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

This paper presents a new approach to shunt capacitor placement in distribution systems having customers with different load patterns. The allocation of capacitors is considered in a system comprising a network of feeders fed from an upstream equivalent transmission system through a substation transformer. The benefits of capacitor placement, such as the system capacity release and reduction of overall power and energy losses, are considered. The fast method of total energy loss calculation based on the computation of the moments of normalized daily load curves is used to calculate the annual energy loss reduction. An example of optimal capacitor allocation in a distribution system is presented in which customers with commercial, urban residential, rural and light industrial load patterns are considered.

This work presents a hybrid heuristic search algorithm called Moth Swarm Algorithm (MSA) in the context of power loss minimization of radial distribution networks (RDN) through optimal allocation and rating of shunt capacitors for enhancing the performance of distribution networks. With MSA, different optimization operators are used to mimic a set of behavioral patterns of moths in nature, which allows for flexible and powerful optimizer. Hence, a new dynamic selection strategy of crossover points is proposed based on population diversity to handle the difference vectors Lévy-mutation to force MSA jump out of stagnation and enhance its exploration ability. In addition, a spiral motion, adaptive Gaussian walks, and a novel associative learning mechanism with immediate memory are implemented to exploit the promising areas in the search space. In this article, the MSA is tested to adapt the objective function to reduce the system power losses, reduce total system cost and consequently increase the annual net saving with inequity constrains on capacitor size and voltage limits. The validation of the proposed algorithm has been tested and verified through small, medium and large scales of standard RDN of IEEE (33, 69, 85-bus) systems and also on ring main systems of 33 and 69-bus. In addition, the obtained results are compared with other algorithms to highlight the advantages of the proposed approach. Numerical results stated that the MSA can achieve optimal solutions for losses reduction and capacitor locations with finest performance compared with many existing algorithms.

Reduction of I2R loss in distribution systems is very essential to improve the overall efficiency of power delivery. The I2R loss can be separated into two parts based on the active and reactive components of branch currents. The paper presents a method of minimising the loss associated with the reactive component of branch currents by placing shunt capacitors. This method first determines a sequence of nodes to be compensated by capacitors. The size of the optimal capacitor at the compensated nodes is then determined by optimising the loss saving equation with respect to the capacitor currents. The performance of the proposed method was investigated on two distribution systems consisting of 15 and 33 buses and it was found that a significant loss saving can be achieved by placing optimal capacitors in the system.

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).

This article presents a simple method for investigating the problem of contemporaneously choosing optimal location and size of shunt capacitors in three-phase unbalanced radial distribution systems. The main objective function formulated consists of two terms: cost of energy loss and cost related to capacitor purchase and capacitor installation. The problem of choosing optimal locations and sizes for shunt capacitors in an unbalanced radial distribution system is addressed with the two algorithms in this article—one is for selecting the best locations of capacitor placement and candidate node identification algorithm; the second is for the sizing of capacitors, a variational technique algorithm according to available standard size of capacitors. The objective function used in this article is to maximize the net savings in the distribution system. This article presents the results of simulations for 25-bus and IEEE 37-bus unbalanced radial distribution systems.

The problem of capacitor placement on a radial distribution system is formulated and a solution algorithm is proposed. The location, type, and size of capacitors, voltage constraints, and load variations are considered. The objective of capacitor placement is peak power and energy loss reduction, taking into account the cost of the capacitors. The problem is formulated as a mixed integer programming problem. The power flows in the system are explicitly represented, and the voltage constraints are incorporated. A solution method has been implemented that decomposes the problem into a master problem and a slave problem. The master problem is used to determine the location of the capacitors. The slave problem is used by the master problem to determine the type and size of the capacitors placed on the system. In solving the slave problem, and efficient phase I-phase II algorithm is used.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Shunt capacitors placement is addressed in this paper. A cost based model to find the optimal size and location of shunt capacitors in a power distribution networks is proposed in which the objective is to minimize the total annual cost function of capacitor placement and power losses. Biogeography-Based Optimization (BBO) algorithm is adopted in this work to minimize the cost function while satisfying system constraints. The proposed method is applied to 10, 15, 34 and 69-bus radial distribution networks and the obtained results are compared to previous reported results.

