Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons

Modified effective butterfly optimizer for solving optimal power flow problem

The optimal power flow (OPF) problem remains a popular and challenging work in optimizing power systems. Although researchers have suggested many optimization algorithms to solve this problem in the literature, their comparison studies lack fairness and transparency. As these studies increase in number, they deviate from a standard test system, considering a common security and technical constraints., there is a growing trend away from a standard test system. Different studies used different search ranges for the same decision and constraint parameters, different than the standard ranges suggested by IEEE systems. This caused many unfair comparisons in literature. Furthermore, these studies are generally not transparent enough so that their results cannot be verified. This has resulted in numerous infeasible solutions in the literature, violating the limits of constraint parameters. The recent incorporating of renewable energy sources in OPF studies has made this situation more complicated. Sorting through the literature and identifying those OPF applications having exactly the same test conditions is a challenging process. The main contribution is this paper adapts the modified effective butterfly algorithm (MEBO) to solve OPF problem under the common parameter constraints and sufficient transparency. The focus is on a transparent comparison with works in the literature with the same constraint values. This paper compares the performance of the proposed algorithm with other state-of-the-art algorithms in the literature, focusing on the wind energy and without wind energy IEEE 30-bus and IEEE 57-bus systems and the most commonly used constraints. The results demonstrate the efficiency and superiority of the proposed algorithm. For instance, in the 30-bus test system, compared to the initial case, fuel cost has been reduced by 11.42 %, emission by 14.33 %, L-index by 45.10 %, active power losses by 51.60 %, and voltage deviation by 92.70 %.

A leader supply-demand-based optimization for large scale optimal power flow problem considering renewable energy generations

The supply-demand-based optimization (SDO) is among the recent stochastic approaches that have proven its capability in solving challenging engineering tasks. Owing to the non-linearity and complexity of the real-world IEEE optimal power flow (OPF) in modern power system issues and like the existing algorithms, the SDO optimizer necessitates some enhancement to satisfy the required OPF characteristics integrating hybrid wind and solar powers. Thus, a SDO variant namely leader supply-demand-based optimization (LSDO) is proposed in this research. The LSDO is suggested to improve the exploration based on the simultaneous crossover and mutation mechanisms and thereby reduce the probability of trapping in local optima. The LSDO effectiveness has been first tested on 23 benchmark functions and has been assessed through a comparison with well-regarded state-of-the-art competitors. Afterward, Three well-known constrained IEEE 30, 57, and 118-bus test systems incorporating both wind and solar power sources were investigated in order to authenticate the performance of the LSDO considering a constraint handling technique called superiority of feasible solutions (SF). The statistical outcomes reveal that the LSDO offers promising competitive results not only for its first version but also for the other competitors.

A multi-strategy improved tree-seed algorithm for numerical optimization and engineering optimization problems

Tree-seed algorithm is a stochastic search algorithm with superior performance suitable for solving continuous optimization problems. However, it is also prone to fall into local optimum and slow in convergence. Therefore, this paper proposes an improved tree-seed algorithm based on pattern search, dimension permutation, and elimination update mechanism (PDSTSA). Firstly, a global optimization strategy based on pattern search is used to promote detection ability. Secondly, in order to maintain the diversity of the population, a random mutation strategy of individual dimension replacement is introduced. Finally, the elimination and update mechanism based on inferior trees is introduced in the middle and later stages of the iteration. Subsequently, PDSTSA is compared with seven representative algorithms on the IEEE CEC2015 test function for simulation experiments and convergence curve analysis. The experimental results indicate that PDSTSA has better optimization accuracy and convergence speed than other comparison algorithms. Then, the Wilcoxon rank sum test demonstrates that there is a significant difference between the optimization results of PDSTSA and each comparison algorithm. In addition, the results of eight algorithms for solving engineering constrained optimization problems further prove the feasibility, practicability, and superiority of PDSTSA.

