Capacitor Placement Problem Research Articles

Capacitor Allocation in Distribution Networks Based on a Two-Stage Analytical-Heuristic Approach

In distribution networks, reduction of search space can be an efficient way to conquer the complexity of capacitor placement. In this paper, based on search space reduction, a two-stage procedure is proposed to efficiently solve capacitor placement problem. For this aim, as the first stage, analytical indices are introduced to determine the importance of network buses for compensation. The indices prioritize buses based on the network losses sensitivity to change of voltage and/or reactive power. As a result of the first stage, a number of most important buses are considered as the candidates for compensation. Then, the second stage is conducted using an optimization method to solve the capacitor placement problem with respect to the candidate buses. To do the second stage, an enhanced metaheuristic method, named enhanced crow search algorithm (ECSA), is developed. Compared to popular methods of search space reduction, loss sensitivity factor (LSF) and loss sensitivity indices (LSI1 and LSI2), simulation results confirm the superiority of the proposed two-stage procedure. On 33-bus network with respect to peak condition, when 3 buses are regarded as the candidate buses (around 10% of the total network buses), the optimal solution is found. In this case, compared to LSF, LSI1 and LSI2, objective function value decreases 2.9, 11.2 and 6.6%, respectively. On 69-bus network, when 6 buses are selected as the candidate buses (around 10% of the total network buses), the optimal solution is obtained. In this case, compared to LSF, LSI1 and LSI2, objective function value decreases around 0.7%.

Optimal capacitor allocation for minimizing cost of energy loss in active distribution network with different load levels

This paper proposes an effective technique to allocate a shunt capacitor using a meta-heuristic optimization-approach for minimizing the cost of energy losses. Particle swarm optimization (PSO) algorithm incorporated with MATPOWER is trained for minimizing the targeted function of the optical capacitor placement problem. The 115-node active distribution network supplied by MESC in the Mandalay distribution area is applied as a scenario. The results including active power loss and system energy loss, size and location of the optimized capacitor, voltage profiles, and the cost of energy loss are attained and analyzed. The simulations results revealed that the optimal allocation of the capacitor provides a significant reduction in the cost of energy losses as well as improvement in voltage profile with compensation of reactive power.

Solving the capacitor placement problem in radial distribution networks

The optimal capacitor allocation problem is suggested in this article. This study purposes to maximize the voltage stability, minimize the power losses, and consolidate the annual net savings. Calculating the optimal locations and sizes of fixed and switched capacitors is done in two steps. The first step is using the fuzzy expert rules in calculating the most candidate buses for capacitor allocation. While the second step is using a nondominated sorting genetic algorithm II (NSGA-II) in determining the list of Pareto optimal solutions and then applying a fuzzy decision maker to pick the most compromise. To emphasize the effectiveness of the proposed method, radial distribution systems are proposed; IEEE 33-bus system and the actual Portuguese IEEE 94-bus system. To demonstrate the strength and applicability of this method, a multiobjective water cycle algorithm (MOWCA), multiobjective grey wolf optimizer (MOGWO), and other optimizers used in the published papers are used. From simulation and analysis, the proposed NSGA-II outperforms other optimizers considered for comparison in achieving the maximum percentages of minimization in a real power loss of 32.369% and 31.1011% for the 33-bus system and 25.6296% and 25.3027% for the 94-bus system, the maximum percentages of minimization in a reactive power loss of 31.7916% and 30.4948% for 33-bus system and 25.9457% and 25.8001% for the 94-bus system, the maximum annual net savings of 23,612 $ and 23,131 $ for the 33-bus system for fixed and switched capacitors, respectively, and boosting the total voltage stability, which show its superior ability to give high-grade solutions.

Hybrid Grey Wolf Optimizer Based Optimal Capacitor Placement in Radial Distribution Systems

The problem of optimal capacitor placement (OCP), or the determination of both the optimal bus locations and sizes in radial distribution systems (RDS) has been solved in this article using a new metaheuristic algorithm named as the hybrid grey wolf optimizer (HGWO). The grey wolf optimizer (GWO) is hybridized with the addition of mutation and crossover, to create the hybrid grey wolf optimizer (HGWO). The enhanced performance of the HGWO has been proved by comparison of the solutions and the convergence curves of GWO and HGWO. The objective of the OCP problem—a discrete, non-convex optimization problem—is minimization of the cost of capacitor installations and total real power loss. The proposed HGWO approach has been applied to solve the IEEE 34-, 69-, 119 bus RDSs and a practical 22-bus RDS. Comparisons of the results obtained against those reported in the literature show that the HGWO performs very well, and hence is a highly suitable optimization approach for solving OCP problems.

