Multi-objective Optimal Reactive Power Research Articles

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

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.

Multi objective optimal reactive power dispatch for enrichment of power system behavior using modified ant lion optimizer

Multi objective optimal reactive power dispatch for enrichment of power system behavior using modified ant lion optimizer

A Multiobjective Artificial-Hummingbird-Algorithm-Based Framework for Optimal Reactive Power Dispatch Considering Renewable Energy Sources

This paper proposes a new artificial hummingbird algorithm (AHA)-based framework to investigate the optimal reactive power dispatch (ORPD) problem which is a critical problem in the capacity of power systems. This paper aims to improve the performance of power systems by minimizing two distinct objective functions namely active power loss in the transmission network and total voltage deviation at the load buses subjected to various constraints within multiobjective framework. The proposed AHA-based framework maps the inherent flight and foraging capabilities exhibited by hummingbirds in nature to determine the best settings for the control variables (i.e., voltages at generation buses, the tap positions of on-load tap-changing transformers (OLTCs) and the size of switchable shunt VAR compensators) to minimize the overall objective functions. A multiobjective optimal reactive power dispatch framework (MO-ORPD) considering renewable energy sources (RES) and load uncertainties is also proposed to minimize the individual objectives simultaneously. The competency and robustness of the proposed AHA-based framework is validated and tested on IEEE 14 bus and IEEE 39 bus test systems to solve the ORPD problem. Eventually, the results are compared with other well-known optimization techniques in the literature. Box plots and statistical tests using SPSS are performed and validated to justify the effectiveness of the proposed framework.

A New Self-Adaptive Teaching–Learning-Based Optimization with Different Distributions for Optimal Reactive Power Control in Power Networks

Teaching–learning-based optimization has the disadvantages of weak population diversity and the tendency to fall into local optima, especially for multimodal and high-dimensional problems such as the optimal reactive power dispatch problem. To overcome these shortcomings, first, in this study, a new enhanced TLBO is proposed through novel and effective θ-self-adaptive teaching and learning to optimize voltage and active loss management in power networks, which is called the optimal reactive power control problem with continuous and discontinuous control variables. Voltage and active loss management in any energy network can be optimized by finding the optimal control parameters, including generator voltage, shunt power compensators, and the tap positions of tap changers, among others. As a result, an efficient and powerful optimization algorithm is required to handle this challenging situation. The proposed algorithms utilized in this research were improved by introducing new mutation operators for multi-objective optimal reactive power control in popular standard IEEE 30-bus and IEEE 57-bus networks. The numerical simulation data reveal potential high-quality solutions with better performance and accuracy using the proposed optimization algorithms in comparison with the basic teaching–learning-based optimization algorithm and previously reported results.

Solving Single- and Multi-Objective Optimal Reactive Power Dispatch Problems Using an Improved Salp Swarm Algorithm

The optimal reactive power dispatch (ORPD) problem represents a fundamental concern in the efficient and reliable operation of power systems, based on the proper coordination of numerous devices. Therefore, the ORPD calculation is an elaborate nonlinear optimization problem that requires highly performing computational algorithms to identify the optimal solution. In this paper, the potential of metaheuristic methods is explored for solving complex optimization problems specific to power systems. In this regard, an improved salp swarm algorithm is proposed to solve the ORPD problem for the IEEE-14 and IEEE-30 bus systems, by approaching the reactive power planning as both a single- and a multi- objective problem and aiming at minimizing the real power losses and the bus voltage deviations. Multiple comparison studies are conducted based on the obtained results to assess the proposed approach performance with respect to other state-of-the-art techniques. In all cases, the results demonstrate the potential of the developed method and reflect its effectiveness in solving challenging problems.

Comparison of Algorithms to Solve Multi-objective Optimal Reactive Power Dispatch Problems in Power Systems with Nonlinear Models and a Mixture of Discrete and Continuous Variables

Optimal reactive power dispatch (ORPD) is a way to improve power system performance. Determination of the optimal value of the control variable can reduce the objective function to be achieved. The optimization of the two objective functions simultaneously is called multi-objective ORPD (MORPD). This research has a major contribution in proposing and utilizing original ideas from new algorithms and new ideas from the old algorithm to solve more complex variables and challenging ORPD problems. The ORPD problem is formulated as a nonlinear model with variables consisting of continuous and discrete. The proposed multi-objective algorithm is time-varying particle optimization (MOTVPSO), ant lion objective (MOALO), dragonfly algorithm (MODA), grey wolf optimizer (MOGWO), and multi-objective multi-verse optimization (MOMVO). To measure the effectiveness of those algorithms, testing is performed on the IEEE 57-bus. The simulation results show that the MOTVPSO algorithm can contribute more dominantly from the statistical tests conducted compared to previous studies and all four algorithms in this work to minimize real power loss. Whereas the MOMVO has an advantage in computational time efficiency.

