Reactive Power Optimization in Wind Power Plants Using Cuckoo Search Algorithm

In this article, an enhanced arithmetic optimization algorithm (EAOA) is utilized to resolve the optimal reactive power dispatch problem (ORPD) of power plants, which is a non‐linear, non‐smooth, complex optimization problem. Typically, it is formulated as a constrained optimal power flow problem. This paper utilizes the gamma distribution to generate initial random solutions, which improves the accuracy of the arithmetic optimization algorithm (AOA). The original mode of deviation of math optimizer accelerated (MOA) is replaced with the improved pattern of change in the prey's energy in Harris Hawk Optimization (HHO), which creates a superior balance between the exploration and exploitation of AOA. This paper implements logarithmic and exponential operators in place of division and multiplication operators, which improves the exploration ability of AOA and also utilizes the gamma distribution in the generation of random numbers, which are essential for the selection of operators in both search phase which enlarges the search area and improves the global optimum solution. A parametric analysis is performed on 10 benchmark functions for nine possible values before selecting the algorithm's initial parameters. A comparative statistical analysis along with Friedman's test is carried out on 23 benchmark functions to test the overall performance as compared to Sine‐Cosine Algorithm (SCA), Swarm‐Salp Algorithm, Grey Wolf Optimization (GWO), and basic Arithmetic Optimization Algorithm (AOA). EAOA is applied to the IEEE 57 bus system for optimal reactive power control. EAOA reports a significant reduction in a power loss of 23.2 MW, which is 18.596% smaller than the system's base case power loss of 28.5 MW as compared to Artificial Bee Colony (ABC), Firefly Algorithm (FA), Bat‐inspired Algorithm (BAT), Cuckoo Search Algorithm (CSA), and Modified Ant Lion Algorithm (MALO) which reports a reduction in a power loss of 14.73%, 15.43%, 15.43%, 16.14%, and 16.14% respectively. EAOA reduces the TVD to 0.76 pu, compared to ABC, FA, BAT, CSA, and MALO, which minimizes the TVD to 0.84, 0.82, 0.88, 0.82, and 0.79, respectively. This proves that EAOA performs better in resolving ORCP problems regarding the quality of solutions and convergence. A detailed comparative statistical analysis of EAOA with CSA, BAT, and WOA (Whale Optimization Algorithm) is conducted in terms of Probability Distribution Functions (PDF) and Cumulative Distribution Functions (CDF), along with the Wilcoxson sign rank test, which proves that EAOA gives the solution with a higher degree of precision.

Reactive power optimization is a mixed integer nonlinear programming problem where metaheuristics techniques have proven suitable for providing optimal solutions. Optimal reactive power dispatch (ORPD) is a key instrument to achieve secure and economic operation of power systems. Due to complex characteristics of ORPD, heuristic optimization has become an effective solver. In this paper, swarm and evolutionary algorithm have been applied for reactive power optimization. A two-phase hybrid particle swarm optimization (PSO) approach is used to solve optimal reactive power dispatch (ORPD) problem has been presented in this paper. In this hybrid approach, PSO is used to explore the optimal region and direct search is used as local optimization technique for finer convergence. This paper also presents a particle swarm optimization for reactive power and voltage control considering voltage stability. The proposed method determines a control strategy with continuous and discrete control variables such as AVR operating values, OLTC tap positions, and the amount of reactive power compensation equipment. A novel heuristic optimization algorithm namely the Mean-Variance Mapping Optimization (MVMO) is proposed to handle the ORPD problem. The objective of the proposed PSO is to minimize the total support cost from generators and reactive compensators. It is achieved by maintaining the whole system power loss as minimum thereby reducing cost allocation.

Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms

This paper introduces a newly developed symbiotic organism search algorithm for deal with ORPD problem. The reactive power optimization problem is essential for suitable operation and regulation in power system network. It helps operators to control the voltage limits, to curtail the real power loss in transmission lines, enhances the strength of the electrical power system to withstand and counteract voltage collapse during load variations in an electrical power system. The symbiotic organism search algorithm is one of the assuring, latest developments in the tract of Meta heuristic algorithms. The texture — animated philosophy of symbiotic organism search algorithm resembles the interactive nature among organisms in feature. Organisms in the real cosmos infrequently live in isolation due to their dependence on other organisms for livelihood and longevity. This ORPD problem is formulated by generator output voltages (continuous variable), regulating transformers and switchable VAR devices (discrete variables). The proposed symbiotic organism search algorithm is realized for IEEE-14 bus and 30-bus systems. The improved result values are compared with Evolutionary programming, Differential evolutionary algorithm, dynamic particle swarm optimization, self-adaptive real coded genetic algorithm and modified Gaussian bare bones teaching learning based optimization.

Due to integration of large amount of renewable energy generators (REGs) to the power grid, implementation of reactive power support mechanisms as well as their optimal placement and operation are becoming a real challenge for the transmission/distribution system operators. Besides, because of the stochastic nature of renewable energy generation, reactive power planning and optimization in renewable rich power grids are an arduous task. In this paper, an optimal reactive power dispatch problem is formulated incorporating the reactive power support from the renewable energy generators. Two coordinated optimization algorithms (particle swarm optimization and pattern search algorithm) are combined to enhance the optimization performance. Finally, the IEEE 39 New England test bus system is modified and used to perform the optimization.

The Flexible alternating current transmission systems (FACTS) is considered one of the most developed technologies applied for enhancing the performance of system due to their ability of adjusting different parameters in the transmission systems such as the buses voltage, the transmission line impedance, the active and reactive powers flow in transmission lines. The static synchronous series compensator (SSSC) is an effective member of the FACTS which is connected in series with the transmission lines and it consists of a solid-state voltage source inverter coupled with a transformer which aims to control and secure the operation of the power system. The main function of SSSC is inserting a controllable voltage in series with the transmission line to control the active and reactive powers flow in transmission lines. Solving the optimal reactive power dispatch (ORPD) problem is nonlinear, non-convex and it becomes a complex problem with integration of the SSSC. The contributions of article include, 1) an efficient and reliable optimization algorithm is developed to solve the ORPD problem and identify the optimal location and ratings of the SSSC, 2) The proposed algorithm is based on modifying the salp swarm algorithm (SSSA) using Levy Flight Distribution and spiral movement of particles to enhance the searching capabilities of the SSA, 3) an efficient model of SSSC based on power injection approach is used for representation the SSSC in ORPD. The ORPD is solved with and without the SSSC controller to minimize power losses and voltage deviations as well as improve the voltage stability. The proposed algorithm for ORPD is tested on the standards IEEE 30-bus and 57-bus systems. The simulation results demonstrate that MSSA is more effective and superior for solving the ORPD compared with some other reported meta-heuristic techniques. Moreover, the system performance is enhanced considerably with optimal inclusion the SSSC.

This paper presents an algorithm for solving the multi-objective reactive power dispatch problem in a power system. Modal analysis of the system is used for static voltage stability assessment. Loss minimization and maximization of voltage stability margin are taken as the objectives. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. This paper introduces, an evolutionary algorithm based on the hybrid genetic algorithm (GA) and particle swarm optimization (PSO), denoted by HGAPSO is used to solve reactive power dispatch problem.

This paper proposes a transparent and reliable method between the suppliers and consumers for optimal reactive power pricing. The electric power suppliers compute the optimal reactive power using optimal reactive power dispatch problem by considering nodal voltage stability index ‘I’ as one of the constraints. The computed optimal reactive power of the generator is included in the reactive power pricing. The pricing method to the suppliers based on the opportunity cost method is presented and a detailed analysis using 62 bus Indian utility system has been carried out by considering diverse cases. In this proposed pricing method, the services of the cloud technology have been used to provide transparent pricing based on the demands of the consumers. The power demands at the consumers’ site is calculated without the human involvement using the Internet of Things and the same is uploaded in the cloud. In reactive power pricing, the system operator acts as a mediator between the suppliers and consumers. Based on the demand and availability of power, the system operator provides the cost for the service to the consumer through cloud.