Optimal Capacitor Placement in Power Distribution System

Optimal Capacitor Placement (OCP) determines the locations, the size and the control settings of these capacitors during each load level of a three-phase distribution system. That will reduce peak power and energy losses and minimise the investment costs and installation of the capacitor banks. The optimal solution is obtained by testing various combinations of capacitor banks and candidate nodes and the distribution system and calculating the resultant savings. The capacitor placement problem is a combinational optimisation problem having an objective function composed of energy losses and capacitor bank installation costs subject to the load constraints, network constraints and operational constraints at different load levels. OCP seeks to maximise the net savings resulting from the reduction in power and energy losses less the total costs of capacitors. An Artificial Intelligence (A.I.) based Genetic Algorithm (G.A.) has been used to solve the OCP problem. The proposed method allows the modelling of loads of different power factors for other portions of the power distribution system. The solution algorithm has been implemented and tested on a ten bus power distribution system, and the simulation results of the proposed algorithm are well executed.

Simple Quadratic Interpolation-Inspired Symbiosis Organisms Search Algorithm for Optimal Placement of Capacitors in Radial Distribution Networks with Different Loading Models

This paper proposes a novel hybrid algorithm based on a combination of the simple quadratic interpolation and the symbiosis organisms search algorithm (SQI-SOS) for finding the optimal location and size of capacitors in radial distribution networks. The objective of the problem is to minimize the system operating cost so that the net yearly savings of the system are increased. The effectiveness of the SQI-SOS has been tested on 33-, 69-, and 119-bus radial distribution networks with different load models. The obtained results from the test system by the proposed SQI-SOS are compared with those from the conventional SOS and other mature optimization methods in the literature. The result comparison has shown that the proposed SQI-SOS algorithm can provide a better solution than the other methods. Accordingly, the proposed SQI-SOS can be a very effective and efficient method for dealing with the optimal capacitor placement problem in distribution networks.

A new analytical index for solving capacitor placement problem of distribution networks in bi‐level framework: Total loss index

A new analytical index for solving capacitor placement problem of distribution networks in bi‐level framework: Total loss index

Simultaneous optimal allocation and sizing of DGs and capacitors in radial distribution systems using SPEA2 considering load uncertainty

The rapid growth in load demand results in higher line loses in distribution systems and also demands distribution system augmentation. Apart from this, due to fluctuating loads, it becomes a challenge for the utility sectors to maintain voltage stability of the system under healthy condition. For addressing such problems, simultaneous optimal placement of distributed generations (DGs) and capacitors in radial distribution systems employing multi-objective optimisation technique based approach is explored in this work. In line with this, the present work uses a simple and powerful multi-objective strength Pareto evolutionary algorithm 2 (SPEA2) for solving distributed generator and capacitor placement problem considering load uncertainty. The uncertainty characteristics of load are designed by probabilistic approach and the same is utilised during the optimisation process. Thereafter, a set of non-dominated Pareto optimal solution is obtained according to the objective function value. A compromised solution is selected from the set of Pareto optimal solutions by using fuzzy set theory. Along with the above, the impact of reverse power flow is studied by taking different test cases. The studied algorithm has been tested on different standard IEEE 33-bus and 69-bus radial distribution test systems.

Wild Goats Optimization Approach for Capacitor Placement Problem

This paper deals with Capacitor Placement (CP) issue. The topic is an optimization problem including two types of variables: capacitor location as an integer variable, capacitor size as a continuous one. To cope with this problem, a new approach entitled Wild Goats Algorithm (WGA) is used. WGA is a new heuristic approach which has been proved recently. In this paper, WGA is successfully implemented to the CP problem with the objective of total loss reduction. Power flow criteria as well as operation constraints are all together accommodated in the process of optimization. Two various scenarios at three load levels are also recognized to cover all possible conditions. The validity of the WGA approach in handling CP problem is assured by testifying it on IEEE 33-bus and 69-bus test systems

Reactive Power Compensation on Egypt Electricity Network for Optimal Energy Saving

This paper introduces the load flow on the Egypt Electricity Network system. The effect of capacitor compensation has been studied from three points. First, the problem of the series capacitor compensation was considered. The second type of compensation considered is shunt compensation. Finally, a mixed of shunt and series capacitors compensation was implemented. The analysis results were discussed based on the maximum reduction in the generated MVAR. The load variation is accounted for by considering three different load levels classified as light, medium and peak load with pre-specified durations. When solving the capacitor placement problem, the number, size, location and control settings of the capacitors at different load levels were determined. The load flow program is solved by the Power World Simulator (PWS) software. The results of series capacitor, shunt capacitor, and mixed compensation were studied. The investigation has been done for single capacitor and multi-capacitor compensation. Both 500kV and 220kV overhead lines have been considered.

