Optimal Reactive Power Dispatch Using Improved Pseudo-gradient Search Particle Swarm 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.

ABSTRACTIn the present work, symbiotic organism search (SOS) algorithm is applied for the solution of optimal reactive power dispatch (ORPD) problem of power system considering flexible AC transmission system (FACTS) devices. The proposed method is tested and examined on modified IEEE 30 bus test system with two types of FACTS devices namely thyristor-controlled series capacitor (TCSC) and thyristor-controlled phase shifter (TCPS), placed at some strategic locations. In this study, ORPD problem has been formulated as single objective, constrained optimization problem that aims to reduce active power loss or total absolute voltage deviation individually. The formulation for conventional OPRD problem is evaluated by considering the settings of control parameters and maintaining the constraints of the FACTS devices as an additional entity. The effectiveness of the proposed method is analysed and compared to the results offered by some other optimization methods. The outcomes of the present work prove the potential of the SOS algorithm in solving ORPD problems of the power system incorporating FACTS devices.

In this paper one of the reliable and effective optimization algorithms called “artificial bee colony” algorithm (ABC) for solving the optimal reactive power dispatch (ORPD) problem with the discrete and continuous control variables in an electric power system is presented. In this work ABC algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the number of capacitors banks to be switched, for optimal reactive power dispatch. The original ABC algorithm designed for the continuous nature of optimization problems, cannot be used for discrete cases; but the real ORPD problem has two different nature types of control variables (discrete and continuous), for this reasons a simple rounding operator is included in the main steps of original ABC algorithm to ensure the discretization process. Then, the feasibility and performance of the proposed algorithm are verified by the serial simulations on the IEEE 14-bus, IEEE 30-bus and IEEE 57-bus power systems. The numerical results are compared to those yielded by the other recently published evolutionary optimization algorithms in the literature. This comparison shows that the ABC algorithm is superior to the other mentioned algorithms and can be efficiently used for solving the discrete ORPD problem.

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

A decentralized approach for optimal reactive power dispatch using a Lagrangian decomposition method

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.

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.

Optimal reactive power dispatch (ORPD) intended for reducing the real power losses of the transmission scheme remains one of the supreme concerns for the research community to explore the competence of power schemes. Numerous systems have been deliberate to increase the performance of the optimization method in tunning the operational variables as well as explored through estimating the final results. The research offering a novel approach based on the entropy evolution technique implemented into Fractional PSOGSA algorithm to solve the optimal reactive power dispatch problem. To alleviate the drawback of PSOGSA the fractional and entropy techniques are implemented into the algorithm which enhanced memory effect, stability and robustness of the algorithm. The novel design of FPSOGSA-Entropy is further tested for the optimal reactive power dispatch problems on IEEE-30 and IEEE-57 bus standards to find the two objective functions; minimization of power line losses and voltage deviation. The superior performance of the proposed FPSOGSA-Entropy is further verified with the results of simple FPSOGSA for both single and multiple runs through comparative analysis study with state of art counterparts for each scenario of optimal reactive power dispatch problems.

This article investigates multi‐objective reactive power management while accounting for real‐time generation and load uncertainties. The primary goal of this research is to investigate the effects of uncertainties on reactive power dispatch, while taking into account multiple objectives at the same time and keeping operational constraints in mind. The optimal reactive power dispatch (ORPD) problem is solved using an “indicator‐based evolutionary technique” called “ISDE+,” which considers two different goal functions: real power loss minimization and voltage deviation minimization. IEEE 30 and IEEE 57 bus test systems are taken into account in the simulation. ISDE+ generates a set of non‐dominated optimal solutions, from which the best compromise solution is extracted using the “S” shaped fuzzy membership function. A hyper‐volume indicator is used to evaluate the optimizer's performance. In addition, this work proposes a stochastic ORPD problem for tri‐objective optimization with load demand and wind power uncertainty. The Weibull probability distribution function was used to model stochastic wind power using real‐time wind speed data gathered from the National Institute of Wind Energy. Furthermore, to obtain a generalized wind speed set, a scenario‐based reduction technique based on the Python programming language is developed. The outcomes of simulations in deterministic and stochastic instances were studied and compared using ISDE+, which outperforms other methods documented in the literature.

This study addresses a shuffled frog leaping algorithm for solving the multi-objective reactive power dispatch problem in a power system. Optimal Reactive Power Dispatch (ORPD) is formulated as a nonlinear, multi-modal and mixed-variable problem. The intended technique is based on the minimization of the real power loss, minimization of voltage deviation and maximization of the voltage stability margin. Generator voltages, capacitor banks and tap positions of tap changing transformers are used as optimization variables of this problem. A memetic meta-heuristic named as shuffled frog-leaping algorithm is intended to solve multi-objective optimal reactive power dispatch problems considering voltage stability margin and voltage deviation. The Shuffled Frog-Leaping Algorithm (SFLA) is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The most important benefit of this algorithm is higher speed of convergence to a better solution. The intended method is applied to ORPD problem on IEEE 57 bus power systems and compared with two versions of differential evolutionary algorithm. The simulation results show the effectiveness of the intended method.

