Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems

Multi-objective pathfinder algorithm for multi-objective optimal power flow problem with random renewable energy sources: wind, photovoltaic and tidal

In this paper, the multi-objective optimal power flow (MOOPF) problem optimization objectives focus on four optimization objectives: generation cost, emission, real power loss and voltage deviation (VD). Three renewable energy sources with successful industrial applications, including wind energy, solar energy, and tidal energy are introduced. Renewable energy supply is uncertain, so Weibull distribution probability, lognormal probability and Gumbel probability are used to calculate the instability and intermittency of wind energy, solar energy and tidal energy, respectively. The inclusion of four energy supplies on the IEEE-30 test system and the consideration of renewable energy reserves and penalty cost calculation improve the realism of the model. In order to obtain the control parameters that minimize the four optimization objectives, a named multi-objective pathfinder algorithm (MOPFA) based on elite dominance and crowding distance was proposed to solve this multi-objective optimization problem. Simulation results show the feasibility of the model, and MOPFA can get more evenly distributed Pareto front and provide more diverse solutions. A compromise solution was selected by the fuzzy decision system. Comparison with the recently published literature also shows that the proposed model can effectively reduce emissions and other indicators. In addition, the statistical test results show that MOPFA's multi-objective optimization performance ranks first. In solving this complex optimization problem, results show the MOPFA is superior to other multi-objective algorithms in optimization accuracy and speed.

Gaussian bare-bone slime mould algorithm: performance optimization and case studies on truss structures

The slime mould algorithm (SMA) is a new meta-heuristic algorithm recently proposed. The algorithm is inspired by the foraging behavior of polycephalus slime moulds. It simulates the behavior and morphological changes of slime moulds during foraging through adaptive weights. Although the original SMA's performance is better than most swarm intelligence algorithms, it still has shortcomings, such as quickly falling into local optimal values and insufficient exploitation. This paper proposes a Gaussian barebone mutation enhanced SMA (GBSMA) to alleviate the original SMA's shortcomings. First of all, the Gaussian function in the Gaussian barebone accelerates the convergence while also expanding the search space, which improves the algorithm exploration and exploitation capabilities. Secondly, the differential evolution (DE) update strategy in the Gaussian barebone, using rand as the guiding vector. It also enhances the algorithm's global search performance to a certain extent. Also, the greedy selection is introduced on this basis, which prevents individuals from performing invalid position updates. In the IEEE CEC2017 test function, the proposed GBSMA is compared with a variety of meta-heuristic algorithms to verify the performance of GBSMA. Besides, GBSMA is applied to solve truss structure optimization problems. Experimental results show that the convergence speed and solution accuracy of the proposed GBSMA are significantly better than the original SMA and other similar products.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10462-022-10370-7.

Reactive Power Management Based Hybrid GAEO

Electrical power networks are expanded regularly to meet growing energy requirements. Reactive power dispatch (RPD) optimization is a powerful tool to enhance a system’s efficiency, reliability, and security. RPD optimization is classified as a non-linear and non-convex problem. In this paper, the RPD optimization problem is solved based on novel hybrid genetic algorithms—equilibrium optimizer (GAEO) optimization algorithms. The control variables are determined in such a way that optimizes RPD and minimizes power losses. The efficiency of the proposed optimization algorithms is compared to other techniques that have been used recently to solve the RPD problem. The proposed algorithm has been tested for optimization RPD for three test systems, IEEE14-bus, IEEE-30bus, and IEEE57-bus. The obtained results show the superiority of GAEO over other techniques for small test systems, IEEE14-bus and IEEE-30bus. GAEO shows good results for large system, IEEE 57-bus.

