgrid, which integrates renewable energy sources and electric vehicles (EVs) within its framework. It considers the rapidly growing adoption of EVs and the advent of vehicle-to-grid (V2G) technology, which allows EVs to return energy to the grid during peak demand. The study aims to apply optimization techniques to minimize the installation cost associated with various microgrid components. In the case of microgrids, there are decision-making scenarios where multiple alternatives are present; optimization is a valuable technique for efficiently planning and designing microgrids. This work showcases case studies and sensitivity analysis plots, illustrating how output power fluctuates due to uncertainty in renewable energy sources and the absence of EVs. The findings show how V2G contributes to the demand when renewable generation is low. The sensitivity analysis also provides insights into how the unit cost is affected by demand fluctuations. In summary, the principal contribution of this study is developing a comprehensive planning framework for AC/DC microgrids. This framework considers the escalating adoption of EVs and offers practical solutions for future microgrid designs.

Energy Management Strategy for PV PSO MPPT / Fuel Cell/Battery Hybrid System with Hydrogen Production and Storage

Due to the high uncertainty of renewable energy sources, and the diversity of energy sources and storage systems, it is mandatory to seek a controller that manages all these renewable energy sources and this hybrid energy storage. This paper proposed a renewable energy management system using flatness control and PID and PSO technologies that track the maximum power point from the PV array and manages the energy storage elements. Two energy storage are adopted: battery storage and hydrogen tank. The proposed (Nero-fuzzy) controller also works to fill the hydrogen storage tank wisely and safely by controlling the alkaline electrolyzer and the tank's pressure. The main aim of this combined system is to attain power stability. Since the PV is the primary production source, a PSO MPPT is a proposed system for optimum power delivered by the PV under different radiation and temperature conditions. The fuel cell has been used to compensate for the energy lost when there is a lack of control due to weather conditions or high-power demand by the DC load. A battery was coupled to the DC bus to respond quickly to the power requirement. When the radiation intensity is 1000 W/m2, the PV will generate enough 18 kW to supply the load, run the electrolyzer 7 kW, and charge the batteries. While in the radiation change, when it is 240 W/m2, the solar panels produce (4.3 kW) and the load (4.7 kW). The battery works first because of its quick response, and then the fuel cell works to generate instead of it, which is sufficient to operate the load only. The results show a stable and fast response grid under different weather conditions and load scenarios.

Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part I: Theory

Data-driven sparse estimation of distribution factors (DFs) facilitates online power flow sensitivity analysis for secure system operation. However, existing methods are vulnerable to time-varying non-Gaussian PMU measurement noise, bad data, and uncertain renewable energy sources (RESs). Moreover, they lack scalability to large-scale systems. This two-part paper proposes a robust and scalable sparse DF estimation framework considering PMU data quality and RES uncertainty. In this Part I, a novel Adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -Lasso estimator with theoretically guaranteed robustness is proposed. It mitigates the impacts of measurement and RES uncertainties to yield accurate dominant DF estimates while promoting sparsity. The key idea is to integrate the robust statistics theory with sparse representation techniques, in particular the Huber loss function, adaptively-weighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization, concomitant scale estimate, and pseudo-residuals. Two important robustness properties of this estimator are theoretically proven, i.e., the bounded influence function and the asymptotic consistency of dominant DF estimates given limited samples. The breakdown points of this estimator to measurement and RES uncertainties are derived. Test results validate that the proposed estimator allows accurate estimation without relying on power flow models or massive operating data. It achieves significantly superior robustness over existing methods in multiple scenarios.