Advances in Sparrow Search Algorithm: A Comprehensive Survey

Mathematical programming and meta-heuristics are two types of optimization methods. Meta-heuristic algorithms can identify optimal/near-optimal solutions by mimicking natural behaviours or occurrences and provide benefits such as simplicity of execution, a few parameters, avoidance of local optimization, and flexibility. Many meta-heuristic algorithms have been introduced to solve optimization issues, each of which has advantages and disadvantages. Studies and research on presented meta-heuristic algorithms in prestigious journals showed they had good performance in solving hybrid, improved and mutated problems. This paper reviews the sparrow search algorithm (SSA), one of the new and robust algorithms for solving optimization problems. This paper covers all the SSA literature on variants, improvement, hybridization, and optimization. According to studies, the use of SSA in the mentioned areas has been equal to 32%, 36%, 4%, and 28%, respectively. The highest percentage belongs to Improved, which has been analyzed by three subsections: Meat-Heuristics, artificial neural networks, and Deep Learning.

Chaos-enhanced multi-objective tunicate swarm algorithm for economic-emission load dispatch problem

Climate change and environmental protection have a significant impact on thermal plants. So, the main principles of combined economic-emission dispatch (CEED) problem are indeed to reduce greenhouse gas emissions and fuel costs. Many approaches have demonstrated their efficacy in addressing CEED problem. However, designing a robust algorithm capable of achieving the Pareto optimal solutions under its multimodality and non-convexity natures caused by valve ripple effects is a true challenge. In this paper, chaos-enhanced multi-objective tunicate swarm algorithm (CMOTSA) for CEED problem. To promote the exploration and exploitation abilities of the basic tunicate swarm algorithm (TSA), an exponential strategy based on chaotic logistic map (ESCL) is incorporated. Based on ESCL in CMOTSA, it can improve the possibility of diversification feature to search different areas within the solution space, and then, gradually with the progress of iterative process it converts to emphasize the intensification ability. The efficacy of CMOTSA is approved by applying it to some of multi-objective benchmarking functions which have different Pareto front characteristics including convex, discrete, and non-convex. The inverted generational distance (IGD) and generational distance (GD) are employed to assess the robustness and the good quality of CMOTSA against some successful algorithms. Additionally, the computational time is evaluated, the CMOTSA consumes less time for most functions. The CMOTSA is applied to one of the practical engineering problems such as combined economic and emission dispatch (CEED) with including the valve ripples. By using three different systems (IEEE 30-bus with 6 generators system, 10 units system and IEEE 118-bus with 14 generating units), the methodology validation is made. It can be stated for the large-scale case of 118-bus systems that the results of the CMOTSA are equal to 8741.3 $/h for the minimum cost and 2747.6 ton/h for the minimum emission which are very viable to others. It can be pointed out that the cropped results of the proposed CMOTSA based methodology as an efficient tool for CEED is proven.

A Novel Chaotic Rao-2 Algorithm for Optimal Power Flow Solution

This article suggests a novel chaotic Rao-2 algorithm to solve various optimal power flow (OPF) problems. The basic Rao-2 solver is a newly developed metaphor-less optimization tool. The novel optimization course of the basic Rao-2 algorithm relies on the finest and inferior solutions within the population and the indiscriminate interrelations among the nominee individuals. This tactic allows superior directions to scrutinize the exploration space. In this work, a novel chaotic Rao-2 algorithm-inspired scheme for handling the OPF problem is offered. In the offered solver, a chaotic tactic is amalgamated into the movement formula of the basic Rao-2 algorithm to enhance the variety of solutions and enhance both its global and local search capabilities. This novel scheme, which incorporates the features of the basic Rao-2 algorithm and chaotic dynamics, is then utilized to solve various OPF problems. For the OPF solution, five situations are investigated. The offered solver is examined on two standard IEEE test grids and the emulation outcomes are evaluated with the outcomes offered in the other publications and deemed competitive in terms of the features of the solution. The offered chaotic Rao-2 algorithm outperforms the basic Rao-2 algorithm regarding convergence velocity and solution competence. Furthermore, a test is performed to validate the statistical worth of the offered chaotic Rao-2-inspired solver. The offered chaotic Rao-2 algorithm presents a vigorous and simple solution for the OPF framework under various objectives.

