Capacitor Banks In Distribution Networks Research Articles

Optimal distributed generators allocation with various load models under load growth using a meta-heuristic technique

Distribution network planning and operation are facing several problems, including asset congestion, voltage fluctuations, and system instability. The adequate planning and modeling of distributed generators and capacitor banks must quantify these problems. This article presents the optimal allocation of distributed generators in parallel with capacitor banks in distribution networks with single and multi-objectives using the Gazelle Optimization Algorithm (GOA) and Mountain Gazelle Optimization Algorithm (MGOA). The single objective framework includes technical objectives like minimization of active power losses. The multi-objective framework includes technical and non-technical objectives like simultaneously minimization of active power losses, voltage stability, and voltage deviation, and minimization of polluting greenhouse gases and total electricity purchase cost. Furthermore, these planning problems are investigated by three case studies on different nonlinear voltage-dependent models at two different loading conditions from future planning perspectives. The effectiveness and feasibility of the MGOA are evaluated on the IEEE standard 33 bus system. As a result, the MGOA demonstrates a remarkable reduction in technical and non-technical objectives in all types of distributed generator placement. Moreover, a comparative analysis of other existing research works validated the efficiency and feasibility of established algorithms at each use case with different load models by improving all the objective functions of network planning. In single-objective and multi-objective frameworks, the active power losses reduce to 94.42% and 93.57% in the voltage-independent model, respectively. Meanwhile, the non-technical objectives are also significantly improved for each load model, further validating the efficiency of the proposed algorithms.

Selection and Location of Fixed-Step Capacitor Banks in Distribution Grids for Minimization of Annual Operating Costs: A Two-Stage Approach

The problem regarding the optimal location and sizing of fixed-step capacitor banks in distribution networks with radial configuration is studied in this research by applying a two-stage optimization approach. The first stage consists of determining the nodes where the capacitor banks will be placed. In this stage, the exact mixed-integer nonlinear programming (MINLP) model that represents the studied problem is transformed into a mixed-integer quadratic convex (MIQC) model. The solution of the MIQC model ensures that the global optimum is reached given the convexity of the solution space for each combination of nodes where the capacitor banks will be installed. With the solution of the MIQC, the suitable nodes for the installation of the fixed-step capacitors are fixed, and their sizes are recursively evaluated in a power flow methodology that allows for determining the optimal sizes. In the second stage, the successive approximation power flow method is applied to determine the optimal sizes assigned to these compensation devices. Numerical results in three test feeders with 33, 69, and 85 buses demonstrate the effectiveness of the proposed two-stage solution method for two operation scenarios: (i) operation of the distribution system under peak load conditions throughout the year, and (ii) operation considering daily demand variations and renewable generation penetration. Comparative results with the GAMS software confirm the excellent results reached using the proposed optimization approach. All the simulations were carried out in the MATLAB programming environment, version 2021b, as well as using the Gurobi solver in the convex programming tool known as CVX.

On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks

The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.

Strategic integration of photovoltaic, battery energy storage and switchable capacitor for multi-objective optimization of low voltage electricity grid: Assessing grid benefits

Battery energy storage system has become an inevitable element in smart distribution network due to massive deployment of community level distributed photovoltaic power generation system. The battery energy storage system not only participates in the backup power supply but also have the potential to provide numerous distributed ancillary services. In this paper, Slime mold optimization algorithm is applied to optimally allocate the photovoltaic generation units, battery energy storage systems and switchable shunt capacitor banks in distribution network while minimizing the two objective functions i.e., active power loss of distribution system and annualized capital cost of integrated equipments (photovoltaic units, battery energy storage systems and shunt capacitors) simultaneously. The proposed optimization framework is implemented on an IEEE 33 bus distribution network for different cases and compared with Non-dominated Sorting Genetic Algorithm II. The comparison of simulation results for different cases reveals the promising advantages in various technical and economic issues along with an additional benefit of investment deferral for distribution feeder up-gradation up to a significant span of years.

