Capacitor Placement Problem Research Articles

Optimal placement of capacitors in radial distribution system using shark smell optimization algorithm

Abstract Optimal size and location of shunt capacitors in the distribution system plays a significant role in minimizing the energy loss and the cost of reactive power compensation. This paper presents a new efficient technique to find optimal size and location of shunt capacitors with the objective of minimizing cost due to energy loss and reactive power compensation of distribution system. A new Shark Smell Optimization (SSO) algorithm is proposed to solve the optimal capacitor placement problem satisfying the operating constraints. The SSO algorithm is a recently developed metaheuristic optimization algorithm conceptualized using the shark’s hunting ability. It uses a momentum incorporated gradient search and a rotational movement based local search for optimization. To demonstrate the applicability of proposed method, it is tested on IEEE 34-bus and 118-bus radial distribution systems. The simulation results obtained are compared with previous methods reported in the literature and found to be encouraging.

Optimal capacitor placement in distorted distribution networks with different load models using Penalty Free Genetic Algorithm

Abstract Genetic Algorithm with special constraint handling procedure is proposed for the discrete optimization problem of capacitor placement and sizing in distribution system for cost reduction and power quality improvement. We use gene encoding that enables simple integer representation of possible different number of capacitors of various standard sizes to be placed on a bus. A pair-wise comparison in tournament selection operator is used so that it does not require any penalty parameter tuning, thus avoiding the most difficult aspect of the selection of appropriate penalty parameters. Proposed Penalty Free Genetic Algorithm (PFGA) is tested on 18-bus, 69-bus and 141-bus systems and the obtained results are better than the results from other methods. Simulations with different load models are also performed. It is shown that load models where active and reactive loads are voltage dependent, such as residential, commercial and industrial, constant Z and constant I model lead to completely different solutions. Therefore, careful load modeling should be put in place in order to obtain more realistic picture of the total savings.

Reliability and economic‐driven switchable capacitor placement in distribution network

In this study, reliability and economic-driven capacitor allocation problem in electrical distribution system is investigated for a definite planning horizon considering several technical and economic aspects. Also, the system reliability modelling is performed based on a new approach, which is considering values of reactive component of currents flowing through branches of the feeder and applying different feeder's failure rate models. The aim of this study is minimising total cost of the system including system power loss cost, system risk cost, investment cost and maintenance cost. Herein, in order to achieve practical outcomes, inflation and interest rates as the economic factors considered in the planning, and yearly load growth, hourly and daily varying load, and customers’ load types are applied in the modelling, and also load model-based power flow is run rather than simple power flow. In this study, it is demonstrated that considering unreal model for the system load types or ignoring dependence of system reliability on the reactive component of current can significantly affect the results of the capacitor placement problem and also it can impose extra cost to the local distribution company.

Ant Colony Optimization Technique in Optimal Capacitor Placement and Sizing Problem in Unbalanced Electrical Distribution System

The optimal capacitor placement problem involves determination on the type, number, location and size of capacitors to be placed in a distribution system for the attainment of energy efficiency. The main objectives of the capacitors placement and sizing are to reduce total line loss and energy consumption while satisfying the operational constraints. This paper presents the optimal capacitor placement and sizing problems solved by using the Ant Colony Optimization (ACO) technique with the integrated of circuitry unbalanced electrical distribution modeled in SIMULINK®MATLAB®software. The proposed technique was tested on a modified IEEE 13-bus unbalanced radial distribution system and the results revealed that the proposed technique has the merit in achieving optimal solution for addressing the problems.

An intelligent approach for optimal capacitor placement problem as a reliability reinforcement strategy

This paper proposes a new method based Cuckoo Search Algorithm (CSA) to investigate the optimal capacitor placement and sizing from the reliability point of view. In this regard, System Average Interruption Frequency Index (SAIFI) and System Average Interruption Duration Index (SAIDI) as the customer-orientated indices and Average Energy Not Supplied (AENS) as the load and energy-orientated index are utilized as the reliability objective functions. Meanwhile, to reach a compromise between the original objective functions and reliability ones, the total system cost including the MW cost of power losses as well as the capacitor investment cost is also considered as an objective function. In order to handle the proposed nonlinear constraint multi-objective optimization problem suitably, a new self adaptive modification method based on Cuckoo Search Algorithm (CSA) is proposed. The feasibility and effectiveness of the proposed method is investigated through a standard test system.

