Size Of Shunt Capacitors Research Articles

The League Championship Algorithm (LCA) for optimal placement and sizing of shunt capacitors

The League Championship Algorithm (LCA) for optimal placement and sizing of shunt capacitors

Influence of Load Models and DG Operational Power Factor on Optimization of Shunt Capacitor Placement in Distribution Grids Considering Voltage Stability

The paper proposes a mathematical model of mixed-integer nonlinear programming (MINLP) to optimize the location and size of shunt capacitors in power distribution grids with distributed generation (DG), considering voltage stability constraints. At the same time, the paper also analyzes the influence of the load models, such as voltage-dependence load (ZIP load) and constant power load, together with DG’s operating power factor on the optimal solution. The objective function of the proposed optimization formulation is minimizing the total expenses, including the capital investment of capacitors and the expense incurred by network energy loss. This MINLP model includes constraints in the current and critical loading conditions, such as the system of power flow equations, nodal voltage limits, branch thermal limits, capacitor-related constraints, and restrictions of minimum security level. The proposed optimization model was evaluated on a modified IEEE 33-node distribution grid using the KNITRO commercial solver with the GAMS programming language. The calculation results show that the voltage stability constraints, load models, and operational power factor of the DG units have an essential influence on the optimal position and capacity of the shunt capacitors.

Optimal sizing and placement of capacitors in the isolated microgrid throughout the day considering the demand response program

Reactive power compensation (RPC) is a big problem during power system operation. Parenthetically, capacitor allocation and sizing may be the only convenient solution for RPC of power systems. The loss sensitivity factor (LSF) is applied here for finding the optimum capacitor position. This paper presents quasi-oppositional fast convergence evolutionary programming (QOFCEP), fast convergence evolutionary programming (FCEP), and evolutionary programming (EP) for the optimum location and sizing of shunt capacitors in the isolated microgrid (MG) for minimizing total real power loss throughout the day with and without the demand response program (DRP). The 33-node, 69-node, and 118-node isolated MGs have been studied to authenticate the efficacy of the suggested approach. Each MG includes small hydro power plants (SHPPs), solar PV plants (SPVPs), wind turbine generators (WTGs), diesel generators (DGs), and plug-in electric vehicles (PEVs).

A meta‐heuristic capacitor placement framework for distribution grids using modal resonance analysis

Shunt capacitors are usually installed in distribution grids for power factor correction. On the other hand, the number of harmonic-producing sources such as wind turbines (WTs), photovoltaic (PV) panels, storage units, and electronic loads is rapidly growing in distribution grids. Since improper placement and sizing of shunt capacitors in harmonic-polluted grids may aggravate power quality conditions and lead to harmonic resonance, special attention should be paid to this optimization problem when harmonics are present. In this paper, a framework based on shuffled frog leaping algorithm (SFLA) is proposed for optimal placement of fixed capacitor banks. Moreover, a resonance index (RI) is proposed for assessment and mitigation of potential harmonic resonance based on resonance mode analysis (RMA). The resonance mitigation method helps in avoiding power quality constraint violations and directs the algorithm toward the feasible solution space. It thus results in a higher efficiency, and the chance of reaching (near) globally optimum solutions increases. The proposed algorithm is particularly useful when detailed data regarding the harmonic injection pattern of nonlinear sources is not available. The proposed framework is implemented on the IEEE 18, 34, and 69-bus test systems, and the results demonstrate its advantages, especially in larger grids.

Optimal sizing and placement of shunt capacitors on the distribution system using Whale Optimization Algorithm

This paper aims at power loss minimization and reduction of cost due to losses in the distribution network as well as improvement of the network voltage stability and profile via optimal shunt capacitor allocation. The optimal shunt capacitor allocation was obtained using Whale Optimization Algorithm considering technical (real power loss and VSI) and economic objective functions as sub-optimal allocation may result in undesired effects on the network. The obtained optimal sizes of the shunt capacitors were placed on the obtained location of the distribution networks to ascertain the behavior of the networks before and after their placements taking power loss, cost due to losses, and voltage stability index as the performance metrics. A comparison of these performance metrics under four cases, namely base case (case one), installation of one SC (case two), installation of two SCs (case three), and installation of three SCs (case four) were demonstrated using standard IEEE 33-bus and Dada 46-bus distribution networks. The results gave a percentage loss reduction of 33.74% with 27.60% annual net saving for the IEEE 33-bus network and 22.24% loss reduction with 25.60% annual net saving for the Dada 46-bus network. Hence, reduction in the total power losses and costs. Also, the voltage profile and voltage stability index were significantly improved.