A Mixed-Integer Linear Programming Model for Simultaneous Optimal Reconfiguration and Optimal Placement of Capacitor Banks in Distribution Networks

Optimal capacitor placement and network reconfiguration are well-known methods to minimize losses, enhance reliability, and improve the voltage profile of electric distribution networks (EDNs). Distribution network reconfiguration (DNR) consists of altering the system topology by changing the states of ties and sectionalizing switches, while the optimal placement of capacitors (OPCAs) involves sizing and finding the optimal location of capacitor banks within the distribution network for reactive power control. DNR and OPCAs are challenging optimization problems involving both integer and continuous decision variables. Due to the nature of these problems (combinatorial optimization problems), most approaches that deal with DNR and OPCAs resort to metaheuristic techniques, and they are limited to applications in small-size distribution networks. Although these techniques have proven to be effective when dealing with non-convex optimization problems, their main drawbacks lie in the fact that they require the fine-tuning of several parameters and do not guarantee the finding of a globally optimal solution. This paper presents a mixed-integer linear programming (MILP) model to solve simultaneous DNR and OPCAs in radial distribution networks. The proposed model can be solved by commercially available software; it guarantees to obtain globally optimal solutions and requires low computational effort when compared with metaheuristic techniques employed for the same purpose. Several tests were carried out on seven benchmark EDNs ranging from 33 to 417 buses. In all cases, the proposed methodology was able to replicate the results reported in the specialized literature. Regarding the DNR alone, a novel solution was found for the 119-bus test system which is 1.86 % better than that previously reported in the specialized literature. Furthermore, new solutions are reported for the simultaneous optimal DNR and OPCAs for medium and large-size EDNs. The power loss reduction in the test system ranged from 21.12 % to 68.93 % evidencing the positive impact of the proposed approach in EDNs.

Optimal Sizing and Placement of Capacitor Banks in Distribution Networks Using a Genetic Algorithm

Nowadays, response to electricity consumption growth is mainly supported by efficiency; therefore, this is the new main goal in the development of electric distribution networks, which must fully comply with the system’s constraints. In recent decades, the issue of independent reactive power services, including the optimal placement of capacitors in the grid due to the restructuring of the electricity industry and the creation of a competitive electricity market, has received attention from related companies. In this context, a genetic algorithm is proposed for optimal planning of capacitor banks. A case study derived from a real network, considering the application of suitable daily profiles for loads and generators, to obtain a better representation of the electrical conditions, is discussed in the present paper. The results confirmed that some placement solutions can be obtained with a good compromise between costs and benefits; the adopted benefits are energy losses and power factor infringements, taking into account the network technical limits. The feasibility and effectiveness of the proposed algorithm for optimal placement and sizing of capacitor banks in distribution systems, with the definition of a suitable control pattern, have been proved.

Optimal Selection and Location of Fixed-Step Capacitor Banks in Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

This paper deals with the problem of the optimal selection of capacitor banks in electrical AC distribution systems for minimizing the costs of energy losses during a year of operation through a discrete version of the vortex search algorithm (DVSA). This algorithm works with a hypersphere with a variable radius defined by an exponential function where a Gaussian distribution is used to generate a set of candidate solutions uniformly distributed around the center of this hypersphere. This center corresponds to the best solution obtained at the iteration t, which is initialized at the center of the solution space at the iterative search beginning. The main advantage of combining the exponential function with the Gaussian distribution is the correct balance between the exploration and exploitation of the solution space, which allows reaching the global optimal solution of the optimization problem with a low standard deviation, i.e., guaranteeing repeatability at each simulation. Two classical distribution networks composed of 33 and 69 nodes were used to validate the proposed DVSA algorithm. They demonstrated that the DVSA improves numerical reports found in specialized literature regarding the optimal selection and location of fixed-step capacitor banks with a low computational burden. All the simulations were carried out in MATLAB software.