A New Self-Adaptive Teaching–Learning-Based Optimization with Different Distributions for Optimal Reactive Power Control in Power Networks

Teaching–learning-based optimization has the disadvantages of weak population diversity and the tendency to fall into local optima, especially for multimodal and high-dimensional problems such as the optimal reactive power dispatch problem. To overcome these shortcomings, first, in this study, a new enhanced TLBO is proposed through novel and effective θ-self-adaptive teaching and learning to optimize voltage and active loss management in power networks, which is called the optimal reactive power control problem with continuous and discontinuous control variables. Voltage and active loss management in any energy network can be optimized by finding the optimal control parameters, including generator voltage, shunt power compensators, and the tap positions of tap changers, among others. As a result, an efficient and powerful optimization algorithm is required to handle this challenging situation. The proposed algorithms utilized in this research were improved by introducing new mutation operators for multi-objective optimal reactive power control in popular standard IEEE 30-bus and IEEE 57-bus networks. The numerical simulation data reveal potential high-quality solutions with better performance and accuracy using the proposed optimization algorithms in comparison with the basic teaching–learning-based optimization algorithm and previously reported results.

Optimal Reactive Power Dispatch Using a Chaotic Turbulent Flow of Water-Based Optimization Algorithm

In this study, an optimization algorithm called chaotic turbulent flow of water-based optimization (CTFWO) algorithm is proposed to find the optimal solution for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a complicated, mixed-integer nonlinear optimization problem, comprising control variables which are discrete and continuous. The CTFWO algorithm is used to minimize voltage deviation (VD) and real power loss (P_loss) for IEEE 30-bus and IEEE 57-bus power systems. These goals can be achieved by obtaining the optimized voltage values of the generator, the transformer tap changing positions, and the reactive compensation. In order to evaluate the ability of the proposed algorithm to obtain ORPD problem solutions, the results of the proposed CTFWO algorithm are compared with different algorithms, including artificial ecosystem-based optimization (AEO), the equilibrium optimizer (EO), the gradient-based optimizer (GBO), and the original turbulent flow of water-based optimization (TFWO) algorithm. These are also compared with the results of the evaluated performance of various methods that are used in many recent papers. The experimental results show that the proposed CTFWO algorithm has superior performance, and is competitive with many state-of-the-art algorithms outlined in some of the recent studies in terms of solution accuracy, convergence rate, and stability.

New modified algorithm: θ-turbulent flow of water-based optimization

The reactive power control of a power system is discussed under two types of variables: continuous variables (e.g., generator bus voltages) and discrete variables (e.g., transformer taps and the size of switched shunt capacitors). This paper proposes a novel and powerful algorithm, named turbulent flow of water-based optimization (TFWO) as well as a new improved version of this algorithm, called θ-TFWO, for optimal reactive power distribution (ORPD) to reduce losses. The proposed method is applied to two large-scale IEEE 57-bus systems. Furthermore, to demonstrate the competitive performance of the suggested algorithm, its performance was compared to that of several other algorithms, including biogeography-based optimization (BBO), social spider algorithm (SSA), and optics inspired optimization (OIO), in terms of solving the ORPD problem. The results confirmed the robustness and effectiveness of the proposed method as a powerful optimizer applicable to optimal reactive power distribution in power systems.

Optimal Reactive Power Generation for Transmission Power Systems Considering Discrete Values of Capacitors and Tap Changers

In this paper, an improved coyote optimization algorithm (ICOA) is developed for determining control parameters of transmission power networks to deal with an optimal reactive power dispatch (ORPD) problem. The performance of ICOA method is superior to its conventional coyote optimization algorithm (COA) thanks to modifications of two new solution generations of COA. COA uses a center solution to generate an update step size in the first solution generation and produced one new solution by using random factors to diversify the search space in the second solution generation. By tackling the drawbacks of COA, ICOA can reduce control parameters and computation steps, shorten execution time, and provide better results. ICOA is compared to its conventional COA for three standard IEEE systems of 30-, 57-, and 118-buses with continuous and discrete control variables. Moreover, three other algorithms such as water cycle algorithm (WCA), salp swarm algorithm (SSA), and sunflower optimization algorithm (SFOA) have been also implemented for further investigation of the real performance of the proposed method. All the applied methods are metaheuristic algorithms based on population and randomization. The result comparison from the test systems has indicated that ICOA can provide higher solution quality than other methods with reasonable execution time. Therefore, ICOA is a reliable tool for finding optimal solutions of the ORPD problem.