Probabilistic optimal power flow in wind energy integrated power system based on the K‐medoids data clustering method considering correlated uncertain variables

AbstractRenewable energy sources have increasingly been integrated into power systems because of their superior environmental, technical, and economic advantages. However, the uncertainty of these sources besides load fluctuations and equipment outages brings new challenges to power system operating and planning studies. Also, the correlation between uncertain variables makes operational decisions more and more complicated. Probabilistic assessment of power systems is essential to evaluate uncertainties’ effects and make reasonable decisions. Methods with high accuracy and low computational burden are efficient for online and fast requirements such as optimal power flow (OPF) problems. A clustering method based on the K‐medoids technique is used for the probabilistic assessment of the power system in the OPF problem. Unlike other clustering techniques the K‐medoids method can manage discrete variables such as equipment outages besides other continuous variables such as load and wind generation. This paper presents an OPF problem considering the uncertainty of renewable energy sources, load fluctuations, and transmission lines outage as well as the correlation among them. The probabilistic assessment is conducted by the K‐medoids method and the optimization problem is solved by the cooperation search algorithm (CSA) as an efficient evolutionary algorithm. Numerical results using the IEEE standard 30 and 118 bus test systems show the efficiency of the proposed method in terms of accuracy and computational burden.

An interval power flow method for radial distribution systems based on hybrid second-order cone and linear programming

Interval power flow (IPF) analysis is a promising approach to handling the uncertainty of renewable energy sources and loads in power systems. However, most existing studies are based on standard interval arithmetic or affine arithmetic. Little work can be found that employs traditional optimization methods to obtain the interval results, especially based on convexified power flow formulation. Therefore, this paper proposes an IPF method based on a hybrid second-order cone and linear programming for radial distribution systems. First, the optimization process of IPF based on the standard power flow model is introduced. Given the non-convexity of the standard power flow model, an IPF framework based on second-order cone programming (SOCP) for radial distribution systems is proposed. Moreover, considering that the SOCP formulation can only achieve half of the whole IPF process, a revised linear DistFlow formulation is adopted, and the IPF method based on a hybrid second-order cone and linear programming is devised. Finally, the proposed IPF method is compared with the standard power flow equation-based IPF method and the Monte Carlo method. The simulation results on modified IEEE 33-node and 69-node distribution systems demonstrate the effectiveness and prospects of the proposed IPF method.

Flexible renewable energy planning based on multi-step forecasting of interregional electricity supply and demand: Graph-enhanced AI approach

Jeju Island faces curtailment problems when renewable energy generation exceeds the facility capacity. In addition, the renewable energy system cannot achieve consistent operation because of the uncertainty of renewable energy sources (RES) and their complex spatiotemporal patterns. Climate change and extreme meteorological phenomena also affect the energy system of the island. Therefore, it is essential to maximize RES exploitation to accomplish carbon-free energy production. This study developed a rolling horizon optimization–based flexible renewable energy distribution planning (FxRE-Plan) based on an artificial intelligence-driven spatiotemporal RES prediction model. An adaptive graph convolutional recurrent network (AGCRN) was used to develop a spatiotemporal prediction model. Then, FxRE-Plan was determined using a multiobjective genetic algorithm to maximize the RES potential under climate change scenarios. The FxRE-Plan was evaluated and compared with the current operation of the electric grid in Jeju Island through economic, environmental cost, and climate change vulnerability assessment index. The results of this research show that the AGCRN–based spatiotemporal prediction model exhibited superior prediction performance, achieving a 95% R2. In addition, the FxRE-Plan reduced greenhouse gas emissions by approximately 11.5% at maximum and climate change vulnerability. Hence, the proposed FxRE-Plan can be used to solve curtailments in real electric grids by pursuing carbon-free islands.

Robust optimal energy management with dynamic price response: A non-cooperative multi-community aggregative game perspective

Energy management system gradually becomes an effective means in smart grid for paving the way to low carbon economy. However, information privacy, a large population of users, and the uncertainties of renewable energy sources and consumers’ behaviors have led to significant challenges for energy management system operation in terms of security and robustness. To conquer such difficulties, a bilevel energy management scheme for the day-ahead optimal scheduling of multi-community system combined with distributed energy sources is first proposed. Meanwhile, uncertainties induced by renewable energy sources generation and load consumption are handled through adjustable robust optimization. Secondly, a non-cooperative multi-community aggregative game is formulated to describe the interaction of numerous residential users which are coupled through the dynamic electricity price. Then, to seek the ɛ-Nash Equilibrium of the proposed game, an improved decentralized iterative algorithm based on Mean-Field control and consensus is presented which is benchmarked with centralized algorithm and a decentralized optimization method based on quadratic programming. Since each player in the proposed algorithm does not need to exchange information directly with other players, the information privacy is fully preserved. Also, the convergence of the proposed algorithm is provided. Case studies of a five-community system are conducted and the comparison results show that our proposed approach has better performance in terms of computational time and electricity cost.