Power loss minimization and voltage profile improvement on electrical power distribution systems using optimal capacitor placement and sizing

Distribution system operators are having difficulties maintaining a correct voltage profile across its network. As the standard of living of its customers increases, suppressed loads tend to come up and this in turn would require and increased demand in power supply. The increase in power demand and high load density at distribution ends have been seen to have key consequences of increasing the power loss and reducing the voltage profile in power systems, which seriously jeopardizes the ability of radial distribution networks to faithfully account for the power received from transmission stations. This work is aimed at improving the power quality that gets to the end users. Shunt capacitors have been suggested to be a suitable solution to this problem as they supply the reactive power needed for compensation. As a result, the optimum placement and size of these shunt capacitors have received a great deal of attention. Despite its efficacy, meta-heuristic algorithms are seldom utilized in the Nigerian RDS (radial distribution system), since most published research instead uses analytical and numerical programming methods. As a result, this research explains how to use a Hybrid Solution (HS) of Particle Swarm Optimization (PSO and GA) to identify and size shunt capacitors for real-time power loss reduction on an 11-kV distribution feeder. The backward-forward sweep load flow method with Loss Sensitivity Factor (LSF) is used to identify suitable buses for shunt capacitor installation, and the HS algorithm is then used to estimate the optimum size. This method was discovered to decrease the system's real power loss by 54.88% while raising the minimum bus voltage magnitude to the acceptable limit and thus improving the minimum system Voltage Stability Index (VSI). Based on these findings, the suggested technique is regarded as a viable way for placement and determining the size of shunt capacitors in a real-world Radial Distribution System. The numerical results shows that the approach has a high capability of improving the voltage profile of the distribution network, leading to an improved system power quality, minimize the system losses, correct the power factor, and maximize the net savings. The numerical results were gotten by using MATLAB package.

Optimal Location and Sizing of Shunt Capacitors with Distributed Generation in Distribution Systems

This paper proposes a novel approach to determine an optimal location and sizing of shunt capacitors for reactive power compensation in distribution systems with distributed generation. Here, the optimal location for installing the shunt capacitors is determined using the loss sensitivity factor approach. The stochastic nature of distributed generation (i.e., wind and solar PV powers) has been considered in this paper. Optimal sizing of shunt capacitors has been determined by considering the power loss minimization as objective function and this problem is solved using the differential evolution algorithm (DEA). The results obtained with DEA are also compared with genetic algorithm (GA) and particle swarm optimization (PSO) algorithms. The effectiveness of this proposed approach has been simulated on the IEEE 15, 33, 69 and 85 bus test systems.

Optimal placement and sizing of shunt capacitors in distorted distribution systems using a hybrid algorithm

In this paper, a novel hybrid phasor particle swarm optimization and gravitational search algorithm, namely the hybrid PPSOGSA algorithm, is proposed to find the optimal size and location of shunt capacitors in distribution systems with non-linear loads. The performance of PPSOGSA are studied and evaluated using the IEEE 9- and 85-bus test systems with the objective of minimizing the total annual cost of the system. The procedure is conducted taking into account effects of harmonic distortion and discrete size of capacitors available in the market. Simulation results are compared with those obtained by other optimization techniques, and verified using the Electrical Transient Analysis Program (ETAP). It was established that that the hybrid PPSOGSA algorithm provides better solutions in terms of convergence and accuracy.

Optimal Placement and Sizing of Shunt Capacitors in Radial Distribution System Using Polar Bear Optimization Algorithm