PSO Embedded Artificial Bee Colony Algorithm for Optimal Shunt Capacitor Allocation and Sizing in Radial Distribution Networks with Voltage Dependent Load Models

This paper attempts to reduce power loss in radial distribution network and facilitates improvement in bus voltage profile by determining optimal locations and optimal sized shunt capacitors. Particle swarm optimization algorithm (PSO) is embedded with Artificial Bee Colony algorithm (ABC) to balance exploration and exploitation ability to improve the solution accuracy and the convergence rate of the ABC algorithm as Particle-ABC (PABC) algorithm. In the first formulation, the capacitor placement is based on loss sensitivity factors (LSF) and thereafter decides on the optimal rating of capacitors through the use of proposed hybrid algorithm (PABC).The second approach encircles the role of PABC algorithm to search for the optimal candidate nodes within the nodes nominated by LSF and the optimal sizing of shunt capacitors simultaneously in the pursuit of enhancing the performance of radial distribution network with the former approach. The procedure travels to examine the robustness of the strategy on 41 and 69 nodes test systems with different load models at different load conditions and the simulation results are compared with the heuristic techniques existing in the literature. The simulation results reveal the efficiency and robustness of the PABC to find the optimal solution for capacitor placement problem.

Stochastic reactive power planning in distribution systems considering wind turbines electric power variations

Optimal reactive power planning in the distribution systems is a very significant issue which can reduces the amount of power losses and increase the power quality of the electrical services, effectively. Nevertheless, by the rapid growth of the renewable power sources especially wind turbines WTs this problem has been affected greatly. The stochastic nature of WT and its output variable power has become a challenging issue for optimal reactive power planning of the distribution systems such as capacitor placement problem. In this way, this paper suggests a new stochastic framework based on point estimate method PEM to solve the capacitor placement problem considering several WTs in the system. The PEM makes use of the first few statistical data of the random variables to find the expected value of the output, here the system total costs. The uncertainties of the forecast error in the WT output power as well as the active and reactive loads are modeled in the proposed framework. Meanwhile, a powerful optimization algorithm called Krill Herd KH algorithm is used to solve this problem suitably. The performance of the proposed method is examined on the IEEE distribution test system.

Capacitor placement of distribution systems using particle swarm optimization approaches

Capacitor placement plays an important role in distribution system planning and operation. In distribution systems of electrical energy, banks of capacitors are widely installed to compensate the reactive power, reduce the energy loss in system, voltage profile improvement, and feeder capacity release. The capacitor placement problem is a combinatorial optimization problem having an objective function composed of power losses and capacitor installation costs subject to bus voltage constraints. Recently, many approaches have been proposed to solve the capacitor placement problem as a mixed integer programming problem. This paper presents a new capacitor placement method which employs particle swarm optimization (PSO) approaches with operators based on Gaussian and Cauchy probability distribution functions and also in chaotic sequences for a given load pattern of distribution systems. The proposed approaches are demonstrated by two examples of application. Simulation results show that the proposed method can achieve an optimal solution as the exhaustive search can but with much less computational time.

Optimal stochastic capacitor placement problem from the reliability and cost views using firefly algorithm

This study suggests a new stochastic framework based on point estimate method to capture the uncertainty associated with the forecast error of the active and reactive loads and failure rate and repair rate values. The objective functions to be investigated are system interruption frequency index, system average interruption duration index and average energy not supplied. Meanwhile, since the total MW cost is an attractive issue to the power utilities, the active power losses is also considered as an objective function. In order to explore the problem search space globally, a novel self-adaptive modification method based on firefly algorithm is proposed. The feasibility and effectiveness of the proposed method are examined on the IEEE 34-bus test system. According to the simulation results, the proposed framework based on capacitor placement problem can improve the reliability of the system effectively.

Solving capacitor placement problem considering uncertainty in load variation

The paper reports on the solution of the capacitor placement problem in distribution system considering uncertainty in the variation of loads. Solution techniques available in the literature generally consider load variation as deterministic. In the present paper uncertainty in load variation is considered using fuzzy interval arithmetic technique. Load variations are represented as lower and upper bounds around base levels. Both fixed and switchable capacitors have been considered and results for standard test systems are presented.

A Novel Evolutionary Algorithm for Capacitor Placement in Distribution Systems

AbstractThis paper uses an effective method, CODEQ method, with integer programming for solving the capacitor placement problems in distribution systems. Different from the original differential evolution (DE), the concepts of chaotic search, opposition-based learning, and quantum mechanics are used in the CODEQ method to overcome the drawback of selection of the crossover factor and scaling factor used in the original DE method. One benchmark function and one 9-bus system from the literature are used to compare the performance of the CODEQ method with the DE, and simulated annealing (SA). Numerical results show that the performance of the CODEQ method is better than the other methods. Also, the CODEQ method used in 9-bus system is superior to some other methods in terms of solution power loss and costs.