Performance enhancement of smart grid with demand side management program contemplating the effect of uncertainty of renewable energy sources

ABSTRACT In a day ahead electricity market, all candidates of the electricity market, i.e. electricity users, aggregator, and grid operator urge to grow individual profit, but it is quite challenging to assure profit for all the candidates at a time. In this work, a multi-objective problem is formulated by combining the concept of demand side management (DSM) and Dynamic Economic Emission Dispatch (DEED). The multi-objective DSM – DEED problem is optimized by class topper optimization algorithm. In addition, an energy management algorithm (EMA) is proposed for optimal power utilization from various energy sources and to match the load demand with generated energy in presence of uncertainties of RESs. To get an accurate model, a random forest regression-based machine learning approach is considered in this paper to predict load demand, wind, and solar power on an hourly basis for a span of 24 hours. The objective here is to optimally schedule load consumption and power generation patterns simultaneously for a day to improve load factor, minimize operational cost, and maximize the profit of all the candidates of the electricity market simultaneously. The simulation findings highlight the effects of the proposed EMA and modified DSM program on the smart grid’s economy and performance.

Energy management in microgrids using IoT considering uncertainties of renewable energy sources and electric demands: GBDT-JS approach

Energy management in microgrids using IoT considering uncertainties of renewable energy sources and electric demands: GBDT-JS approach

Stochastic planning of integrated energy system based on correlation scenario generation method via Copula function considering multiple uncertainties in renewable energy sources and demands

AbstractThe main goal of integrated energy service providers (IESP) in the future is to pursue profitability and reduce carbon emissions while ensuring sufficient energy supply. However, the multiple uncertainties associated with renewable energy resources and the multi‐energy consumers pose significant challenges in the optimal planning of the integrated energy system (IES) based on energy hubs (EH). This includes the global optimization of device types, EH capacity, and the optional interconnections between adjacent EHs. This study aims to develop a comprehensive mathematical model of EH that considers the temperature limitations on device operation. The thermal bus and associated devices are divided into high and low temperature parts, and a multi‐scenario stochastic programming model is proposed for IES planning. Scenarios are generated using non‐parametric kernel density estimation and the Copula function, a scenario reduction technique is implemented to alleviate computational burden. Additionally, case studies illustrate effectiveness of the proposed approach, the operation and forms of EHs, effect of the interconnections and the trade‐off between carbon emissions and economic costs are further studied by extensive simulations. This study can be a good guide for IESPs to invest in the construction of the EH‐based IES.

A fast linearized AC power flow-constrained robust unit commitment approach with customized redundant constraint identification method

The large-scale integration of renewable energy resources in the power system challenges its economic and secure operation. Particularly, the increasing penetration of renewable energy will result in insufficient system voltage regulation and reactive power support capabilities, and may cause high risks of nodal voltage and branch flow violations. Therefore, to hedge the operational risks under the worst realization of uncertainties of renewable energy sources, a two-stage robust unit commitment (UC) model is developed. Meanwhile, the convexified AC power flow model is incorporated in the robust UC model to more accurately characterize the real-time operating status of power systems. On this basis, an AC power flow-constrained robust unit commitment (ACRUC) model is formulated. A circular linearization method is then adopted to handle the quadratic constraints in the original AC power flow model, transforming them into tractable linear constraints. Furthermore, to reduce the computational complexity caused by the large-scale newly-added constraints after the linearization process, a customized redundant constraint identification (RCI) method is developed, in which two different modes (i.e., cold and warm start modes) are designed considering the difference in base case system operating condition for linearizing branch losses. Then, the redundant network security constraints could be identified by solving a series of relatively simple optimization subproblems. Numerical results on the modified NERL-118 test system indicate that the proposed model could accurately depict actual operation and scheduling conditions, and also verify that the proposed customized RCI method could effectively reduce the problem scale and improve the solution efficiency.