Solving the Optimal Reactive Power Dispatch (ORPD) problem in power system is a vital task to capture the most secure and stable operation of reactive power resources. In this paper, the ORPD problem is solved using a new modified sine cosine algorithm (MSCA). Sine cosine algorithm (SCA) is a well-known population-based optimization technique. Despite the SCA is an effective algorithm, it may prone to stagnation and stuck in local minima for some cases. The modified sine cosine algorithm (MSCA) is based on Levy flight distribution with adaptive operators. This algorithm is developed to avoid the shortage of the conventional SCA and enhance its searching abilities. The considered objective functions are minimizing the power losses, improving the voltage profile and enhancing the stability of system. The proposed algorithm is applied to IEEE 30-bus system and the yielded results are compared with other well-known optimization algorithms. The simulation results demonstrate the superiority and efficiency of the MSCA for solving the ORPD compared to the other listed techniques in literature.

Secure and economical operation of distribution networks needs the management of reactive power resources. Optimal Reactive Power Dispatch (ORPD) optimally manages the reactive power scheduling of generators and distribution generations as well as the Reactive Power Compensation (RPC) devices. This paper investigates the effect of load models on the multi-objective ORPD problem in active distribution networks. Moreover, a modified Grey Wolf Optimizer (GWO), which is called in this paper as Civilized GWO (CGWO), is introduced to solve the ORPD problem. The proposed strategy including multi-objective function, various load models, DG’s reactive power, RPCs and the introduced CGWO, is tested on standard IEEE 33- and 69-bus distribution systems. The obtained results indicate the load models have significant impact on the cost function amount. Moreover, the performance of the proposed algorithm is evaluated using ten standard benchmark functions. The optimization results demonstrate the robustness of the introduced optimization algorithm and its ability in finding the better solutions compared to the Particle Swarm Optimization (PSO), Exchange Market Algorithm (EMA), and original GWO.

This paper proposes a novel fractional-order African vulture optimization algorithm (FO-AVOA) for solving the optimal reactive power dispatch (ORPD) problem. By integrating fractional calculus into the conventional AVOA framework, the proposed method enhances the exploration–exploitation balance, accelerates convergence, and improves solution robustness. The ORPD problem is formulated as a constrained optimization task with the objective of minimizing real power losses while satisfying generator voltage limits, transformer tap ratios, and reactive power compensator constraints. The general optimization capability of the FO-AVOA is verified using the CEC 2017, 2020, and 2022 benchmark functions. In addition, the method is applied to the IEEE 30-bus and IEEE 57-bus test systems. The results demonstrate significant power loss reductions of up to 15.888% and 24.39% for the IEEE 30-bus and IEEE 57-bus systems, respectively, compared with the conventional AVOA and other state-of-the-art optimization algorithms, along with strong robustness and stability across independent runs. These findings confirm the effectiveness of the FO-AVOA as a reliable optimization tool for modern power system applications.

This paper presents the solution of multi-objective based optimal reactive power dispatch (MO-ORPD) problem by optimizing the system power losses and voltage stability enhancement index (VSEI)/L-index objectives. ORPD problem is considered as an important issue from system security and operational point of view for optimal steady-state operation of power system. Here, single-objective based ORPD problem is solved using Crow Search Algorithm (CSA) and multi-objective based ORPD problem is solved using multi-objective CSA (MO-CSA). The CSA is considered as an efficient and robust algorithm which determines the global optimal solution for solving the non-linear and discontinuous objective functions. Two standard test systems, i.e., IEEE 30 and 57 bus systems are considered to show the effectiveness, suitability and robustness of CSA and MO-CSA for solving the ORPD problem.

