Optimal Capacitor Placement for IEEE 14 bus system using Genetic Algorithm

Transcription

1 Optimal Capacitor Placement for IEEE 14 bus system using Genetic Algorithm 1 Dnyaneshvar Y. Watpade, 2 P. M. Sonwane 1 Maharashtra State Electricity Distribution Company Limited, Nasik 2 K. K. Wagh Institute of Engineering Education & Research, Nasik Abstract Genetic Algorithm (GA) is a non-parametric optimization technique that is frequently used in problems of combinatory nature with discrete or continuous variables. Depending on the evaluation function used this optimization technique may be applied to solve problems containing more than one objective. In treating with multi-objective evaluation functions it is important to have an adequate methodology to solve the multiple objectives problem so that each partial objective composing the evaluation function is adequately treated in the overall optimal solution. In this paper the multiobjective optimization problem is treated in details and a typical example concerning the allocation of capacitor banks in a real distribution grid is presented. The allocation of capacitor banks corresponds to one of the most important problems related to the planning of electrical distribution networks. This problem consists of determining, with the smallest possible cost, the placement and the dimension of each capacitor bank to be installed in the electrical distribution grid with the additional objectives of minimizing the voltage deviations and power losses. As many other problems of planning electrical distribution networks, the allocation of capacitor banks are characterized by the high complexity in the search of the optimum solution. In this context, the GA comes as a viable tool to obtaining practical solutions to this problem. Simulation results obtained with a electrical distribution grid are presented and demonstrate the effectiveness of the methodology used. Keywords Genetic Algorithm, Multiple Objectives, Allocation of Capacitor Banks and Electric Distribution Grid. I. INTRODUCTION This Appropriate planning and maintenance of distribution systems are crucial for an efficient operation, with high quality services being provided to consumers. In this context, power quality becomes a very important issue, since it defines the final product delivered to consumers. Voltages must be maintained within the limits specified by regulatory agencies, without introducing harmonics, and the service should not suffer any interruptions. The maintenance of power quality regarding the voltage profile is taken into effect by using several measures, including preventive, corrective and emergency tools. Substation transformers equipped with tap-changing control can limit voltage variations within a certain range, thus reducing voltage deviations. However, with the load increase (for instance, at peak hours), tap position adjustments may happen to be insufficient for maintaining the voltage within the desired range, resulting in low voltages at the secondary windings of distribution transformers. Installing capacitor banks can be an interesting strategy for decreasing reactive power flows through the network, thus reducing voltage drops and real power losses. Several other benefits can be obtained with the appropriate allocation of capacitor banks, such as released feeder capacity, released distribution substation capacity, and financial benefits due to voltage improvement and loss reduction. The majority of power systems operate at a lagging power factor due to inductive loads and delivery apparatus (lines and transformers). Power systems are inductive in nature, and require additional reactive power flow from the power grid. But excessive reactive power demands result in reduced system capacity, increased losses, and decreased voltage, as well as higher operating costs. Shunt capacitor banks are able to compensate for var requirements, but bank size, location, the capacitor control method, and cost considerations are important issues that need to be optimized during the design phase. An ideal solution would be a capacitor placement tool able to weigh all these factors and that considers load levels. This solution should also be able to place capacitors for voltage support and power factor correction, while minimizing the total cost of installation and operation , IJIRAE- All Rights Reserved Page -43