Optimal reconfiguration and capacitor allocation in radial distribution systems for energy losses minimization

In this paper we describe a new technique for placing fixed capacitors in radial distribution systems based on genetic algorithms (GA). Actually, current optimization models of capacitor placement only consider losses reduction and voltage profile simultaneously, but the compensation cost and the load changes are not taking into account as part of the objective function. Also, the result may be not the best choice because this is a very large optimization problem and there are too many combinations. We present here a general approach for the optimal solution of this problem considering all the parameters of the distribution system involved: capacitor cost, voltage, angle and load changes per hour. An exhaustive search through all possible solutions is needed. Therefore, GA is an ideal candidate to solve this situation. Working with this algorithm, a Microsoft Excel Program has been developed in order to answer the capacitor placement problem for any kind of radial distribution system. The test results are presented along with the discussion of the algorithm.

In this paper, a problem of optimal capacitor placement and conductor selection is solved for a nonuniform radial distribution system with lateral subfeeders. In this optimization problem the loads of the system is considered to be nonlinear. The voltage of each bus along the feeder after capacitor and conductor installation is calculated for each harmonic order. The total voltage and current harmonic distortions are calculated and added to the fundamental values. The new updated voltage and current values are used to solve for the capacitor and conductor optimal size and location as well as the net dollar savings. The algorithm is applied on a 27-bus radial distribution system with lateral subfeeders, and the results are given for different cases; before and after optimization.

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 aims to propose an optimization method for optimal allocation of shunt capacitors in distribution networks to minimize the total active power losses and total energy cost with enhancing the voltage profile. The proposed method is carried out using two stages. In the first stage, candidates’ buses are determined using fuzzy logic control based on Normalized Loss Sensitivity Factor (NLSF) and voltage magnitude at each bus. The system buses are ordered descending based on the fuzzy output where the highest buses are chosen as candidate buses. In the second stage, a recent metaheuristic technique, Sine Cosine Algorithm (SCA), is used to calculate the shunt capacitor size where the candidate buses are used as initialized locations to decrease the search area of SCA. The final optimal size and location of shunt capacitors are specified through the SCA iterative process. The developed optimization method is comprehensively compared with the other optimization methods used for the same pattern to prove its effectiveness. The simulation results are performed on the 15-bus and 69-bus distribution networks using MATLAB M. Files.

This study introduces a multi-criteria optimization approach using the Grey Wolf Optimizer (GWO) algorithm to determine the optimal capacity, locations of DG units and capacitor banks, and network reconfiguration in distribution systems. The objective function incorporates six key performance metrics: real losses, imaginary losses, voltage variation, voltage stability index, section load ability, and current balancing index. The proposed GWO technique was evaluated on IEEE 33- and 69-bus systems and benchmarked against Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Results demonstrate that GWO effectively optimizes the placement and sizing of DGs and capacitor banks under diverse conditions, enhancing system performance and reducing active power losses.

Chapter 10 - Optimal Placement and Sizing of Shunt Capacitor Banks in the Presence of Harmonics

Assessment of customer power supply reliability is an important part of distribution system operation and planning. Distribution system reliability assessment is a measure of continuity and quality of power supply to the consumers, which mainly depends on interruption profile, based on system topology and component reliability data. The paper mainly describes about the radial Distribution system reliability is evaluated in two methods. One by placing capacitor at weak voltage nodes for improvement of voltage profiles, reducing the total losses. Second way by improving reliability indices by placing protective equipment (isolators) in the feeder. This paper present an effective approach for real time evaluation of distribution power flow solutions with an objective of determining the voltage profiles and total losses. To improve the voltage profiles and reducing losses by placing capacitors at weak voltage profile nodes using Particle Swarm Optimization (PSO) technique. The Distribution System Reliability Indices are also calculated for the existing radial distribution system before and after placement of isolator. In this paper we have considered the load diversity factor for analysis of load data for real time system. Two matrices the bus-injection to branch-current matrix (BIBC), the branch-current to bus voltage matrix (BCBV) and a simple matrix multiplication are used to obtain power flow solutions. This paper also presents an approach that determines optimal location and size of capacitors on existing radial distribution systems to improve the voltage profiles and reduce the active power loss. The performance of the method was investigated on an 11kV real time Upadyayanagar radial distribution feeder as system of case study. A matlab program was developed and results are presented.