Optimal capacitor placement for distribution systems using genetic algorithms

Installation of capacitors in primary and secondary networks of distribution systems is one of the efficient methods for energy and peak load loss reduction. Also voltage profile in the feeder is improved and static voltage stability is enhanced. The main challenge is the determination of optimal location and size of fixed and switchable capacitors with respect to network configuration, distribution of load in the feeder, time variation of load and uncertainty in load forecasting or load allocation process. To solve this complex problem, an efficient method for simultaneous allocation of fixed and switchable capacitors in radial distribution systems is presented. Energy and peak load loss reduction, and capacitor cost are considered in the cost function. Time variation and uncertainty of load are also involved in problem formulation. Genetic algorithm with a new coding as two rows chromosomes is used for optimisation. Numerical studies show the effectiveness of the proposed procedure.

This paper presents an efficient methodology for the optimal location and sizing of fixed and switched shunt capacitors in radial distribution systems using Genetic Algorithms. Unlike the conventional objective function, a new constraint objective cost function has been formulated to maximize the net annual savings by minimizing real power loss and optimizing the purchase cost of shunt capacitors while maintaining a better node voltage profile of the system. The application results of the proposed method are demonstrated and compared with other method available in literature. The suitability of the proposed method is tested on a large-scale distribution system. The effectiveness of the proposed algorithm is indicated by higher savings in energy loss, lower amounts of capacitive compensation, better allocation of fixed and switched shunt capacitor ratings and increased net annual savings.

Controlling active/reactive power in distribution systems has a great impact on its performance. The placement of distributed generators (DGs) and shunt capacitors (SCs) are the most popular mechanisms to improve the distribution system performance. In this line, this paper proposes an enhanced genetic algorithm (EGA) that combines the merits of genetic algorithm and local search to find the optimal placement and capacity of the simultaneous allocation of DGs/SCs in the radial systems. Incorporating local search scheme enhances the search space capability and increases the exploration rate for finding the global solution. The proposed procedure aims at minimizing both total real power losses and the total voltage deviation in order to enhance the distribution system performance. To prove the proposed algorithm ability and scalability, three standard test systems, IEEE 33 bus, 69 bus, and 119-bus test distribution networks, are considered. The simulation results show that the proposed EGA can efficiently search for the optimal solutions of the problem and outperforms the other existing algorithms in the literature. Moreover, an economic based cost analysis is provided for light, shoulder and heavy loading levels. It was proven, the proposed EGA leads to significant improvements in the technical and economic points of view.

This paper presents optimized distribution loss evaluation in ring main distribution system with Distributed Generation (DG) placement, reconfiguration and capacitor placement using Genetic Algorithm (GA). This paper compare results obtained with Radial Distribution System (RDS) and Ring Main Distribution System (RMDS) and proves that loss can be minimized just by modifying the type of distribution network from RDS to RMDS and can further be reduced to high level by DG and capacitor placements at strategic locations. Genetic algorithm (GA) is used to evaluate highly non-linear problem of evaluating total power loss of RDS and RMDS which are subjected to operational equality & inequality constraints. The efficacy of this method is illustrated by comparative analysis of the results with Harmony search algorithm (HSA) and GA from the literature. The solution to the objective of minimization of total loss is obtained using MATLAB optimization toolbox and MATLAB programming environment on standard IEEE 33-bus test system with variety (different/various combinations) of case studies.

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.

In this paper, a mine blast algorithm (MBA) is proposed for optimal allocations and sizing of capacitors in various distribution systems. First, the most candidate buses for installing capacitors are suggested using loss sensitivity factors (LSF). Then, the proposed MBA is employed to deduce the size of capacitors and their locations from the elected buses. The objective function is designed to reduce the total cost and, consequently, to increase the net saving per year. The proposed algorithm is tested on 10 and 85 bus radial distribution systems. The obtained results via the proposed algorithm are compared with others to highlight their benefits. Moreover, the results are introduced to verify the effectiveness of the suggested algorithm to minimize the losses and total cost and to enhance the voltage profile and net saving for various distribution systems and loading conditions.

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allotment of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which include limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus distribution network and the results are compared with conventional binary particle swarm optimization.

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.