Optimal reactive power dispatch (ORPD) is carried out to reduce losses, to improve the voltage profile and voltage stability in a power system. In recent years, several evolutionary computing based optimization techniques to solve optimal reactive power dispatch problem has been proposed. These techniques include genetic algorithm (GA), artificial bee colony (ABC), particle swarm optimization (PSO) and differential evolution (DE) etc. The ORPD problem has been solved as a single objective as well as multi-objective optimization problem using these techniques. This paper presents a brief literature review of the work carried out by the various researchers in this field by using evolutionary computing based techniques.

Maximum power point tracking (MPPT) control is one of the essential requirements in harnessing wind power of wind energy conversion systems (WECS). The more precise the maximum power point (MPP) is determined, the more optimal the WECS is operated. Amongst MPPT algorithms, a hill-climb search (HCS) algorithm is preferred because of its simplicity however it also has few drawbacks such as the difficulty of selecting an appropriate step size, the premature convergence phenomenon and the speed-efficiency trade-off. A cuckoo search (CS) algorithm is proposed in this paper for finding out a MPP of a WECS driven by a doubly-fed induction generator (DFIG) under various wind speeds which mostly overcomes the above disadvantages. Then, the DFIG-WECS is controlled to track the MPP. This ensures that the DFIG-WECS is always operated at MPPs regardless of various wind speeds. It is realized that the proposed CS algorithm is also a population-based algorithm inspired from the breeding behavior of cuckoos but it is quite simple, powerful and especially requires less parameters to define optimal solutions than a genetic algorithm (GA) and a particle swarm optimization (PSO) algorithm. Though numerical results, the CS algorithm shows its effectiveness in finding out MPPs in the DFIG-WECS. Furthermore, the obtained results using the CS algorithm are also compared with those using the HCS and PSO algorithms. The comparison demonstrates that the convergence value and speed of the CS algorithm are always better than those of the HCS and PSO algorithms in the MPPT application in the DFIG-WECS.

This study presents a modern version of the economic load dispatch (MELD) problem with the contribution of renewable energies and conventional energy, including wind, solar and thermal power plants. In the study, reduction of electricity generation cost is the first priority, while the use of multiple fuels in the thermal power plant is considered in addition to the consideration of all constraints of power plants. Two meta-heuristic algorithms, one conventional and one recently published, including Particle swarm optimization (PSO) and Equilibrium optimizer (EO), are applied to determine the optimal solutions for MELD. A power system with ten thermal power plants using multiple fossil fuels, one wind power plant, and three solar power plants is utilized to evaluate the performance of both PSO and EO. Unlike other previous studies, this paper considers the MELD problem with the change of load demands over one day with 24 periods as a real power system. In addition, the power generated by both wind and solar power plants varies at each period. The results obtained by applying the two algorithms indicate that EO is completely superior to PSO, and the solutions found by EO can satisfy all constraints. Particularly in Case 1 with different load demand values, EO achieves better total electricity production cost (TEGC) than PSO by 0.75%, 0.87%, 0.13%, and 0.45% for the loads of 2400 MW, 2500 MW, 2600 MW and 2700 MW. Moreover, EO also provides a faster response capability over PSO through the four subcases although EO and PSO are run by the same selection of control parameters. In Case 2, the high efficiency provided by EO is still maintained, though the scale of the considered problem has been substantially enlarged. Specifically, EO can save $51.2 compared to PSO for the minimum TEGC. The savings cost is equal to 0.33% for the whole schedule of 24 hours. With these results, EO is acknowledged as a favourable search method for dealing with the MELD problem. Besides, this study also points out the difference in performance between a modern meta-heuristic algorithm (EO) and the classical one (PSO). The modern metaheuristic algorithm with special structure is highly valuable for complicated problem as MELD.