Slime Mold Algorithm for Optimal Reactive Power Dispatch Combining with Renewable Energy Sources

The optimal reactive power dispatch (ORPD) is a complex, nonlinear, and constrained optimization problem. This paper presents the application of a new metaheuristic optimization technique called the slime mold algorithm (SMA) for solving the developed objective function of ORPD combining with renewable energy sources. The presented objective function is to minimize the total operating cost of the system through the minimization of all reactive power costs, total real power loss, voltage deviation of load buses, the system overload and improve voltage stability. The formulation of the ORPD problem combining with renewable energy sources with five different objective functions is then converted to a coefficient single objective function achieving various operating constraints. The SMA technique has been tested and proven on the IEEE 30-bus system and IEEE-118 bus system using different scenarios. Five different scenarios, with and without renewable energy sources, are presented on the two-test system and the simulation results of the SMA is compared to some optimization techniques from the literature under the same test system data, optimal control variables, and operational constraints. The superiority and effectiveness of the SMA are proven through comparison with the other obtained results from recently published optimization techniques.

Scenario-Based Stochastic Framework for Optimal Planning of Distribution Systems Including Renewable-Based DG Units

Renewable energy-based distributed generators are widely embedded into distribution systems for several economical, technical, and environmental tasks. The main concern related to the renewable-based distributed generators, especially photovoltaic and wind turbine generators, is the continuous variations in their output powers due to variations in solar irradiance and wind speed, which leads to uncertainties in the power system. Therefore, the uncertainties of these resources should be considered for feasible planning. The main innovation of this paper is that it proposes an efficient stochastic framework for the optimal planning of distribution systems with optimal inclusion of renewable-based distributed generators, considering the uncertainties of load demands and the output powers of the distributed generators. The proposed stochastic framework depends upon the scenario-based method for modeling the uncertainties in distribution systems. In this framework, a multi-objective function is considered for optimal planning, including minimization of the expected total power loss, the total system voltage deviation, the total cost, and the total emissions, in addition to enhancing the expected total voltage stability. A novel efficient technique known as the Equilibrium Optimizer (EO) is actualized to appoint the ratings and locations of renewable-based distributed generators. The effectiveness of the proposed strategy is applied on an IEEE 69-bus network and a 94-bus practical distribution system situated in Portugal. The simulations verify the feasibility of the framework for optimal power planning. Additionally, the results show that the optimal integration of the photovoltaic and wind turbine generators using the proposed method leads to a reduction in the expected power losses, voltage deviations, cost, and emission rate and enhances the voltage stability by 60.95%, 37.09%, 2.91%, 70.66%, and 48.73%, respectively, in the 69-bus system, while in the 94-bus system these values are enhanced to be 48.38%, 39.73%, 57.06%, 76.42%, and 11.99%, respectively.

Design of fractional evolutionary processing for reactive power planning with FACTS devices

Reactive power dispatch is a vital problem in the operation, planning and control of power system for obtaining a fixed economic load expedition. An optimal dispatch reduces the grid congestion through the minimization of the active power loss. This strategy involves adjusting the transformer tap settings, generator voltages and reactive power sources, such as flexible alternating current transmission systems (FACTS). The optimal dispatch improves the system security, voltage profile, power transfer capability and overall network efficiency. In the present work, a fractional evolutionary approach achieves the desired objectives of reactive power planning by incorporating FACTS devices. Two compensation arrangements are possible: the shunt type compensation, through Static Var compensator (SVC) and the series compensation through the Thyristor controlled series compensator (TCSC). The fractional order Darwinian Particle Swarm Optimization (FO-DPSO) is implemented on the standard IEEE 30, IEEE 57 and IEEE 118 bus test systems. The power flow analysis is used for determining the location of TCSC, while the voltage collapse proximity indication (VCPI) method identifies the location of the SVC. The superiority of the FO-DPSO is demonstrated by comparing the results with those obtained by other techniques in terms of measure of central tendency, variation indices and time complexity.