A novel optimal capacitor placement algorithm using Nelder-Mead PSO

In this paper, a new efficient algorithm is developed for optimal placement of capacitor using Nelder-Mead particle swarm optimisation (NM-PSO). The developed capacitor placement problem (CPP) has been formulated to make the objective function (i.e., planning method) more realistic by incorporating essential economic factors, viz., maintenance cost, interest on investment cost and inflation. This developed CPP is found capable of providing more cost-effective solution than existing approaches. Simulation results are obtained for IEEE 9-bus and 69-bus radial distribution system. Results obtained with NM-PSO, are compared with the PSO approach. For both the IEEE test systems, simulation results reveal more effective and profitable planning with NM-PSO. In addition, sensitivity analysis is carried out to highlight the impact of newly incorporated economic factors, justifying their inclusion in CPP.

Capacitor Allocation in Unbalanced Distribution System under Unbalances and Loading Conditions

It is well known fact that distribution systems can operate under unbalanced loading conditions, means that the distribution system planner have to account for any unbalances in the system for reliable operation of the system. In this paper optimal sizes and locations of capacitors is determined using Index Vector method in unbalanced radial distribution system (ubds). In this paper two types of load unbalances and different loading conditions are considered to investigate its impact on optimal capacitor sizes and locations. The main objective of this paper is:•Finding optimal size and locations of capacitors in ubds.•Impact of different loading conditions (low, medium and high loading) on optimal placement of capacitors in ubds is evaluated.•Impact of type-A and type-B unbalances on voltage profile, voltage unbalance, total power losses and cost of energy losses in ubds is determined.•Impact of type-A and type-B unbalances on optimal capacitor allocation problem is addressed.•Impact of realistic load model as ZIP load model has been considered in optimal capacitor placement problem.•Computing required amount of capacitive reactive power to minimise total power losses and improve voltage profile under different load unbalances, different loading conditions and realistic ZIP load model.

Optimal allocation of capacitors in radial/mesh distribution systems using mixed integer nonlinear programming approach

Capacitors in radial/mesh distribution systems are used to supply reactive power to minimize loss and to improve the voltage profile. The appropriate placement of capacitors is also important to ensure that system power losses and total investment capacitor costs are minimal. The capacitor placement problem consists of finding specific sitting and sizing to install capacitor banks in an electrical distribution system. Consequently, the losses are reduced due to the compensation of the reactive component of power flow. This paper presents a new mixed integer nonlinear programming approach for capacitor placement in radial/mesh distribution systems that determine the optimal sitting and sizing of capacitors with an objective of reduction power loss and investment capacitor costs. The proposed method is applied to 10, 34, and 85-bus radial distribution systems and CIVANLAR mesh distribution system. Various-scale application systems are used to compare the performance of the proposed method with the Fuzzy reasoning, particle swim optimization (PSO), plant growth simulation algorithm (PGSA), and Heuristic based. Numerical results show that the performance of the proposed MINLP method is better than the other methods. Also, the MINLP method is superior to some other methods in terms of solution power loss and costs.

Multi-objective Performance Management of the Capacitor Allocation Problem in Distributed System Based on Adaptive Modified Honey Bee Mating Optimization Evolutionary Algorithm

Optimal capacitor placement as a precious and significant strategy to improve the performance of the power systems has attracted much attention in recent years. However, the non-linear and discrete nature of the optimal capacitor placement problem is a big barrier in front of the traditional optimization methods for global search. Therefore, this article proposes a powerful optimization technique based adaptive modified honey bee mating optimization algorithm to solve the optimal capacitor placement problem effectively. The proposed method consists of two sub-modification methods to let each solution choose the modification methods which best fit its situation. Also, in order to preserve the random search ability of the algorithm, the idea of the roulette wheel mechanism is employed in the selection process. The proposed algorithm can overcome the main shortcomings in the traditional honey bee mating optimization algorithm by using both local and global search schemes. Therefore, the problem investigated is formulated in a multi-objective framework optimizing the total power losses, voltage deviation, and cost of both power losses and capacitor investment simultaneously. As the result of the conflicting behavior of the objective functions, the idea of a non-dominated solution, called the Pareto solution, is employed to find the set of optimal solutions. During the optimization process, the set of Pareto solutions found is stored in an external memory called a repository. In order to avoid excessive growth of the repository, a fuzzy-based clustering technique is applied to the problem. The feasibility and superiority of the proposed method is tested through three standard test systems.