2 AS DESCRIBED IN THE IEEE STANDARD (IEEE GUIDE FOR APPLICATION OF SHUNT POWER CAPACITORS), THE PURPOSES OF SHUNT CAPACITOR APPLICATIONS ARE: PURPOSE Var support Voltage control System capacity increase System power loss reduction Billing charge reduction BENEFITS To place shunt capacitors in power systems, it is necessary to: Determine bank size in kvar Determine connection location Determine a control method Determine a connection type (wye or delta) Yields a primary benefit for transmission systems and a secondary benefit for distribution systems. Yields a primary benefit for both transmission and distribution systems. Yields a secondary benefit for transmission systems and a primary benefit for distribution systems. Yields a secondary benefit for transmission systems and a primary benefit for distribution systems. Does not apply to transmission systems, but yields a primary benefit for distribution systems. The capacitor size and the appropriate location for voltage support and power factor correction can be determined in different ways. A common method applies rules of thumb techniques, and then runs multiple load flow studies to fine-tune the size and location. This method may not yield the optimal solution. And it can also be very time consuming and impractical for large systems. It is also important to minimize cost, while mathematically determining the capacitor size and location. Because this is an optimization issue, an optimization approach should be employed. A. OBJECTIVE : In the Objective group select the capacitor placement objective. This allows the OCP module to place capacitors to perform voltage support, power factor correction, or perform both at the same time. VOLTAGE SUPPORT : The OCP module checks voltage limits and places capacitors to meet the voltage limits when minimizing the cost. POWER FACTOR CORRECTION : The OCP module checks load power factor limits and places capacitors to meet the load power factor limits when minimizing the cost. BOTH: The OCP module checks voltage limits and load power factor limits, and places capacitors to meet the voltage limits and load power factor limits when minimizing the cost. GENETIC ALGORITHM FOR OCP GA is a search algorithm based on the mechanic of natural selection. Basically, a GA makes a population that evolves through time using reproduction and mutation process. Only individuals representing good solutions of the capacitor placement problem will survive longer, and their genetic information will be present in the next generation. At the end, after several generations, the interaction between these high quality individuals will produce a final population which represent the best solutions set of the problem. Three most important aspects of using GA are: Definition of objective function Definition and implementation of genetic representation Definition and representation of genetic operators Before of the genetic algorithm procedure, the real parameters of the problem must be represented in genetic algorithm language. It means that location and size of the capacitors used are codified as a chromosome. The representation chosen for this application is a chromosome divided in two parts. First part indexes location of the capacitors. The second part indicates the size of the capacitors used. In reproduction process, first we randomly select a pair of chromosomes, with the same structure. In the next step, chromosomes are treated separately; one for binary part and another for integer part. In binary part, for a given position, if two parents share value, the chromosome produced by reproduction will keep it. If values are different, the result for new chromosome is selected at random. In integer part, for a given position, result will be the average of values found in the parents. If result is not an integer value, it will be approximated until closer value at random , IJIRAE- All Rights Reserved Page -44

3 In mutation process, chromosome structure is modified. This change is performed at random, but there is a difference between binary and integer part. The GA was able to improve the quality of the randomly generated population very fast, and created good solutions in a very short time. In the selection of individuals for recombination, selection of a leader uniformly at random is required. The next step is to choose which one of the three supporters will take part in the recombination. This choice is also uniformly at random. Following this selection strategy, any pair of parents will belong to the same cluster. That makes the population act similarly to a multiple-population approach with a high migration rate. After the parents were selected, following the criterion described before, they are utilized as input parameters in the recombination operator. The recombination returns a new individual the offspring. Since the chromosome is composed of two distinct parts, they should be treated separately during the recombination process. The mutation operator aims to add diversity to the population of individuals. Similarly to the crossover, the mutation is divided into two parts. The first modifies the binary portion of the chromosome by choosing a position of the individual at random. The second part acts on the integer values by adding or subtracting a unity from its value. The choice of whether to add or subtract is also decided at random. Mutation is applied to 10% of the offspring. In general, higher mutation rates may slow down evaluation speed and hence should be avoided. After recombination and mutation, GA submits all or some of the new individuals to a local search