Optimal locations and sizing of capacitors in radial distribution systems using mine blast algorithm

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.

In this paper, the problem of optimal siting and sizing of capacitors is brought up using the Grey Wolf optimization Algorithm and Loss Sensitivity Factor. This Loss Sensitivity Factor is being used for screening the few most optimal sites (buses) for the placement of capacitors. Then these screened buses are taken as the search space in the optimization algorithm. The objective function is so designed that it reduces the total power loss. The algorithm is separately used on a single as well as three capacitor locations and the results for the same are shown. To check the feasibility of the proposed method, it is applied on standard 69 bus Radial Distribution System. Moreover, the results under different loading conditions (viz. 75% and 50% loading) are also shown to showcase the effectiveness of proposed 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.

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.

To reach an optimal size, location and commitment schedule of shunt capacitors on a yearly based operations planning interval under the fuzzy environment, a fuzzy set theory based multistage optimisation is developed, where the loads, source voltage and objective function are all expressed in fuzzy set notations. To verify its effectiveness, the proposed approach is applied to a real distribution system. Results from the simulation show the advantages of this approach over the conventional crisp shunt capacitors compensation method in radial distribution systems. This provides good prospects for its application in practical distribution system compensation problems in an environment of uncertainty and vagueness.

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.

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.

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.

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 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.

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.

Shunt capacitors are broadly applied in distribution systems to scale down power losses, improve voltage profile and boost system capacity. The amount of capacitors added and location of deployment in the system highly determine the advantage of compensation. A novel global harmony search (GHS) algorithm in parallel with the backward/ forward sweep power flow technique and radial harmonic power flow was used to investigate the optimal placement and sizing of capacitors in radial distribution networks for minimizing power loss and total cost by taking account load unbalancing, mutual coupling and harmonics. The optimal capacitor placement outcomes show that the GHS algorithm can reduce total power losses up to 60 kW and leads to more than 18% of cost saving. The results also demonstrate that the GHS algorithm is more effective in minimization of power loss and total costs compared with genetic algorithm (GA), particle swarm optimization (PSO) and harmony search (HS) algorithm. Moreover, the proposed algorithm converges within 800 iterations and is faster in terms of computational time and gives better performance in finding optimal capacitor location and size compared with other optimization techniques.

This paper presents a two-stage procedure to determine the optimal locations and sizes of capacitor in distribution network to achieve maximum energy savings. In first stage, loss sensitivity factor (LSF) is adopted to determine the optimal capacitor locations. Later stage, a new analytical approach is proposed to find the optimal capacitor sizes. The proposed method is implemented on well-known test cases such as 15-bus, 34-bus and 69-bus radial distribution networks. Besides the cost of energy savings, installation and operation costs have been considered in present investigation. The test results demonstrate the significance of the proposed method in energy savings compare to other methods as reported in literature survey.

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

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.