Optimized Capacitor Placement Considering Load and Network Variability

This paper proposes a methodology for the optimized location and sizing of capacitor banks in distribution networks. The variabilities of system load and grid configuration are both considered. Cluster analysis on daily load curves is employed to model the load variability adequately, while changes in the grid configuration concern feeders’ reconfigurations associated with load transfers among them. Voltage profile improvement, energy loss reduction, and minimization of installation costs are pursued objectives, selected here for planning the investment in capacitor banks. The problem is combinatorial in nature and its solution using a genetic algorithm is proposed. Tests with a real distribution system are performed, exploring the knowledge about common network switching operations and employing system loading measurement data. The obtained results show the importance of adequately considering, during the planning phase, loading and topological conditions to which the distribution system will be submitted during operation.

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.

Optimal location and sizing of capacitor banks in distribution networks to reduce harmonic distortion and improve voltage profile using genetic algorithm

This paper considers the problem of determination of optimum locations and sizes of capacitor banks (CB) for reactive power compensation in distribution systems to reduce harmonic distortion and improve voltage profile. Genetic Algorithm (GA) was used for solving this non-linear multi-objective optimization problem with constraints. A detailed methodology was presented for solving the power flow problem at fundamental and higher harmonic frequencies of interest and models of network components in harmonic analysis. The proposed procedure was successfully tested on the standard IEEE 33-bus test system for three different objective functions. Calculations showed the efficiency of GA for solving this complex problem.

An approach for placement and sizing of capacitor banks in distribution networks with distributed wind generation

In this paper, a modified simulated annealing technique is proposed for the simultaneous improvement of power quality and optimal placement and the sizing of fixed capacitor banks in a modern distribution network. The latter is supplying a mix of linear and nonlinear loads imposing voltage and current harmonics. Besides, the network includes integrated variable-speed wind turbines as distributed generation. The stochastic power output of the wind generation is considered by performing the Monte Carlo simulation of the distribution power flow. Operational and power quality constraints include the bounds of node voltage magnitude, the node voltage total harmonic distortion, and the number/size of installed capacitors. The net annual economic saving is defined as the associated objective function that accounts for the cost of the released power capacity because of the power losses reduction, the cost change of energy losses, and the extra cost of the searched capacitor banks. Solution results are discussed for a model-distorted distribution system under different conditions. Copyright © 2012 John Wiley & Sons, Ltd.

Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in Distorted Distribution Networks

A genetic algorithm (GA), in conjunction with fuzzy logic (FL) (approximate reasoning), is proposed for simultaneous improvement of power quality (PQ) and optimal placement and sizing of fixed capacitor banks in distribution networks with nonlinear loads imposing voltage and current harmonics. Economic cost is defined as the objective function and includes the cost of power losses, energy losses, and that of the capacitor banks while the voltage limits, number/size of installed capacitors at each bus, and the PQ limits of harmonic standard IEEE-519 are considered constraints. Fuzzy approximate reasoning is used to calculate the fitness function in order to consider the uncertainty of decision making based on the suitability of constraints (STHD, SV) and the objective function (cost index) for each chromosome. Simulation results for the 18-bus and 123-bus IEEE distorted networks using the proposed GA-FL approach are presented and compared with those of previous methods. The main contribution is an improved fitness function for GA, capable of improving the objective function while directing the PQ constraints toward the permissible region using fuzzy approximate reasoning. This method leads to computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions while avoiding numerical problems in large systems.

Microgenetic Algorithms and Fuzzy Logic Applied to the Optimal Placement of Capacitor Banks in Distribution Networks

A microgenetic algorithm (MGA) in conjunction with fuzzy logic (FL) is proposed for solving the capacitor placement problem. The objective function includes economic savings obtained by energy loss reduction in contrast with acquisition and installation costs of fixed and switched capacitors. Voltage constraints are considered. A simple and efficient method for load-flow solution is used, with acceptable CPU time, even for very large distribution systems under full load. An approximate load-duration curve divided in different load levels is used to compute energy losses. A 34-bus test system is presented and the results are compared to the solution given by another search technique. This comparison confirms the efficiency of the proposed method which makes it promising to solve complex problems of capacitor placement in distribution feeders.