Optimal reactive power dispatch using θ-social mimic optimization (θ-SMO)

The social mimic optimization algorithm (SMO) and its enhanced version (θ-SMO) is presented in the current study for the optimal dispatch problem of the reactive power (ORPD) with continuous and discrete control variables in the IEEE standard networks. The feasibleness and functioning of the θ-SMO and SMO algorithms are indicated for the IEEE 57-bus, and IEEE 118-bus standard networks. The outcomes of the simulation were compared, and it was shown that the optimization efficacy of these algorithms is higher than other rooted algorithms, such as optics in-spired optimization (OIO), the social spider algorithm (SSA) algorithm, and biogeography-based optimization (BBO). Results obtained for ORPD problem indicate better performance concerning the θ-SMO algorithm’s solution quality compared to original SMO algorithm and other algorithms.

A New Fractional Particle Swarm Optimization with Entropy Diversity Based Velocity for Reactive Power Planning

Optimal Reactive Power Dispatch (ORPD) is the vital concern of network operators in the planning and management of electrical systems to reduce the real and reactive losses of the transmission and distribution system in order to augment the overall efficiency of the electrical network. The principle objective of the ORPD problem is to explore the best setting of decision variables such as rating of the shunt capacitors, output voltage of the generators and tap setting of the transformers in order to diminish the line loss, and improve the voltage profile index (VPI) and operating cost minimization of standard electrical systems while keeping the variables within the allowable limits. This research study demonstrates a compelling transformative approach for resolving ORPD problems faced by the operators through exploiting the strength of the meta-heuristic optimization model based on a new fractional swarming strategy, namely fractional order (FO)-particle swarm optimization (PSO), with consideration of the entropy metric in the velocity update mechanism. To perceive ORPD for standard 30 and 57-bus networks, the complex nonlinear objective functions, including minimization of the system, VPI improvement and operating cost minimization, are constructed with emphasis on efficacy enhancement of the overall electrical system. Assessment of the results show that the proposed FO-PSO with entropy metric performs better than the other state of the art algorithms by means of improvement in VPI, operating cost and line loss minimization. The statistical outcomes in terms of quantile-quantile illustrations, probability plots, cumulative distribution function, box plots, histograms and minimum fitness evaluation in a set of autonomous trials validate the capability of the proposed optimization scheme and exhibit sufficiency and also vigor in resolving ORPD problems.

Solving the Optimal Reactive Power Dispatch Using Marine Predators Algorithm Considering the Uncertainties in Load and Wind-Solar Generation Systems

The optimal reactive power dispatch (ORPD) problem is an important issue to assign the most efficient and secure operating point of the electrical system. The ORPD became a strenuous task, especially with the high penetration of renewable energy resources due to the intermittent and stochastic nature of wind speed and solar irradiance. In this paper, the ORPD is solved using a new natural inspired algorithm called the marine predators’ algorithm (MPA) considering the uncertainties of the load demand and the output powers of wind and solar generation systems. The scenario-based method is applied to handle the uncertainties of the system by generating deterministic scenarios from the probability density functions of the system parameters. The proposed algorithm is applied to solve the ORPD of the IEEE-30 bus system to minimize the power loss and the system voltage devotions. The result verifies that the proposed method is an efficient method for solving the ORPD compared with the state-of-the-art techniques.