Reduction in power loss while maintaining the acceptable voltage profile has become a challenge for distribution system operators due to expanded living standards. Properly sized shunt capacitors (SCs) allocated at suitable locations of the distribution system can enhance its performance by tackling the power quality issues and foster multiple technical and economic benefits. Most of the existing research work in this domain is accomplished at fixed loading conditions without incorporating purchasing, installation, operation and degradation costs of the SCs. In this work, an intelligent metaheuristic polar bear optimization algorithm (PBOA) is applied to solve the optimal capacitor placement and sizing problem in the radial distribution system (RDS) at various loading conditions. By formulating multiple objective functions for the annual operating cost (AOC), this work incorporates the cost of real power loss ( $$ P_{\text{loss}} $$ ) and various costs associated with SCs. The proposed technique is tested on various IEEE standard bus systems under different loading conditions. The proposed PBOA reduces AOC and $$ P_{\text{loss}} $$ of RDS while maintaining tolerable voltages at systems’ buses. The reductions of 51%, 35%, 26% and 53% in $$ P_{\text{loss}} $$ are observed for IEEE standard 15-, 33-, 34- and 85-bus systems, respectively, at 100% loading from their uncompensated cases. Similarly, reductions in AOCs for the same systems at 100% loading are 32%, 25%, 16% and 45%, respectively. These results prove superiority of proposed method over recent state-of-the-art algorithmic approaches. The results of this work can be useful for distribution system operators in achieving reliable and efficient operation of the power grid.

FPA Pareto optimality-based multiobjective approach for capacitor placement and reconductoring of urban distribution systems with solar DG units

ABSTRACT In this paper, Flower Pollination Algorithm (FPA)-based Pareto optimal approach is proposed for optimal network reconductoring of urban distribution systems integrated with solar Distributed Generations (DGs) along with shunt capacitor placement. Predefined fixed Solar DG installation is considered at every node for peak load operation. Multiple Pareto objective functions are formed considering the objectives of minimising conductor investment cost, annual energy loss cost at different load factors and the optimum sizing of shunt capacitors at optimum locations. The proposed algorithm is simulated on 51 bus and 85 bus radial distribution networks. The results obtained with the proposed Pareto FPA are compared with the conventional cost objective function and PSO Pareto algorithms. The economical savings with and without government subsidy on solar DG purchase are analysed. The effect of load growth and increase in solar DG penetration levels on the performance of distribution systems are demonstrated.

Optimation of Capacitor Bank Placement in Electric Network Using Genetic Algorithm

Minimizing losses in electric network should be considered the placing a shunt capacitor, the voltage level on each bus, the size and number of shunt capacitors to be used, and the supply of maximum and minimum of generator power. This paper is conducted the determination of location and size of shunt capacitor to be allocated in electric power transmission networks. The simulation using Genetic Algorithms (GA) method was applied to solve the problem of reactive power compensation optimation. To find out amount of compensation for voltage drop and power losses that occur in the system, a load flow analysis was performed using the Newton-Raphson method. The result of capacitor placement and capacitor capacity were shown the highest voltage conditions on bus 4 of 1.050 Mvar and the lowest on bus 24 of 9.69 Mvar. The optimization system was revealed the total losses system of 12.793 MW with a total generation cost of 15447.44 $/h for the capacitor reduction size of 18.8 Mvar. Therefore, the system can save 6.2 Mvar’s capacitors.

Optimal Reactive Power Management Problem: A Solution Using Evolutionary Algorithms

ABSTRACT In a competitive electricity power market, reactive power planning (RPP) is a pivotal matter for the power system researchers from operational and economical view points. RPP is concerned with the installation or removal of reactive power equipment in power system. This article proposes an effective way to find out the optimal parameter settings related to the system active power loss as well as operational cost. Genetic Algorithm (GA)-based strategy is applied to determine the optimal values of reactive power generation of generators, size of shunt capacitors, transformer tap settings prior to minimizing the system operating cost due to active power loss, installation cost of shunt capacitors at the weak nodes, and the cost of line-charging elements. The proposed approach is applied to IEEE 30 and IEEE 57 bus test system. Finally, a comparative analysis has been done to validate the efficacy of GA-based approach with some well-established meta-heuristic algorithms.

Optimal sitting and sizing of shunt capacitor for real power loss reduction on radial distribution system using firefly algorithm: A case study of Nigerian system