This paper presents an algorithm to solve the multi-objective Optimal Reactive Power Dispatch (ORPD) problem in an unbalanced bus system. Unlike the traditional ORPD problem, loadability maximization, voltage profile enhancement, loss minimization, and ATC enhancement are achieved under unbalanced conditions. Here, ORPD is effectuated through determining the optimal location and size of the UPFC using a hybrid version of GA and FF. Experimental results on the benchmark IEEE test bus systems demonstrate the ORPD performance of the proposed algorithm over the traditional algorithms, under unbalanced conditions. Moreover, the proposed algorithm is proved for its performance in maintaining a better trade-off among multiple objectives, even under overloading conditions. The analysis also includes an investigation on the sensitivity of the algorithm against the overloading conditions of the bus system. Finally, the experimental results confirm that the proposed algorithm is superior to the conventional algorithms like GA, PSO, a hybrid version of GA-PSO, and the traditional FF algorithm.Abbreviations: ATC: Available Transfer Capability; CMAES: Covariance Matrix-Adapted Evolutionary Strategy; CPF: Continuation Power Flow; DE: Differential Evolution; FACTS: Flexible AC Transmission System; FF: Firefly Algorithm; GA: Genetic Algorithm; GSA: Gravitational Search Algorithm; KHA: Krill Herd Algorithm; LSI: Loss Sensitivity Index; NSGA-II: Non-Dominated Sorting Genetic Algorithm-II; OKHA: Oppositional Krill Herd Algorithms; ORPD: Optimal Reactive Power Dispatch; PSO: Particle Swarm Optimization; UPFC: Unified Power Flow Controller; VDI: Voltage Deviation Index

The Optimal Reactive Power Dispatch (ORPD) is non-linear problem and is a very effective tool in modern power system for designing a more secure and economic system. It has control variables, which are a combination of continuous and discrete and helps in obtaining the most optimized result satisfying all the equality and inequality constraints. The results obtained not only reduces the real power losses of the system but also helps in restricting the voltage deviation to a much greater extent and thus maintaining the stability of the entire system. In this paper, the ORPD problem is solved as a single objective problem with two different objectives like minimization of real power loss and minimization of voltage deviation. Here, four different variants of PSO are used to solve the problem and the results are compared. The algorithms considered in this paper are tested on IEEE 30 bus and IEEE 57 bus system.

Voltage stability enhancement is obtained by adjusting the control variables to nearer optimal solutions for the selected objective function. This paper presents the biological swarm behaviour of a bird flocking or fish schooling for solving the optimal reactive power dispatch (ORPD) problem using PSO algorithm. The main idea of this paper is to minimize the sum of the square of voltage deviations at load buses using fast decoupled load flow (FDLF) method and sensitivity parameters relating control and dependent variables. The on-load tap changing transformers (OLTC), Generator exciters, Static VAR Compensators (SVC) are used as control variables for improvement of system parameters like voltage deviation (V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ), L-index and real power loss. The effectiveness of the proposed method is demonstrated on IEEE New England 39-bus power system for near optimal solutions. The performance of the proposed method is compared with conventional optimization technique and presented for illustration purpose.

This paper presents a new solution method for optimal reactive power dispatch (ORPD) problem based on principal component analysis (PCA). In heavily loaded power system, security, reliability and economy are some unavoidable concerns. Therefore, ORPD becomes an essential tool to achieve these goals. It is a highly non-linear constrained optimisation problem. A PCA-based real coded genetic algorithm (PCA-RCGA) is proposed in this paper to deal with such type of problem. In PCA-RCGA, PCA theory is applied in mutation operator to enhance convergence of conventional genetic algorithm by guiding the direction of stochastic search to reach near the global optimal solution effectively. The proposed PCA-RCGA is tested on standard IEEE-30 bus and IEEE-118 bus system for ORPD problem. The simulation results for both cases are compared with various optimisation techniques applied to ORPD available in literature.

This paper deals with solving optimal power flow problems using one of the new meta-heuristic optimizations inspired by the behavior of grey wolves (Canis lupus). Optimal power flow (OPF) faced several challenged such as increased of fuel cost of generation units, increased the real power losses at transmission lines, increased of voltage deviation of each bus, and uncontrolled of voltage stability for whole system. Therefore, in this paper, the objective functions that have been optimized include generation cost (GC), power loss (PL), voltage deviation (VD), and voltage stability index (VSI). The GWO algorithm has been applied on the Iraqi Super Grid High Voltage 400 kV (ISGHV 400 kV) to set the optimal control variables. The results obtained by this algorithm have been compared with the results obtained by the initial study case to determine the percentage of reduction rate. This comparison proved the efficiency and superiority of the GWO algorithm when applied to the power system networks. The percentages of reduction rates compared with the initial case are 45.08%, 27.28%, 70.64%, and 15.40% of generation cost (GC), power loss (PL), voltage deviation (VD), and voltage stability index (VSI), respectively.KeywordsOptimal Power Flow (OPF)Grey Wolf Optimizer (GWO)Iraqi Super Grid High Voltage (ISGHV) 400 kV