procedure for the purpose of improving their fitness function. This local search acts at the first part of the chromosome, i.e., trying to improve capacitor location. If a specific location already has a capacitor, the local search tests the possibility of dropping that capacitor ( drop ). In case of deterioration of the solution, the position returns to the original value and the local search proceeds to the next one. This local search acts on the second part of the chromosome. It adjusts the sizes of the capacitors already present in the solution, trying to find the best size for each location. Only the sizes immediately above and below the present capacitor s size are tested. For instance, if a 600 kvar capacitor is installed in a given position, the procedure tries the capacitors with sizes 400 and 800 kvar, looking for any improvement. Such tries are executed in a similar manner to the add/drop procedure, in one capacitor at a time; accepting any change that improves the fitness. The fitness function quantifies the quality of the individual. Therefore, it will keep a close relation with the objective function of the problem. The first factor to be observed is the cost of the power losses, which takes into account the maximum voltage deviation observed in the distribution network s nodes for a given solution. Calculation of the power losses requires the execution of a load-flow algorithm. The objective of optimal capacitor placement is to minimize the cost of the system. This cost is measured in four ways: 1. FIXED CAPACITOR INSTALLATION COST 2. CAPACITOR PURCHASE COST 3. CAPACITOR BANK OPERATING COST (MAINTENANCE AND DEPRECIATION) 4. COST OF REAL POWER LOSSES Figure 1 The Genetic Algorithm Procedure , IJIRAE- All Rights Reserved Page -45

4 To understand in a clear way the applied methodology for equally considering the different evaluation functions (objectives) in a multi-objective fitness function it is initially made use of the fundamental concepts of the basic GA for a single evaluation function and, subsequently, this same principles are used so that each evaluation function behaves in the selection process as if the others didn t exist. The GA processing begins with an initial population in which the genetic material for each individual of the population is established randomly. The Evaluation Process calculates the evaluation values for each chromosome (solution). To avoid problems related to super-individuals or when the evaluation values of the individuals of the population are very close amongst themselves and very distant from the reference, fitness evaluation techniques are adopted such as Linear Normalization and Windowing. For this work the Linear Normalization is used as the fitness evaluation technique. This avoids not only the two mentioned aspects as well as it allows the evaluation values to be negative. THE GA PROCEDURE IS SUMMARIZED BY THE STEPS ILLUSTRATED IN FIGURE 1. In other words, the Linear Normalization is equal to establishing fitness values uniformly distributed in an interval and linearly related with the rank of the best fit individuals. Therefore, what defines the selection frequency of each individual in the population is its position in the rank of the best fit individuals. In the end of the evaluation process, the fitness values are passed to the selection process. The selection process characterizes the most important step of the GA, because it is this process that imitates the Natural Selection. The selection process is governed by selection techniques such as the Roulette- Wheel Selection, the Tournament Selection and the Stochastic Universal Sampling. The genetic operators of crossover and mutation act after the selection process and they determine the balance among the exploitation and exploration elements during the evalution of the Genetic Algorithm. The crossover is commonly accomplished by techniques such as the crossover of One-Point, Two-Points and Uniform. After the application of the genetic operators, a new population is obtained. According to Figure 1, all of the individuals of the population are changed by their descendants. But, with the purpose of adding components of memory of previous evolutions, individuals of the old population can be added to the new population. That is accomplished through techniques such as Elitism and Stead State. The methodology proposed in this work doesn't interfere in the way of processing the phases of the basic GA, described previously. It just adds one more particularity to the process that will be presented in the next section. The Lab WASF software, used to simulate the results presented in this paper, incorporate the basic GA configuration as well as the proposed methodology. B. CALCULATION OF THE TOTAL FITNESS VALUE In general, one aspect that distinguishes an evaluation function from another is its metric, such as MW, Volts, $, among others. It is common to observe the use of constant factors to penalize the values of the different