ABSTRACT Geometrical increase in power demand and high load density at the distribution ends of modern power systems have key consequential problems of high power loss and poor voltage profile, as a result of which the integrity of radial distribution networks to faithfully account for the energy received from transmission subsystems has been seriously undermined. This challenge is, however, being overcome by placement of shunt capacitors to supply the reactive power required for compensation; hence, optimal sitting and sizing of compensators has been intensively researched. As efficient as the use of meta-heuristic algorithms for joint optimal placement and sizing of the shunt capacitors are, employment of the approach on the Nigerian radial distribution system (RDS) is not yet popular as most of the earlier works reported rather used analytical and numerical programming approaches. In this study, therefore, the use of firefly algorithm (FA) on a Nigerian 11-kV feeder is presented as an approach to optimally site and size shunt capacitor for real power loss reduction on such network. Backward-forward sweep load flow technique, with voltage stability index (VSI), is employed to find the candidate buses where the shunt capacitors would be installed, then FA is employed to determine the optimal size required. This approach is implemented on a 34-bus 11-kV feeder and it is found out that the system’s real power loss reduced from 762.6419 to 597.7486 kW, while the minimum bus voltage magnitude was raised from 0.8295 to 0.8456 p.u. and the minimum system VSI was improved from 0.4741 to 0.5121 p.u. Based on these results, the proposed approach is, therefore, considered a promising technique for sitting and sizing shunt capacitor optimally in real practical RDS.

A Review of Cuckoo Search Algorithm Based Optimal Siting and Sizing of Shunt Capacitors in Radial Distribution Systems

Compensating reactive power deficiency on power grids is a central concern in the distribution of energy management systems. Several approaches have been adopted over time to minimize the total real power loss and enhancing bus voltage profile. Shunt capacitor has been used from time immemorial for addressing issue of reactive power compensation at the distribution end of power systems, and the extent of benefits derivable from its usage depend solely on correct siting and sizing. To this effect, meta-heuristic algorithms are promising optimization tools for achieving these objectives. This paper, therefore, presents a comprehensive review of cuckoo search algorithm based on optimal siting and sizing of shunt capacitors in radial distribution systems. The suitability, in addition to strengths and weakness of each approaches reported in the reviewed articles have been painstakingly x-rayed. Based on the review, it was observed that a two-stage approach is always adopted in the compensation process: the pre-selection of potential or sensitive nodes and the optimal sizing of shunt capacitors needed for the compensation. For the pre-location, Voltage Stability Index and Loss Sensitivity Factor were found to be comparatively less complex and highly suitable techniques. Another cogent discovery from this review is that less attention has been drawn to the use of cuckoo search algorithm by Nigerian researchers. Therefore, regarding Nigerian electric grid system, the use of cuckoo search algorithm in reactive power support presents a research gap for further investigations.

Data clustering‐based approach for optimal capacitor allocation in distribution systems including wind farms

Optimal placement and sizing of shunt capacitors are important issues to improve voltage profile and reduce power losses in distribution networks. In this regard, dealing with stochastic nature of wind farms (WFs), the issue becomes more complex in wind-integrated radial distribution networks. This study aims at optimal siting and sizing of shunt capacitors considering wind uncertainty. Application of probabilistic approach causes to access more real and extensive information about the network. To do so, Monte Carlo simulation (MCS) is employed to assess stochastic variation of wind farm output. As the salient feature of this research, K -means-based data clustering approach is utilised, in which all data-points of the output power of WFs are bunched into desired clusters to ease the solving of simple MCS. The voltage profile and power losses are analysed to do the optimal siting and sizing of capacitors. In order to assess the effectiveness of the proposed method, results are compared with the simple MCS that proves the efficiency of the proposed method from the viewpoint of computation time.

Application of hybrid heuristic technique for optimal shunt capacitors planning problem in radial distribution network

This paper proposes a hybrid HS–DE algorithm-based optimal node identification and sizing of shunt capacitors with an aim to enhance the performance of the radial distribution network. To enhance the exploitation power of harmony search algorithm (HSA), differential evolution algorithm (DE) is embedded with it. The combination of sensitivity analysis and hybrid HS–DE algorithm is used to trace the optimal solution for the installation of shunt capacitive compensation. A comprehensive objective function is formulated to minimize real power loss, improve the voltage stability and voltage profile of the distribution network. The suitability of the proposed hybrid HS–DE-based approach has been validated using IEEE 69 node radial distribution test network at three discrete load scenarios, and the result outcomes are compared with HSA, DE and other similar methods in the literature. The simulation results reflect the superiority and robustness of the hybrid HS–DE-based approach for solving shunt capacitor planning problem in radial distribution networks.