Weiszfeld, tree-seed, and whale optimization algorithms comparison via locating transportation facilities with weightings considering the vulnerability and uncertainty

Searching for an optimum transportation facility location with emergency equipment and staff is essential for a specific region or a country. In this direction, this study addresses the following problems. First, the performances of the Weiszfeld, tree-seed, and whale optimization algorithms are compared, which is the first of its kind in the literature. Second, a new approach that tests the importance parameters' effectiveness in searching for an optimum transportation facility location with emergency equipment and staff is proposed. The Weiszfeld algorithm finds viable solutions with compact data, but it may not handle big data. In contrast, the flexibility of the tree-seed and whale optimization algorithm is literally an advantage when the number of parameters and variables increases. Therefore, there is a notable need to directly compare those algorithms' performances. If we do, the significance of extending the number of parameters with multiple weightings is appraised. According to the results, the Weiszfeld algorithm can be an almost flexible technique in continuous networks; however, it has reasonable drawbacks with discrete networks, while the tree-seed and whale optimization algorithms fit such conditions. On the other hand, these three methods do not show a fluctuating performance compared to one another based on the locating transportation facilities, and thus they deliver similar performance. Besides, although the value of accuracy is high with the application of the conventional technique Weiszfeld algorithm, it does not provide a significant performance accuracy advantage over the meta-heuristic methods.

Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony

A new optimization technique is proposed for solving optimization problems having single and multiple objectives, with objective functions such as generation cost, loss, and severity value. This algorithm was developed to satisfy the constraints, such as OPF constraints, and practical constraints, such as ram rate limits. Single and multi-objective optimization problems were implemented with the proposed hybrid fruit fly-based artificial bee colony (HFABC) algorithm and the non-dominated sorting hybrid fruit fly-based artificial bee colony (NSHFABC) algorithm. HFABC is a hybrid model of the fruit fly and ABC algorithms. Selecting the user choice-based solution from the Pareto set by the proposed NSHFABC algorithm is performed by a fuzzy decision-based mechanism. The proposed HFABC method for single-objective optimization was analyzed using the Himmelblau test function, Booth’s test function, and IEEE 30 and IEEE 118 bus standard test systems. The proposed NSHFABC method for multi-objective optimization was analyzed using Schaffer1, Schaffer2, and Kursawe test functions, and the IEEE 30 bus test system. The obtained results of the proposed methods were compared with the existing literature.

Stability Enhancement of Wind Energy Conversion Systems Based on Optimal Superconducting Magnetic Energy Storage Systems Using the Archimedes Optimization Algorithm

Throughout the past several years, the renewable energy contribution and particularly the contribution of wind energy to electrical grid systems increased significantly, along with the problem of keeping the systems stable. This article presents a new optimization technique entitled the Archimedes optimization algorithm (AOA) that enhances the wind energy conversion system’s stability, integrated with a superconducting magnetic energy storage (SMES) system that uses a proportional integral (PI) controller. The AOA is a modern population technique based on Archimedes’ law of physics. The SMES system has a big impact in integrating wind generators with the electrical grid by regulating the output of wind generators and strengthening the power system’s performance. In this study, the AOA was employed to determine the optimum conditions of the PI controller that regulates the charging and discharging of the SMES system. The simulation outcomes of the AOA, the genetic algorithm (GA), and particle swarm optimization (PSO) were compared to ensure the efficacy of the introduced optimization algorithm. The simulation results showed the effectiveness of the optimally controlled SMES system, using the AOA in smoothing the output power variations and increasing the stability of the system under various operating conditions.