RETRACTED: Pareto-based allocations of multi-type flexible AC transmission system devices for optimal reactive power dispatch using Kinetic Gas Molecule Optimization algorithm

Optimal reactive power dispatch is one of the key factors to attain cost-effective and stable functioning of power system. It is a complicated non-linear optimization issue with a combination of discrete and continuous control variables. Due to this complex feature of optimal reactive power dispatch, optimization technique has become an efficient method to solve this problem. In this work, Kinetic Gas Molecule Optimization algorithm with Pareto optimality is proposed for solving multi-objective optimal reactive power dispatch problem. The presentation of Kinetic Gas Molecule Optimization is improved by computing inertia weight and acceleration coefficients dynamically rather than a fixed value. Because of this reason, the searching capability of the particles in each iteration is improved. However, to improve the power system performance in optimal reactive power dispatch scenario, additional flexible AC transmission system devices like static VAR compensator, thyristor-controlled series compensator, and unified power flow controller are introduced to provide stable results when compared to conventional output because flexible AC transmission system devices are capable of controlling the flow of real power and reactive power. These details are implemented and tested on IEEE 30-bus test system with various objectives. The performance of proposed method is validated from MATLAB, which shows the value of power loss as 4.3583 and voltage deviation as 0.26499 with cost of US$469.6417 per MVAR, which shows considerably superior results when compared with implemented particle swarm optimization results. The proposed method provides an efficient result for solving multi-objective optimal reactive power dispatch issues.

Multi-Objective Optimal Reactive Power Dispatch of Power Systems by Combining Classification-Based Multi-Objective Evolutionary Algorithm and Integrated Decision Making

For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming to minimize active power loss and voltage deviation is formulated. And then the two-step approach integrating decision-making into optimization is proposed to solve the model. Specifically speaking, the first step aims to seek the Pareto optimal solutions (POSs) with good distribution by using a multi-objective optimization (MOO) algorithm named classification and Pareto domination based multi-objective evolutionary algorithm (CPSMOEA). Furthermore, the reference Pareto-optimal front is generated to validate the Pareto front obtained using CPSMOEA; in the second step, integrated decision-making by combining fuzzy c-means algorithm (FCM) with grey relation projection method (GRP) aims to extract the best compromise solutions which reflect the preferences of decision-makers from the POSs. Based on the test results on the IEEE 30-bus and IEEE 118-bus test systems, it is demonstrated that the proposed approach not only manages to address the MORPD issue but also outperforms other commonly-used MOO algorithms including multi-objective particle swarm optimization (MOPSO), preference-inspired coevolutionary algorithm (PICEAg) and the third evolution step of generalized differential evolution (GDE3).

Exploring Innovative Design Principles using Innovization in Multi- Objective Optimal Reactive Power Dispatch Problem

Recently, researchers in the field of Evolutionary Multi-Objective Optimization give a systematic approach for exploring innovative design principles in a conflicting multi-objective optimization problem by analyzing pareto optimal solution using either manual or automated approach. They call it “Innovization” and defined as: “innovation through optimization”. This paper applies manual innovization to multi-objective Optimal Reactive Power Dispatch Problem using Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) as multi-objective optimization algorithm and manually searches for all possible innovative design principles by analyzing multiple pareto optimal solutions. Standard IEEE 30 bus test system is considered for the current work. Simulation results reveal number of innovative design principles. Innovative design principles includes function approximation of relationship between conflicting objectives, characteristics of decision variable with respect to different objectives and actual range of decision variables. Simulation results clearly show much faster convergence when decision variables were obtained using innovative design principles for specified desired objectives as compared to normal case. Results also show some decision variables can be eliminated by setting it to a fixed value, which leads to simplification of optimization problem as the values of these variables remains constant with respect to the values of objective function.

Single and Multiobjective Optimal Reactive Power Dispatch Based on Hybrid Artificial Physics–Particle Swarm Optimization

The optimal reactive power dispatch (ORPD) problem represents a noncontinuous, nonlinear, highly constrained optimization problem that has recently attracted wide research investigation. This paper presents a new hybridization technique for solving the ORPD problem based on the integration of particle swarm optimization (PSO) with artificial physics optimization (APO). This hybridized algorithm is tested and verified on the IEEE 30, IEEE 57, and IEEE 118 bus test systems to solve both single and multiobjective ORPD problems, considering three main aspects. These aspects include active power loss minimization, voltage deviation minimization, and voltage stability improvement. The results prove that the algorithm is effective and displays great consistency and robustness in solving both the single and multiobjective functions while improving the convergence performance of the PSO. It also shows superiority when compared with results obtained from previously reported literature for solving the ORPD problem.