Optimal integration of shunt capacitor banks in distribution networks for assessment of techno-economic asset

This article presents optimal incorporation of shunt capacitor banks in distribution feeders for the purpose of reduction of power loss, total annual expenses and voltage deviations. Additionally, it improves the voltage level, power factor and voltage stability of the network. To attain these proposed goals, a new multi-objective function has been formulated subjected to some operating constraints. This problem has been solved through Modified Gbest-guided Artificial Bee Colony (MGABC) meta-heuristic optimization technique. This proposed methodology is divided into two parts. In first part, the sensitivity buses are determined using Loss Sensitivity Factor (LSF) approach. In second, the optimization algorithm identifies the optimal buses from derived sensitive buses along with optimal size of shunt capacitors. This proposed methodology is implemented on standard 34-bus and 118-bus distribution feeders. In addition, the achieved numerical outcomes have been compared to the various intelligent approaches for showing the viability and effectiveness of the proposed approach.

Impact of Ambient Temperature on Shunt Capacitor Placement in a Distorted Radial Distribution System

In electrical distribution systems, shunt capacitors are installed in order to reduce system losses, to enhance the voltage profile, and to free up system capacity. Nevertheless, the installation of shunt capacitors in distribution systems with distorted waveforms will magnify the distortion level of harmonics if they are not set at appropriate locations relative to the harmonics. This paper proposes a hybrid method to determine the placement and sizing of shunt capacitors in distorted radial distribution systems, taking into account the presence of harmonic distortion with consideration of ambient temperature effects, (this technique consists of the fuzzy expert system approach and the Genetic Algorithm method). This hybrid technique is applied to an IEEE 34-bus radial standard distribution system as well as a real distribution system in the Saudi Electricity Company. The simulation results show that harmonic distortion considerably reduces and the efficiency of distribution systems increases with a reduction in power loss and enhancement of voltage regulation.

Particle swarm optimization algorithm for simultaneous optimal placement and sizing of shunt active power conditioner (APC) and shunt capacitor in harmonic distorted distribution system

Due to development of distribution systems and increase in electricity demand, the use of capacitor banks increases. From the other point of view, nonlinear loads generate and inject considerable harmonic currents into power system. Under this condition if capacitor banks are not properly selected and placed in the power system, they could amplify and propagate these harmonics and deteriorate power quality to unacceptable levels. With attention of disadvantages of passive filters, such as occurring resonance, nowadays the usage of this type of harmonic compensator is restricted. On the other side, one of parallel multi-function compensating devices which are recently used in distribution system to mitigate voltage sag and harmonic distortion, performs power factor correction, and improves the overall power quality as active power conditioner (APC). Therefore, the utilization of APC in harmonic distorted system can affect and change the optimal location and size of shunt capacitor bank under harmonic distortion condition. This paper presents an optimization algorithm for improvement of power quality using simultaneous optimal placement and sizing of APC and shunt capacitor banks in radial distribution networks in the presence of voltage and current harmonics. The algorithm is based on particle swarm optimization (PSO). The objective function includes the cost of power losses, energy losses and those of the capacitor banks and APCs.

Derivative load voltage and particle swarm optimization to determine optimum sizing and placement of shunt capacitor in improving line losses

The purpose of this research is to study optimal size and placement of shunt capacitor in order to minimize line loss. Derivative load bus voltage was calculated to determine the sensitive load buses which further being optimum with the placement of shunt capacitor. Particle swarm optimization (PSO) was demonstrated on the IEEE 14 bus power system to find optimum size of shunt capacitor in reducing line loss. The objective function was applied to determine the proper placement of capacitor and get satisfied solutions towards constraints. The simulation was run over Matlab under two scenarios namely base case and increasing 100% load. Derivative load bus voltage was simulated to determine the most sensitive load bus. PSO was carried out to determine the optimum sizing of shunt capacitor at the most sensitive bus. The results have been determined that the most sensitive bus was bus number 14 for the base case and increasing 100% load. The optimum sizing was 8.17 Mvar for the base case and 23.98 Mvar for increasing load about 100%. Line losses were able to reduce approximately 0.98% for the base case and increasing 100% load reduced about 3.16%. The proposed method was also proven as a better result compared with harmony search algorithm (HSA) method. HSA method recorded loss reduction ratio about 0.44% for the base case and 2.67% when the load was increased by 100% while PSO calculated loss reduction ratio about 1.12% and 4.02% for the base case and increasing 100% load respectively. The result of this study will support the previous study and it is concluded that PSO was successfully able to solve some engineering problems as well as to find a solution in determining shunt capacitor sizing on the power system simply and accurately compared with other evolutionary optimization methods.