Optimal Reactive Power Dispatch Using Modified Sine Cosine Algorithm

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.

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

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.

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.

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.

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

In this paper, a Hybrid Whale and Sine Cosine Optimization Algorithm (HWSCOA) is presented that solves the Optimal Reactive Power Dispatch (ORPD) problem effectively in a deregulated electricity market. The proposed hybrid approach allows combining the global search ability of the Whale Optimization Algorithm (WOA) with the local exploitation ability of the Sine Cosine Algorithm (SCA), which also overcomes the limitation of convergence of single metaheuristic methods. This technique is applied to the IEEE 30-bus test system to optimise essential objectives, i.e. minimising active power loss and voltage deviation under operational constraints. Compared to other strategies for optimisation, HWSCOA results in a 15.7% reduction of active power loss and an increase of voltage stability of 9.4%, thereby confirming its superiority in the accuracy, convergence rate, and robustness. The novelty of this study is the integration of hybrid optimisation in deregulated market systems, where reactive power management is adaptive and cost-effective. The HWSCOA market-based operating approach also improves the reliability and economic efficiency of the system. This study introduced HWSCOA as a powerful optimisation framework for a contemporary power system with technical and economic dimensions of ORPD. It is thus very helpful as one step toward sustainable and efficient grid operation.

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.

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 paper presents a new hybrid intelligent algorithm for assessing and enhancing voltage security. The problem is decomposed into two stages. Firstly, the security of current operating point is assessed by learning vector quantization (LVQ) network according to the pre-specified criterion. Throughout the paper, continuation power flow (CPF) is adopted as a tool for defining voltage security margin (VSM). If an insecure state is indicated by the LVQ, the power system operator is given the suggestion for appropriate control settings so as to maintain the specified security level. In the second stage, the optimal reactive power dispatch (ORPD) problem is formulated and VSM is considered as an additional constraint. To include VSM determined by CPF along the optimization process, feed-forward neural network (FFNN) is trained to learn and perform similarly to CPF to relieve the intensive computing requirement. Ant colony optimization (ACO) is applied to handle the VSM constrained ORPD problem. The proposed method was tested on IEEE 30-bus system and successful results were obtained.

The power system is a complex network which is expected to operate with consumption of minimal resources giving the maximum security and reliability. The optimal power flow (OPF) problem is an important tool to help the operator to achieve these goals by providing the optimal setting of all control variables. Due to its significant influence on security and economic operation of power systems, one of the OPF problems namely optimal reactive power dispatch (ORPD), has received an ever-increasing interest from electric utilities. This paper proposes a recent nature inspired algorithm called moth-flame optimizer (MFO) to solve the ORPD problem. MFO is utilized to find the best combination of control variables such as the real power generation to be generated, generator voltages, tap changing transformers' ratios and the size of reactive power compensation devices so that the total minimum loss in the network can be obtained. The effectiveness of MFO is tested on IEEE-30 bus system with 25 control variables and the comparison with other recent algorithms such as grey wolf optimizer (GWO), ant-lion optimizer (ALO) and multi-verse optimizer (MVO) also will be presented in this paper.