Optimal capacitor placement on radial distribution systems

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.

In distribution system, the size and location of shunt capacitors for peak power loss and energy loss reduction plays a vital role. This paper proposes a new method, Nelder-Mead particle swarm optimization (NM-PSO) for the optimal capacitor placement problem. The NM-PSO method is applied to IEEE 69-bus radial distribution system and the results obtained are compared with that of particle swarm optimization (PSO). Also, the problem has been reformulated to include the maintenance cost and economic factors such as inflation and interest rates. The results obtained clearly indicate the better performance of NM-PSO over PSO, confirming its superiority to PSO in finding the optimal solution and handling more complex, nonlinear objective functions.

Optimal capacitor placement for enhancing voltage stability in distribution systems using analytical algorithm and Fuzzy-Real Coded GA

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (Non Polynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

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.

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).

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

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.

Capacitor sizing and placement problem is an important task for planning studies in distribution networks. This task impacts on voltage regulation as well as the loadability of lines, which are key elements for modern distribution companies. However, the capacitor placement problem usually leads to a combinatorial optimization problem classified as a NP-hard. Because of its complexity, different models based on heuristic strategies have been proposed to solve this problem. In this work, an evolutionary strategy -as a global search methodology- is proposed. The corresponding capacitor placement problem is formulated as a second stage of the solution for the distribution planning problem when the planner deals with large distribution systems. This stage defines the placement and dimension of the required capacitor banks to reduce both losses and voltage drop. Final results are presented for a 4083 nodes system.

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.

Installing shunt capacitors in a radial distribution system can provide a lot of benefit to utility and users. There are many ways to install capacitors as long as the sizes do not exceed the original inductive reactive power of a system. But it is very difficult to determine the best locations and size of capacitors. In addition, the unbalance nature of distribution system make the placement becomes more complicated. Optimal placement of capacitor is a highly nonlinear optimization problem which requires discrete control variables. This paper proposed an artificial intelligence approach to obtain optimal total line loss reduction and total cost of capacitor while improving the voltage profile along the feeders. It was done by integrating the circuitry distribution model in SIMULINK with particle swarm optimization (PSO) technique constructed in MATLAB. The optimization process was done in two stage where the first stage is to determine the early optimal locations while second stage is to determine optimal sizes. A modified IEEE 13-bus three phase unbalanced radial distribution system is used to validate effectiveness of the proposed technique in solving the problem.

Radial distribution systems (RDSs), which dominate electricity delivery in many developing countries, are inherently prone to high technical losses and poor voltage regulation due to long feeder lengths and predominantly inductive loads. Optimal capacitor placement has therefore emerged as a cost-effective strategy for reducing power losses and enhancing voltage profiles. This paper presents a structured narrative review of optimization-based capacitor placement approaches applied to RDSs, synthesizing analytical, heuristic, and metaheuristic methods reported in the literature. The review systematically examines commonly used power-flow techniques and compares major optimization algorithms, including Genetic Algorithms, Particle Swarm Optimization, Ant Colony Optimization, and hybrid frameworks, with respect to solution quality, convergence behavior, computational effort, and practical applicability. The synthesis reveals broad consensus that metaheuristic methods outperform deterministic approaches in complex, nonlinear networks, while also highlighting important trade-offs: algorithms offering marginally higher loss reduction often incur increased computational cost or parameter sensitivity. The review further identifies persistent gaps related to load variability modeling, economic integration, and real-world validation, particularly in data-constrained rural networks. From a practical perspective, the findings indicate that no single optimization technique is universally superior; rather, algorithm selection should be guided by network characteristics, data availability, and implementation constraints. The paper concludes by outlining context-specific research directions to support the deployment of optimization-based capacitor planning in developing power systems such as those in Uganda.

Today reliability is a significant boundary in Electrical industry to accomplish high security and ampleness of the system. There are three significant boundaries required to present in reliability analysis viz client composite damage function, average load and failure rate. The vast majority of the intelligent techniques incorporate capacitor cost and reserve funds because of decrease in power through loss. In this research work notwithstanding capacitor cost and advantages because of power loss, reliability cost is likewise included. This paper introduces the novel method for failure rate using thermal loading and life expectancy of transformer and overhead transmission line. Modified failure rate is applied to calculate reliability cost and hence accordingly objective function is calculated. Particle swarm optimization (PSO) is used as an intelligent tool to find the optimal locations and capacitor sizing using dot net framework based software. Before applying PSO tool, IEEE 30 bus system is passed through ETAP load flow study. Load flow data is processed through optimal capacitor placement (OCP) module designed in developed novel software. This paper focuses on OCP for reliability enhancement in voltage constraint while applying objectives to PSO tool. Results are used for comparison of voltage profile, power factor improvement, loss reduction, capacity release and objective cost reduction in OCP.

Effects of unbalances and harmonics on optimal capacitor placement in distribution system

With increasing non-linear loads, harmonic currents are injected into networks that distort all of the voltages and currents. This is an issue that must be considered when making a decision regarding capacitor placement so that resonance will not occur, and therefore losses and severe stress on the network equipment is prevented. In this paper, a new method is proposed based on the harmonic source identification and current separation to cope with non-linear loads in the capacitor placement problem. The intrinsic difference between linear and non-linear loads in their V-I characteristics can be used to model harmonic sources. Also, a genetic algorithm is used to solve the related optimisation problem. To validate the proposed method, an IEEE 33-bus test system is simulated. Based on the simulation results, by using the proposed method, the influence of harmonics is considered properly. Consequently, corresponding savings are increased and also the solution will not cause any resonance.