A modified harmony search algorithm applied to capacitor placement of radial distribution networks considering voltage stability index

In power system, capacitor placement of distribution networks is a complex combinatorial optimisation problem. In this paper, in order to effectively solve optimal capacitor placement (OCP), an aggregate harmony search (AHS) optimiser, a stochastic population-based metaheuristic algorithm, is proposed which introduces a new pitch adjustment mechanism for harmony search (HS). The objective function contains three goals: 1) minimisation of the power losses; 2) minimisation of the capacitor installation cost; 3) improvement of the voltage stability index at the weakest bus. On two case studies, 23 kV nine-section feeder and 33-bus radial system, simulation results show that the proposed AHS not only finds more accurate results than the other investigated HS variants and particle swarm optimisation (PSO) techniques but also has the best robustness. Promising performance of AHS makes this technique as an efficient alternative to solve capacitor placement problem.

A modified harmony search algorithm applied to capacitor placement of radial distribution networks considering voltage stability index

In power system, capacitor placement of distribution networks is a complex combinatorial optimisation problem. In this paper, in order to effectively solve optimal capacitor placement (OCP), an aggregate harmony search (AHS) optimiser, a stochastic population-based metaheuristic algorithm, is proposed which introduces a new pitch adjustment mechanism for harmony search (HS). The objective function contains three goals: 1) minimisation of the power losses; 2) minimisation of the capacitor installation cost; 3) improvement of the voltage stability index at the weakest bus. On two case studies, 23 kV nine-section feeder and 33-bus radial system, simulation results show that the proposed AHS not only finds more accurate results than the other investigated HS variants and particle swarm optimisation (PSO) techniques but also has the best robustness. Promising performance of AHS makes this technique as an efficient alternative to solve capacitor placement problem.

Optimal capacitor placement in radial distribution systems using flower pollination algorithm

In this paper, a new metaheuristic algorithm that mimics the pollination process of flowers and is known as the flower pollination algorithm (FPA) has been proposed for the solution of the optimal capacitor placement (OCP) problem in a radial distribution system (RDS). The objective of this problem is to minimize the total power loss and cost of capacitor installation by optimal location and sizing of the capacitors. OCP also improves the voltage profile. In this work, the power flow and losses in the network are obtained with the help of load flow analysis using data structures. The proposed FPA approach has been applied to solve 33-, 34-, 69- and 85 bus RDSs. The results obtained are compared with those of the analytical method, fuzzy real coded genetic algorithm, two stage fuzzy approach and teaching learning based optimization algorithms. The comparison shows that FPA is a highly suitable optimization approach for solving capacitor placement problems.

Optimal capacitor placement on West–East inter-tie in Saudi Arabia using genetic algorithm

The growing demand for renewable energy resources, improved power factor, system stability, reliability and security is the target of Saudi Electricity Company (SEC); most of the loads are inductive and need more reactive power (VARs) thus adequate reactive power need to be provided. SEC has introduced the static voltage compensator (SVC) and capacitive banks to improve volt-ampere-reactive (VAR) power flow. Genetic approach (GA) is used to obtain the optimal data for load flow. This paper provides analysis of new-planned 380 kV West–East transmission line inter-tie networks performance under steady and transient states. It considers the reactive power compensation by the addition of capacitor bank at the terminals of the inter-tie. The GA method is outlined and implemented to dynamically solve the capacitor placement problem. The capacitor bank has improved power losses, operating voltage at different buses.

A Swarm Approach for Improving Voltage Profiles and Reduce Power Loss on Electrical Distribution Networks

As a mean to provide reactive power compensation to radial distribution networks, capacitor banks are commonly installed within these electrical distribution systems. When properly allocated, capacitor banks provide several benefits, including an improvement on the feeder’s voltage profile and significant reductions on power loss, which, in turn, leads to important amounts of energy savings and cost reductions. This formulation is known in the literature as optimal capacitor placement (OCP) problem. From an optimization perspective, OCP is considered remarkably complex due to its high multi-modality, discontinuity, and non-linearity. In this paper, the swarm optimization algorithm known as locust search (LS) is proposed for solving the OCP problem. The proposed approach has been tested by considering several IEEE’s radial distribution test systems, and its performance has also been compared against that of other techniques currently reported on the literature to solve the OCP problem. Our experimental results suggest that the proposed LS-based method is able to competitively solve the OCP problem in terms of accuracy and robustness.

