Multiobjective Optimal Reactive Power Dispatch Considering Voltage Stability Using Shuffled Frog Leaping Algorithm

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 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.

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.

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the 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.

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.

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

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 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 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.

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.

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.

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.