OPF of Modern Power Systems Comprising Renewable Energy Sources Using Improved CHGS Optimization Algorithm

This article introduces an application of the recently developed hunger games search (HGS) optimization algorithm. The HGS is combined with chaotic maps to propose a new Chaotic Hunger Games search (CHGS). It is applied to solve the optimal power flow (OPF) problem. The OPF is solved to minimize the generation costs while satisfying the systems’ constraints. Moreover, the article presents optimal siting for mixed renewable energy sources, photovoltaics, and wind farms. Furthermore, the effect of adding renewable energy sources on the overall generation costs value is investigated. The exploration field of the optimization problem is the active output power of each generator in each studied system. The CHGS also obtains the best candidate design variables, which corresponds to the minimum possible cost function value. The robustness of the introduced CHGS algorithm is verified by performing the simulation 20 independent times for two standard IEEE systems—IEEE 57-bus and 118-bus systems. The results obtained are presented and analyzed. The CHGS-based OPF was found to be competitive and superior to other optimization algorithms applied to solve the same optimization problem in the literature. The contribution of this article is to test the improvement done to the proposed method when applied to the OPF problem, as well as the study of the addition of renewable energy sources on the introduced objective function.

A Robust Optimization Approach for Optimal Power Flow Solutions Using Rao Algorithms

This paper offers three easy-to-use metaphor-less optimization algorithms proposed by Rao to solve the optimal power flow (OPF) problem. Rao algorithms are parameter-less optimization algorithms. As a result, algorithm-specific parameter tuning is not required at all. This quality makes these algorithms simple to use and able to solve various kinds of complex constrained optimization and engineering problems. In this paper, the main aim to solve the OPF problem is to find the optimal values of the control variables in a given electrical network for fuel cost minimization, real power losses minimization, emission cost minimization, voltage profile improvement, and voltage stability enhancement, while all the operating constraints are satisfied. To demonstrate the efficacy of Rao algorithms, these algorithms have been employed in three standard IEEE test systems (30-bus, 57-bus, and 118-bus) to solve the OPF problem. The OPF results of Rao algorithms and the results provided by other swarm intelligence (SI)/evolutionary computing (EC)-based algorithms published in recent literature have been compared. Based on the outcomes, Rao algorithms are found to be robust and superior to their competitors.

Cost Minimizations and Performance Enhancements of Power Systems Using Spherical Prune Differential Evolution Algorithm Including Modal Analysis

A novel application of the spherical prune differential evolution algorithm (SpDEA) to solve optimal power flow (OPF) problems in electric power systems is presented. The SpDEA has several merits, such as its high convergence speed, low number of parameters to be designed, and low computational procedures. Four objectives, complete with their relevant operating constraints, are adopted to be optimized simultaneously. Various case studies of multiple objective scenarios are demonstrated under MATLAB environment. Static voltage stability index of lowest/weak bus using modal analysis is incorporated. The results generated by the SpDEA are investigated and compared to standard multi-objective differential evolution (MODE) to prove their viability. The best answer is chosen carefully among trade-off Pareto points by using the technique of fuzzy Pareto solution. Two power system networks such as IEEE 30-bus and 118-bus systems as large-scale optimization problems with 129 design control variables are utilized to point out the effectiveness of the SpDEA. The realized results among many independent runs indicate the robustness of the SpDEA-based approach on OPF methodology in optimizing the defined objectives simultaneously.

A Novel Application of Improved Marine Predators Algorithm and Particle Swarm Optimization for Solving the ORPD Problem

The appropriate planning of electric power systems has a significant effect on the economic situation of countries. For the protection and reliability of the power system, the optimal reactive power dispatch (ORPD) problem is an essential issue. The ORPD is a non-linear, non-convex, and continuous or non-continuous optimization problem. Therefore, introducing a reliable optimizer is a challenging task to solve this optimization problem. This study proposes a robust and flexible optimization algorithm with the minimum adjustable parameters named Improved Marine Predators Algorithm and Particle Swarm Optimization (IMPAPSO) algorithm, for dealing with the non-linearity of ORPD. The IMPAPSO is evaluated using various test cases, including IEEE 30 bus, IEEE 57 bus, and IEEE 118 bus systems. An effectiveness of the proposed optimization algorithm was verified through a rigorous comparative study with other optimization methods. There was a noticeable enhancement in the electric power networks behavior when using the IMPAPSO method. Moreover, the IMPAPSO high convergence speed was an observed feature in a comparison with its peers.