Multi-objective ant lion optimization algorithm to solve large-scale multi-objective optimal reactive power dispatch problem

PurposeIn the vast majority of published papers, the optimal reactive power dispatch (ORPD) problem is dealt as a single-objective optimization; however, optimization with a single objective is insufficient to achieve better operation performance of power systems. Multi-objective ORPD (MOORPD) aims to minimize simultaneously either the active power losses and voltage stability index, or the active power losses and the voltage deviation. The purpose of this paper is to propose multi-objective ant lion optimization (MOALO) algorithm to solve multi-objective ORPD problem considering large-scale power system in an effort to achieve a good performance with stable and secure operation of electric power systems.Design/methodology/approachA MOALO algorithm is presented and applied to solve the MOORPD problem. Fuzzy set theory was implemented to identify the best compromise solution from the set of the non-dominated solutions. A comparison with enhanced version of multi-objective particle swarm optimization (MOEPSO) algorithm and original (MOPSO) algorithm confirms the solutions. An in-depth analysis on the findings was conducted and the feasibility of solutions were fully verified and discussed.FindingsThree test systems – the IEEE 30-bus, IEEE 57-bus and large-scale IEEE 300-bus – were used to examine the efficiency of the proposed algorithm. The findings obtained amply confirmed the superiority of the proposed approach over the multi-objective enhanced PSO and basic version of MOPSO. In addition to that, the algorithm is benefitted from good distributions of the non-dominated solutions and also guarantees the feasibility of solutions.Originality/valueThe proposed algorithm is applied to solve three versions of ORPD problem, active power losses, voltage deviation and voltage stability index, considering large -scale power system IEEE 300 bus.

Stochastic multi-objective optimal energy and reactive power dispatch considering cost, loading margin and coordinated reactive power reserve management

In the recent years, modern wind farms (WF) are being increasingly integrated in the power systems. Thanks to the capability curve of doubly-fed induction generator (DFIG) wind turbines, these modern WFs are able to separately supply active and reactive powers. Accordingly, by increasing the penetration of this kind of sources, both voltage stability and reactive power reserve (RPR) management of power system can be affected. This issue makes it important to propose a new methodology for optimal energy and reactive power dispatch in a system with integrated modern WFs in order to effectively take into consideration the capabilities of modern WFs in different aspects of power system operation. Under this perspective, this paper proposes a stochastic multi-objective optimal dispatch (SMO-OD) problem in the presence of modern WFs to make a techno-economic framework for the system operators (SOs). The proposed SMO-OD problem aims at minimizing expected payments of energy and reactive power markets, and maximizing expected RPR and loading margin (LM) in the presence of wind power generation uncertainty. This paper also contributes to the relevant literature by formulating a model which determines the RPR of modern WFs to be included in the management of total RPR of the power system. Also, a coordinated RPR (CRPR) scheme is proposed by using this model. The proposed model benefits from a detailed reactive power output model of the DFIG wind turbines in order to handle real-world power system operation. Two studies are considered in the proposed SMO-OD problem: (i) SMO-OD with uncoordinated RPR provision (SMO-OD-URPR), and (ii) SMO-OD with the CRPR provision (SMO-OD-CRPR). The proposed SMO-OD problem is applied to the IEEE 30-bus test system. Simulation results show that using the proposed model, a proper trade-off is made between technical and economic aspects of power system operation, and considerable LM and RPR are provided. In the proposed SMO-OD-CRPR problem, the value of expected RPR increases compared to SMO-OD-URPR problem, and the DFIG-based WF has more expected RPR to inject to grid under contingency or sudden increased load. Moreover, by increasing the wind penetration level, not only does the value of expected payments of energy and reactive power markets reduce, but also the value of expected LM and RPR increases.

Optimal Localization and Sizing of UPFC to Solve the Reactive Power Dispatch Problem Under Unbalanced Conditions

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

Optimal reactive power dispatch problem using a two-archive multi-objective grey wolf optimizer

Abstract In this paper, a novel two-archive Multi-Objective Grey Wolf Optimizer (2ArchMGWO) is proposed for solving Multi-Objective Optimal Reactive Power Dispatch (MORPD) problems. The optimizer has been improved from its original Multi-Objective Grey Wolf Optimizer (MGWO) by modifying the reproduction operator and adding the 2-archive concept to the algorithm. It is then implemented on solving MORPD with objective functions being active power loss minimization and voltage profile improvement (voltage deviation minimization). The generator bus voltages, tap setting transformers and shunt reactive power sources or flexible alternating current transmission systems are set as design variables. The proposed algorithm along with other existing multiobjective optimizers are applied to solve three test problems with the standard IEEE 30-bus, IEEE 57-bus, and the IEEE 118-bus power systems. The optimum results obtained from the various optimizers performance are compared based on the hypervolume indicator and they reveal that 2ArchMGWO is clearly superior to the others.

