Solving the Optimal Reactive Power Dispatch Problem Based on Moth-Flame Optimizer for Power System Operation and Planning

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.

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.

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

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.

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

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.

Reactive power planning problem is the key to secure and economic operation of power systems. Optimal management of existing reactive sources leads to loss minimization and economic performance of the system. Because of the nonlinear inter-relation between the physical parameters of the electric grid, this problem is a highly nonlinear and nonconvex constrained optimization problem. The application of semidefinite programming (SDP) to power system problems has recently gained considerable research attention. A recent SDP formulation uses a convex relaxation to the nonconvex optimal power flow problem under some technical conditions. This paper proposes a novel equivalent convex optimization formulation for the optimal reactive power dispatch (ORPD) problem and presents a new framework for finding the global optimum. Numerical results for the IEEE 30-bus and 118-bus test systems show that the proposed scheme obtains the optimum operation point and outperforms various state-of-the-art methods significantly.

This article proposes an improved pseudo-gradient search-particle swarm optimization (IPG-PSO) approach for solving the optimal reactive power dispatch (ORPD) problem. This ORPD problem is to determine optimal control variables, such as generator bus voltages, settings of shunt VAR compensators, and tap settings of on-load tap change (OLTC) transformers, for minimizing the real power loss, voltage deviation, and voltage stability index satisfying power balance equations and generator and network operating limit constraints. The proposed method is an improved PSO using a linearly decreasing chaotic inertia weight factor and guided by a pseudo-gradient search, which determines an appropriate direction of particles toward a global optimal solution. The proposed IPG-PSO method is used to minimize three different single-objective functions, including real power loss, voltage deviation, and voltage stability index. Test results on the IEEE 30-bus and 118-bus systems indicate that the proposed IPG-PSO method renders a higher solution quality and faster computing time than other methods. Accordingly, the proposed IPG-PSO for solving ORPD problem is potentially viable for online implementation.

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.

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.

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.

This paper introduces a self adaptive differential evolution (SADE) and self-tuning Hybrid differential Evolution (HDE) methods for dealing with optimal reactive power dispatch aiming at power loss reduction. The optimum reactive power dispatch of power systems is to allocate reactive power control variables so that the objective function composed of power losses is minimized and the prescribed voltage limits are satisfied. The proposed method determines the optimum settings of reactive power control variables such as, generator excitation, tap changing transformers, and shunt compensation that reduces the power loss, while maintaining the voltage stability. IEEE 14-bus test system from the literature is used to exemplify the performance of the proposed methods. Numerical results show that the proposed methods are better methods than those reported in the literature.

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 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.

Flexible AC transmission systems (FACTS) and optimal power-flow (OPF) solutions play an important role in solving power operation problems. The volatile nature of the power generation profiles from renewable energy sources, solar and wind systems, and determining the optimal locations and sizes of FACTS devices increase the complexity of the OPF problems in modern power network models, such as transmission power loss, power generation operation cost and voltage deviation, as a highly nonlinear-nonconvex optimization problem. Therefore, this article introduces and employs four new independent, reliable and efficient optimization algorithms inspired by nature and biological nature, namely: Slime Mould Algorithm (SMA), Artificial Ecosystem-based Optimization (AEO), Marine Predators Algorithm (MPA) and Jellyfish Search (JS), for solving both multi- and single-OPF objective problems for a power network incorporating FACTS and stochastic renewable energy sources. The proposed new metaheuristic optimization techniques are compared to the common and available alternatives in the literature, Particle Swarm Optimization (PSO), Moth Flame Optimization (MFO) and Grey Wolf Optimizer (GWO), using IEEE 30-bus test system. To consider and address the challenges of the OPF in modern power network models, the proposed optimization techniques tested under different operation cases such as an increasing in the load, with and without FCTAS and renewable energy sources, different renewable energy sources locations on the network. The result showed that the MPA, SMA, JS and AEO algorithms are more effective solvers for the OPF problems cases compared to the PSO, GWO and MFO algorithms. For example, the AEO obtained 0.0844 p.u. in case of minimizing the voltage deviation compared to 0.1155 p.u. for PSO, which means that the AEO algorithm improved the voltage deviation term by 27% compared to the PSO algorithm.