Optimal Power Flow for Transmission Power Networks Using a Novel Metaheuristic Algorithm

In the paper, a modified coyote optimization algorithm (MCOA) is proposed for finding highly effective solutions for the optimal power flow (OPF) problem. In the OPF problem, total active power losses in all transmission lines and total electric generation cost of all available thermal units are considered to be reduced as much as possible meanwhile all constraints of transmission power systems such as generation and voltage limits of generators, generation limits of capacitors, secondary voltage limits of transformers, and limit of transmission lines are required to be exactly satisfied. MCOA is an improved version of the original coyote optimization algorithm (OCOA) with two modifications in two new solution generation techniques and one modification in the solution exchange technique. As compared to OCOA, the proposed MCOA has high contributions as follows: (i) finding more promising optimal solutions with a faster manner, (ii) shortening computation steps, and (iii) reaching higher success rate. Three IEEE transmission power networks are used for comparing MCOA with OCOA and other existing conventional methods, improved versions of these conventional methods, and hybrid methods. About the constraint handling ability, the success rate of MCOA is, respectively, 100%, 96%, and 52% meanwhile those of OCOA is, respectively, 88%, 74%, and 16%. About the obtained solutions, the improvement level of MCOA over OCOA can be up to 30.21% whereas the improvement level over other existing methods is up to 43.88%. Furthermore, these two methods are also executed for determining the best location of a photovoltaic system (PVS) with rated power of 2.0 MW in an IEEE 30-bus system. As a result, MCOA can reduce fuel cost and power loss by 0.5% and 24.36%. Therefore, MCOA can be recommended to be a powerful method for optimal power flow study on transmission power networks with considering the presence of renewable energies.

Improved multiobjective salp swarm optimization for virtual machine placement in cloud computing

In data center companies, cloud computing can host multiple types of heterogeneous virtual machines (VMs) and provide many features, including flexibility, security, support, and even better maintenance than traditional centers. However, some issues need to be considered, such as the optimization of energy usage, utilization of resources, reduction of time consumption, and optimization of virtual machine placement. Therefore, this paper proposes an alternative multiobjective optimization (MOP) approach that combines the salp swarm and sine-cosine algorithms (MOSSASCA) to determine a suitable solution for virtual machine placement (VMP). The objectives of the proposed MOSSASCA are to maximize mean time before a host shutdown (MTBHS), to reduce power consumption, and to minimize service level agreement violations (SLAVs). The proposed method improves the salp swarm and the sine-cosine algorithms using an MOP technique. The SCA works by using a local search approach to improve the performance of traditional SSA by avoiding trapping in a local optimal solution and by increasing convergence speed. To evaluate the quality of MOSSASCA, we perform a series of experiments using different numbers of VMs and physical machines. The results of MOSSASCA are compared with well-known methods, including the nondominated sorting genetic algorithm (NSGA-II), multiobjective particle swarm optimization (MOPSO), a multiobjective evolutionary algorithm with decomposition (MOEAD), and a multiobjective sine-cosine algorithm (MOSCA). The results reveal that MOSSASCA outperforms the compared methods in terms of solving MOP problems and achieving the three objectives. Compared with the other methods, MOSSASCA exhibits a better ability to reduce power consumption and SLAVs while increasing MTBHS. The main differences in terms of power consumption between the MOSCA, MOPSO, MOEAD, and NSGA-II and the MOSSASCA are 0.53, 1.31, 1.36, and 1.44, respectively. Additionally, the MOSSASCA has higher MTBHS value than MOSCA, MOPSO, MOEAD, and NSGA-II by 362.49, 274.70, 585.73 and 672.94, respectively, and the proposed method has lower SLAV values than MOPSO, MOEAD, and NSGA-II by 0.41, 0.28, and 1.27, respectively.