Summary Random noise perturbs objective functions in a variety of practical optimization problems, and genetic algorithms (GAs) have been widely proposed as an effective optimization tool for dealing with noisy objective functions. In this paper, we investigate GAs applied to objective functions that are perturbed by multiple sources of additive and multiplicative noise that each take on finitely many values. We reveal the convergence properties of GAs by constructing and analyzing a Markov chain that explicitly models the evolution of the algorithms in noisy environments. Our analysis shows that this Markov chain is indecomposable; it has only one positive recurrent communication class. Using this property, we establish a condition that is both necessary and sufficient for GAs to eventually (i.e., as the number of iterations goes to infinity) find a globally optimal solution with probability 1. Similarly, we identify a condition that is both necessary and sufficient for the algorithms to eventually with probability 1 fail to find any globally optimal solution. We also discuss how the transition probabilities of the chain can be used to derive an upper bound for the number of iterations sufficient to ensure with certain probability that a GA selects a globally optimal solution upon termination.

The use of electricity will continue to increase along with technological developments and population growth so that electricity provider must maintain the availability of energy for costumers with various complex problems. Distributed Generation (DG) and Capacitor placement and Network Reconfiguration are optimization technique that have been hotly discussed in the last decade regarding power quality improvements in Radial Distribution System. In this paper discusses the effect of harmonic spreading on Radial Distribution System after optimizing DG and Capacitor placement and Network Reconfiguration simultaneously using Particle Swarm Optimization Method (PSO) by considering of the use non-linear load. The objective function in the from of minimizing active power loss and THD is considered to be able to reduce the spread of harmonic presented in several case studies. The more DG and Capacitor numbers are placed with network reconfiguration simultaneously, the better power quality in the system with a good and efficient computing approach.

In this paper, a new design methodology for determining the size, location, type and number of capacitors to be placed on a radial distribution system is presented. The objective is to minimize the peak power losses and the energy losses in the distribution system considering the capacitor cost. A sensitivity analysis based method is used to select the candidate locations for the capacitors. A new optimization method using a genetic algorithm is proposed to determine the optimal selection of capacitors. Test results have been presented along with the discussion of the algorithm. >

Optimal capacitor allocation in radial distribution systems for loss reduction: A two stage method

This study presents a pelican optimization algorithm (POA) based technique for optimizing the integration of capacitor banks in radial power distribution systems. The proposed approach adopts a hybrid approach that combines the loss sensitivity factors (LSF) and the POA to determine the appropriate placement and sizing of the capacitor banks, respectively, for best system performance. The proposed methodology is tested on the IEEE 33-bus distribution system using MATLAB software. The performance for integrating two capacitor banks is compared to that of the particle swarm optimization (PSO) and the genetic algorithm (GA) methods. The proposed POA method achieved a significant improvement in system performance. Specifically, it reduced active power losses (PLoss) by 68.08%, which surpasses the reductions achieved by PSO (61.79%) and GA (57.73%). In the case of reactive power loss (QLoss), the POA-based approach also proved superior with a 39.035% reduction, while PSO and GA-based methods achieved 28.50% and 22.59% reductions, respectively. These results underscore the effectiveness of the POA-based approach in capacitor bank placement and sizing, making it a promising candidate for enhancing voltage profiles and minimizing power losses in radial distribution systems.

This paper presents a new methodology for optimal capacitor placement problem in Radial Distribution System (RDS) in order to reduce the total power losses, to improve the voltage profile, to enhance voltage stability, and to achieve more energy savings. The main contribution of this paper is (i) fuzzy expert system (FES) is used to find the optimal locations for capacitor placement, (ii) A novel power loss sensitivity method is applied to determine the optimal capacitor size, (iii) Impact of capacitor placement on the system performance of the radial distribution systems is evaluated in terms of voltage profile, power losses, energy savings & voltage stability index (VSI), (iv) the annual cost of energy loss, total annual cost and net savings. The combined fuzzy & novel power loss sensitivity method is implemented on Existing rural 15 bus system and standard IEEE-34 bus distribution system, and the results are compared with an existing PSO method and Fuzzy-Harmony search algorithm (HSA).

In order to increase the voltage profile and to reduce power loss in the distribution system shunt capacitors are to be installed at suitable locations in a large distribution system. When we place the capacitors optimally we will get some benefits. Placing a capacitor in a Electrical distribution system involves various factors like maximizing energy and peak power loss reduction by installing a capacitor. Location of nodes where the capacitor should be placed is decided by fuzzy expert system by incorporating a set of rules into it, Candidate nodes should be found for capacitor placement using fuzzy system. The objective function includes cost of power loss, energy loss and capacitor banks. Constraints include voltage limits, number and location of installed capacitors. Loss sensitivity factors are used to select the candidate location for capacitor placement. The proposed method is applied to 12 bus and 34 bus radial distribution system. Results show robustness of proposed method in solving this difficult task.