Solving the Manufacturing Cell Design Problem through an Autonomous Water Cycle Algorithm

Metaheuristics are multi-purpose problem solvers devoted to particularly tackle large instances of complex optimization problems. However, in spite of the relevance of metaheuristics in the optimization world, their proper design and implementation to reach optimal solutions is not a simple task. Metaheuristics require an initial parameter configuration, which is dramatically relevant for the efficient exploration and exploitation of the search space, and therefore to the effective finding of high-quality solutions. In this paper, the authors propose a variation of the water cycle inspired metaheuristic capable of automatically adjusting its parameter by using the autonomous search paradigm. The goal of our proposal is to explore and to exploit promising regions of the search space to rapidly converge to optimal solutions. To validate the proposal, we tested 160 instances of the manufacturing cell design problem, which is a relevant problem for the industry, whose objective is to minimize the number of movements and exchanges of parts between organizational elements called cells. As a result of the experimental analysis, the authors checked that the proposal performs similarly to the default approach, but without being specifically configured for solving the problem.

Finding Solutions for Optimal Reactive Power Dispatch Problem by a Novel Improved Antlion Optimization Algorithm

In this paper, a novel improved Antlion optimization algorithm (IALO) has been proposed for solving three different IEEE power systems of optimal reactive power dispatch (ORPD) problem. Such three power systems with a set of constraints in transmission power networks such as voltage limitation of all buses, limitations of tap of all transformers, maximum power transmission limitation of all conductors and limitations of all capacitor banks have given a big challenge for global optimal solution search ability of the proposed method. The proposed IALO method has been developed by modifying new solution generation technique of standard antlion optimization algorithm (ALO). By optimizing three single objective functions of systems with 30, 57 and 118 buses, the proposed method has been demonstrated to be more effective than ALO in terms of the most optimal solution search ability, solution search speed and search stabilization. In addition, the proposed method has also been compared to other existing methods and it has obtained better results than approximately all compared ones. Consequently, the proposed IALO method is deserving of a potential optimization tool for solving ORPD problem and other optimization problems in power system optimization fields.

A Novel Constraint Handling Approach for the Optimal Reactive Power Dispatch Problem

This paper presents an alternative constraint handling approach within a specialized genetic algorithm (SGA) for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a nonlinear single-objective optimization problem aiming at minimizing power losses while keeping network constraints. The proposed constraint handling approach is based on a product of sub-functions that represents permissible limits on system variables and that includes a specific goal on power loss reduction. The main advantage of this approach is the fact that it allows a straightforward verification of both feasibility and optimality. The SGA is examined and tested with the recommended constraint handling approach and the traditional penalization of deviations from feasible solutions. Several tests are run in the IEEE 30, 57, 118 and 300 bus test power systems. The results obtained with the proposed approach are compared to those offered by other metaheuristic techniques reported in the specialized literature. Simulation results indicate that the proposed genetic algorithm with the alternative constraint handling approach yields superior solutions when compared to other recently reported techniques.

Enhanced Chaotic Grey Wolf Optimizer for Real-World Optimization Problems

The gray wolf optimizer (GWO) is a new population-based optimizer that is inspired by the hunting procedure and leadership hierarchy in gray wolves. In this chapter, a new enhanced gray wolf optimizer (EGWO) is proposed for tackling several real-world optimization problems. In the EGWO algorithm, a new chaotic operation is embedded in GWO which helps search agents to chaotically move toward a randomly selected wolf. By this operator, the EGWO algorithm is capable of switching between chaotic and random exploration. In order to substantiate the efficiency of EGWO, 22 test cases from IEEE CEC 2011 on real-world problems are chosen. The performance of EGWO is compared with six standard optimizers. A statistical test, known as Wilcoxon rank-sum, is also conducted to prove the significance of the explored results. Moreover, the obtained results compared with those of six advanced algorithms from CEC 2011. The evaluations reveal that the proposed EGWO can obtain superior results compared to the well-known algorithms and its results are better than some advanced variants of optimizers.