Hybrid Symbiotic Organisms Search for Optimal Fuzzified Joint Reconfiguration and Capacitor Placement in Electric Distribution Systems

Network reconfiguration and capacitor allocation are two valuable tools to optimally manage distribution systems. In the present work, an efficient algorithm is proposed for the joint problem of reconfiguration and capacitor placement in distribution systems. The multi-objective problem is formulated to minimize objective functions of total network power losses, bus voltage violation, and branch loading deviations subject to different technical and operational constraints. To enhance exploration ability, the Symbiotic Organisms Search algorithm is strengthened with Particle Swarm Optimization capabilities to develop the Hybrid Symbiotic Organisms Search algorithm, which is applied to solve the proposed problem. Objective functions are fuzzified and aggregated by a geometric mean operator to have the same scales. The proposed joint optimization problem is solved with the introduced Hybrid Symbiotic Organisms Search algorithm in two different case studies of balanced and unbalanced test systems. According to obtained results that are compared with some well-known evolutionary algorithms, the superiority of the Hybrid Symbiotic Organisms Search algorithm is confirmed in terms of solution optimality and convergence speed.

Optimal placement of power factor correction capacitors in power systems using Teaching Learning Based Optimization

This paper presents a method to optimize the placement of capacitors in a distribution system to correct power factor and reduce losses and costs. The method uses the Teaching Learning Based Optimization (TLBO) method to solve the optimal capacitor placement problem. The combinatorial nature of the problem suggests the employment of a mixed binary and real valued TLBO algorithm. To validate the efficiency of the method, it was applied to various examples (different bus systems) and simulation results are discussed.

Multiobjective hybrid evolutionary approach for optimal planning of shunt capacitors in radial distribution systems with load models

Abstract This article proposes a novel hybrid heuristic search algorithm based on Harmony search and particle artificial bee colony algorithm (HSA-PABC) for shunt capacitor placement problem. The objective function is framed to minimize power loss and to maximize voltage stability. To search for the optimal location of shunt capacitors, the combinatorial use of loss sensitivity factor and hybrid HSA-PABC algorithm is utilized. In this paper, different types of voltage dependent load models are taken into consideration to investigate their influence on the active power loss and voltage stability of the RDN. Simulation results shows that the voltage dependent load models lead to completely different solutions interms of power loss reduction, voltage stability improvement and net annual savings which are the crucial parameters in the decision process of optimal shunt capacitor placement problem. The result outcomes of the proposed hybrid algorithm outperform the results of other heuristic techniques in the literature.

Capacitor and passive filter placement in distribution systems by nondominated sorting genetic algorithm-II

The optimization of passive filters in distribution systems has been addressed through different approaches. In general, these approaches can be classified as single-objective and multi-objective formulations. The single-objective formulations normally try to determine the least costly filters that ensure compliance with the relevant power quality standards. In multi-objective approaches, other goals are added. In general, most studies consider the reactive power of filters at a fundamental frequency to be equal to a previously determined magnitude, and the optimization is devoted to calculate the other parameters of the filters that are required to minimize the distortion indices of the network. In the present approach, the capacitor placement and passive filter placement problems are considered as a unified problem in which a set of passive compensators (capacitors and/or tuned filters) that allow to obtain the maximum annual saving in cost and maximum improvement of the power quality of the circuit are determined. In this study, the annual saving is calculated as the equivalent present value of the compensation project to simultaneously account for the benefits of the reactive power compensation and the cost of investment in the compensators. Although many studies have solved the multi-objective problem by minimizing a single function comprising several subobjectives, this study employs the nondominated sorting genetic algorithm for the optimization of several objective functions. The present approach is tested with two example circuits from literature.

Feeder reconfiguration and capacitor allocation in the presence of non‐linear loads using new P‐PSO algorithm

This study proposes a new particle swarm optimisation algorithm for combined problem of capacitor placement and network reconfiguration simultaneously in the presence of non-linear loads. Here, the minimising cost of real power losses and capacitor installation and also improving the power quality criteria have been pursued as the goals of an optimisation problem. In the proposed method, to achieve better control on the algorithm's exploration and exploitation capabilities, particles velocity will be dependent upon both particle's fitness and time. Perturbation module is adopted to perform perturbation on some particles and provide extra diversity to jump out from local optima and avoid premature convergence. The proposed model is implemented on two typical networks including 33-bus IEEE standard well-known test system and a 77-bus radial distribution network of Sirjan, Iran. Through showing numerical results, the performance of the presented method will be discussed in comparison to previously proposed ones. The numeric comparison also indicates that simultaneously capacitor placement and network reconfiguration lead to far better results than they are considered non-simultaneously. Furthermore, in regard to harmonic distortion, as a term of a multi-objective function, it also improves the power quality of the network during the reconfiguration and capacitor placement procedures.