Optimal capacitor allocations using evolutionary algorithms

This article investigates the implementation of integrated evolutionary algorithms based for solving the capacitor placement optimisation problem with reduced annual operating cost. Differential evolution and pattern search (DE-PS) are used as meta-heuristic optimisation tools to solve optimal capacitor placement problem. The objective function is formulated to enhance bus voltage profiles effectively within the specified voltage constraints and reduce line active energy losses whereas maximising the benefits of installing reactive compensators. To tackle and reduce the search space process and computational CPU time, the potential buses candidate for capacitor allocations are pre-identified. At that moment, hybrid DE-PS approach is used for the estimation of required optimum level/size of shunt capacitive compensations. The overall accuracy and reliability of the developed approach were validated and tested on several radial distribution systems with different topologies and varying sizes and complexities. Computational results obtained showed that the proposed approach is capable of producing high-quality solutions, and demonstrated its viability. The results are compared with one of previous studies using recent heuristic methods.

Considering uncertainty in the multi-objective stochastic capacitor allocation problem using a novel self adaptive modification approach

This paper suggests a new stochastic method based on point estimate method (PEM) to consider the uncertainty effects in the optimal capacitor placement problem. The proposed stochastic method will capture the uncertainty associated with the forecast errors of active and reactive loads as well as the cost function coefficients, concurrently. The objective functions to be investigated are the (1) active power losses, (2) voltage deviation and (3) total cost. Investigating the capacitor placement problem in the proposed stochastic framework will convert it to a complex, nonlinear, discrete multi-objective optimization problem which requires a powerful optimization tool to escape from the local optimal. In this regard, a novel self adaptive modification approach based on Honey Bee Mating Optimization (HBMO) algorithm is proposed to enhance the total ability of the algorithm effectively. During the optimization process, the proposed algorithm will find a set of Pareto optimal solutions which are stored in an external memory called repository. In addition, a fuzzy based clustering technique is used to control the size of the repository in the pre-determined values. The feasibility and effectiveness of the proposed method are assessed through 2 standard IEEE test systems.

Shunt Capacitors Placement in Kurdistan Region Power System Using Power Losses Index

Capacitors in power systems are generally used to supply reactive power for the purpose of loss minimization and voltage profile improvement. The shunt capacitor allocation problem is the determination of the location of the capacitor to be placed in power system in a manner to reduce the total power losses of the networks. In this paper loss determination and capacitor placement is studied to reduce power loss in KRPS (Kurdistan Region Power System) using PSAT program under MATLAB Software. The capacitor placement problem aims to determine the locations of capacitors to be installed in a KRPS based on an index called power losses index (PLI) which it indicates the most effective candidate buses that the capacitor banks to be installed. The objective of the paper is aimed to reduce the power losses in the system and retain the voltage magnitudes of the system within prescribed maximum and minimum allowable values.

Strategic capacitor placement in distribution systems by minimisation of harmonics amplification because of resonance

The capacitor placement problem (CPP) has been widely studied throughout the years. However, traditional methodologies either do not consider non-linear loads in the formulations or are highly dependent on the spectrum of the harmonic currents. Therefore the traditional methodologies have become unsuitable for distribution system planning studies. The proposed approach formulates the CPP as a multi-objective optimisation model while including economic and technical aspects in the minimisation process. An additional objective function introduces a quadratic minimisation of the voltage harmonic distortions produced by the harmonic currents drawn by non-linear loads according to the IEEE Std. 519-1992 limits. A new constraint based on a resonance index (RI) is also introduced as a form to extend the capacitors- lifetime. Furthermore, an aging model of capacitor dielectric insulation under a non-sinusoidal waveform scenario is used to estimate the expected real lifetime of capacitors. The proposed methodology was exhaustively tested on a 69-bus system and the results show that the methodology is adequate for planning capacitors and eliminates the need to focus in great detail on harmonic system data.

Optimal reconfiguration and capacitor placement by robust searching hybrid differential evolution

AbstractThis paper aims to study distribution system operations by the robust searching hybrid differential evolution (RSHDE) method. The objective of this study is to present new algorithms for solving the optimal feeder reconfiguration problem, the optimal capacitor placement problem, and the problem of a combination of the two. Mathematically, the problem of this research is a nonlinear programming problem with integer variables. This paper presents a new approach which employs the RSHDE algorithm with integer variables to solve the problem. Depending on the initial assignment of the integer variables, the HDE may fail to find the initial search direction for large‐scale integer system. This is because the HDE applies a random search at its initial stages. Therefore, two new schemes, the multi‐direction search scheme and the search space reduction scheme, are embedded into the HDE. These two schemes are used to enhance the search ability before performing the initialization step of the solution process. The proposed approach is demonstrated using an IEEE illustrative example and one practical distribution network of Taiwan Power Company (TPC). Moreover, the previous HDE, simulated annealing (SA) and genetic algorithms (GA) methods are also applied to the same example systems for the purpose of comparison. Copyright © 2009 John Wiley & Sons, Ltd.