Optimal allocation of SVC and TCSC using quasi-oppositional chemical reaction optimization for solving multi-objective ORPD problem

This paper presents an efficient quasi-oppositional chemical reaction optimization (QOCRO) technique to find the feasible optimal solution of the multi objective optimal reactive power dispatch (RPD) problem with flexible AC transmission system (FACTS) device. The quasi-oppositional based learning (QOBL) is incorporated in conventional chemical reaction optimization (CRO), to improve the solution quality and the convergence speed. To check the superiority of the proposed method, it is applied on IEEE 14-bus and 30-bus systems and the simulation results of the proposed approach are compared to those reported in the literature. The computational results reveal that the proposed algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms.

Multi-objective optimal reactive power dispatch using multi-objective differential evolution

This paper presents multi-objective differential evolution (MODE) to solve multi-objective optimal reactive power dispatch (MORPD) problem by minimizing active power transmission loss and voltage deviation and maximizing voltage stability while varying control variables such as generator terminal voltages, transformer taps and reactive power output of shunt VAR compensators. MODE has been tested on IEEE 30-bus, 57-bus and 118-bus systems. Numerical results for these three test systems have been compared with those acquired from strength pareto evolutionary algorithm 2 (SPEA 2).

A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem

Abstract Due to nonlinear and discrete variables and constraints, optimal reactive power dispatch (ORPD) is a complex optimization problem in power systems. In this paper, the purpose is to solve multi objective ORPD (MO-ORPD) problem considering bus voltage limits, the limits of branches power flow, generators voltages, transformers tap changers and the amount of compensation on weak buses. The objectives of this paper are real power losses and voltage deviations from their corresponding nominal values, which are conflicting objectives. Because of the stochastic behavior of loads, the MO-ORPD problem requires a probabilistic approach. Hence, in this paper, a two-point estimate method (TPEM) is proposed to model the load uncertainty in MO-ORPD problem. Moreover, the proposed method is compared with some other methods such as deterministic approaches and Monte Carlo simulations (MCS). The obtained results approve the efficiency of the proposed methodology. The proposed models are implemented and solved using GAMS optimization package and verified using IEEE 14-bus and IEEE 30-bus standard test systems.

Multi-objective optimal reactive power dispatch to maximize power system social welfare in the presence of generalized unified power flow controller

Abstract In this paper a novel non-linear optimization problem is formulated to maximize the social welfare in restructured environment with generalized unified power flow controller (GUPFC). This paper presents a methodology to optimally allocate the reactive power by minimizing voltage deviation at load buses and total transmission power losses so as to maximize the social welfare. The conventional active power generation cost function is modified by combining costs of reactive power generated by the generators, shunt capacitors and total power losses to it. The formulated objectives are optimized individually and simultaneously as multi-objective optimization problem, while satisfying equality, in-equality, practical and device operational constraints. A new optimization method, based on two stage initialization and random distribution processes is proposed to test the effectiveness of the proposed approach on IEEE-30 bus system, and the detailed analysis is carried out.

Voltage stability constrained multi-objective optimal reactive power dispatch under load and wind power uncertainties: A stochastic approach

Optimal reactive power dispatch (ORPD) problem is an important problem in the operation of power systems. It is a nonlinear and mixed integer programming problem, which determines optimal values for control parameters of reactive power producers to optimize specific objective functions while satisfying several technical constraints. In this paper, stochastic multi-objective ORPD (SMO-ORPD) problem is studied in a wind integrated power system considering the loads and wind power generation uncertainties. The proposed multi objective optimization problem is solved using ε-constraint method, and fuzzy satisfying approach is employed to select the best compromise solution. Two different objective functions are considered as follow: 1) minimization of the active power losses and 2) minimization of the voltage stability index (named L-index). In this paper VAR compensation devices are modeled as discrete variables. Moreover, to evaluate the performance of the proposed method for solution of multi-objective problem, the obtained results for deterministic case (DMO-ORPD), are compared with the available methods in literature. The proposed method is examined on the IEEE-57 bus system. The proposed models are implemented in GAMS environment. The numerical results substantiate the capability of the proposed SMO-ORPD problem to deal with uncertainties and to determine the best settings of control variables.

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

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.