Segmentation of interconnected power systems considering microgrids and the uncertainty of renewable energy sources

AbstractThis paper proposes an approach for segmentation of power systems to prevent uncontrolled islanding. With the development of microgrids (MGs) and increased penetration of renewable energy sources (RESs) in the power system, it is necessary to consider the effect of MGs and the stochastic behaviour of RESs in the controlled islanding process. First, the enormous search space for finding the boundary points is reduced by the clustering of the coherent generators and the buses which are placed in sections that cannot be separated from the coherent groups. Then, linear AC power flow is defined as a sub‐problem and solved by linear programming to satisfy the power system and MG constraints. In this step, an optimization model is defined, and a mixed‐integer linear programming (MILP)‐based model is suggested to find cut‐sets and islands arrangement with reduced load shedding. In view of the fact that the fluctuation of RESs may have the significant effects on the power imbalance, to cover the uncertainties a scenario based stochastic simulation is considered. Finally, the effect of uncertainties on cut‐sets and load curtailment is evaluated. The effectiveness of the proposed methodology is demonstrated by the simulation on the test system.

Optimal Allocation of Virtual Inertia and Droop Control for Renewable Energy in Stochastic Look-Ahead Power Dispatch

To stabilize the frequency of the renewable energy sources (RESs) dominated power system, frequency supports are required by RESs through virtual inertia emulation or droop control in the newly published grid codes. Since the long-term RES prediction involves significant errors, we need online configure the frequency control parameters of RESs in a rolling manner to improve the operation economics under the premise of stabilizing system frequency. To address this concern, this paper proposes a frequency constrained stochastic look-ahead power dispatch (FCS-LAPD) model to formulate the frequency control parameters of RESs and Energy Storage Systems (ESSs) as scheduling variables, which can optimally allocate the virtual inertia and droop coefficient of RESs and ESSs. In this FCS-LAPD model, the uncertainties of RESs are characterized using Gaussian Mixture Model (GMM). The required reserves are determined by frequency control parameters, and the reserve cost coefficients are adjusted properly to allocate the reserves according to the predicted power generation. Due to the nonlinearity of the frequency nadir constraint, a convex hull approximation method is proposed to linearize it with guaranteed feasibility. The proposed FCS-LAPD is ultimately cast as an instance of quadratic programming and can be efficiently solved. Case studies on modified IEEE 24-bus system and a provincial power system in China are conducted to show the effectiveness of the proposed model.

Stochastic optimal power flow analysis of power system with renewable energy sources using Adaptive Lightning Attachment Procedure Optimizer

The integration of several renewable energy sources (RESs), such as photovoltaic generation (PVG) and wind turbine generation (WTG), introduces a significant amount of uncertainty for the optimal planning of the electrical power systems. The optimal power flow (OPF) problem became more difficult to solve when RESs uncertainties were taken into account. In this research, the stochastic OPF problem is solved using an Adaptive Lightning Attachment Procedure Optimizer (ALAPO) with the integration of RESs. The ALAPO is proposed in this study to improve both the exploration and exploitation process of the conventional Lightning Attachment Procedure Optimizer (LAPO). In order to create a number of scenarios that account for the uncertainties associated with load demand, wind speed, and solar irradiation, the scenario based reduction method is utilized. Further, to determine the optimal setting of active power of generators, tap setting of the transformers, reactive power of the capacitor banks, and the voltage profile at the generator buses for each scenario of RESs the objective function considered in this study is to minimize the power loss, voltage deviation, and voltage stability index of the power system. The effectiveness of the proposed algorithm is tested on IEEE 57-bus system. The results in this study show that the proposed ALAPO is superior for solving the OPF with the integration of RESs compared to the conventional methods like LAPO, Particle Swarm Optimization (PSO), Sand Cat Swarm Optimizer (SCSO), Gray Wolf Optimizer (GOW), Whale Optimization Algorithm (WOA), Black Widow Optimization Algorithm (BWO), and Capuchin Search Algorithm (CapSA).