evaluation functions. However, the values of these constants must be defined by the user in a trial and error approach and may cause additional difficulty in the interaction between the user and GA. In the following analyses it is considered only the evaluation process without losing of view the impacts in the selection process. It is supposed a population with M chromosomes and that each chromosome of the population must be evaluated by N evaluation functions. The value corresponding to the evaluation function i of the chromosome k is defined as: Evaluation ik, Where 1 k M and 1 i N. In this point, no effort should be made to join the evaluation functions. It is calculated the individuals aptitudes according to the adopted fitness evaluation technique (Linear Normalization). However, to apply this technique it is necessary to establish the rank values of the most capable individuals for each evaluation function. In this context, each one of the evaluation function i is used without considering the other functions, as what happens in a GA that makes use of a single evaluation function. Then, each evaluation function i will create a rank i. Figure 2 allows to observe the classification of the individuals of a hypothetical population for each rank i. In this figure, j is the placement of the chromosomes in the rank, i indicates the evaluation function to which the rank is associated and k is the index of the chromosome. Then, Figure 2 illustrates a rank matrix whose elements are the indexes k of the chromosomes, the lines are given by j and the columns by i. Each rank i creates a fitness value for each chromosome of the population and, therefore, for the N ranks there is, for each chromosome, N fitness values. Considering the technique of Linear Normalization the aptitude value of chromosome k with placement j in the rank i is given for: Fitnesski = max-[(max-min)/(1-m)].(j-1) Where k = rank[ j][i], 1 j M and 1 i N , IJIRAE- All Rights Reserved Page -46

5 Figure 2 Ranks associated to each evaluation function. The values of min and max are defined by the user. However, if the selection method is the Roulette-Wheel Selection and the size of the population is not very big, a good choice would be min=1 and max=m. This choice gives to the less fit chromosome a chance of survival equal to the difference among the chances of two any consecutive chromosomes. However, if the selection method is the Tournament, the less fit individual will be dead for any value min. In this case a convenient value would be min=0 and max=100. SYSTEM IDENTIFICATION INTRODUCTION A new and efficient approach for optimal capacitor configuration in IEEE 14 bus system is selected as case study. Determination of optimal locations and size of capacitor with an objective function for the constraints like maintaining the voltage profile and power factor as per standard. Other benefits of optimal capacitor configuration are reduction in power loss and enhancement of reliability of the system. The solution methodology genetic algorithm is used to optimal capacitor placement using ETAP software. The Capacitor Location or Placement for low voltage systems determines capacitor size, location and control schemes. Optimal capacitor placement is generally a hard combinatorial optimization problem that can be formulated as a nonlinear multiobjective problem. Many researchers had carried out work on optimal capacitor placement including Neural Network, Partial Swarm Optimization and Fuzzy theory. This dissertation work is based on Genetic Algorithm based optimal capacitor placement and sizing. ETAP software is used to evaluate the capacitor size and place in the system network. IEEE 14 bus system is selected as test system for OCP using ETAP software. This system consist of 14 bus in addition to 20 branches and 11 Load points. It is observed that capacitor placement in this system improves voltage profile attain the marginal power factor and reduces active and reactive losses. This also supports in capacity release. CAPACITOR PLACEMENT PROBLEMS CAN BE SOLVED IN TWO STEPS: Use of load flow model and find system parameters including feeder losses Minimize the cost function-min f- subject to constraints, like practical limits of voltage and capacitor size available, power factor. OBJECTIVE FUNCTION Min COST = ni=0 KpLP + KE LE + CC Where, KpLP= Peak Power Loss, KE LE = Energy Loss,CC = Cost of capacitor, N= No. of buses For constraint <= V=<1.05; pf=>0.95 ASSUMPTIONS CONSIDERED IN THE DEVELOPMENT OF THE OBJECTIVE FUNCTION ARE (a) Balanced network considered for simplicity (b) Capacitors are available in step size and (c) Capacitor placement affects only the flow of reactive power in the feeder. II. SYSTEM DESCRIPTION OF IEEE 14 BUS Optimal capacitor placement and sizing problem is formulated based on the requirements of benefits due to reliability cost, cost of capacitor, purchase cost, operating cost, maintenance cost and savings due to transmission and distribution loss for IEEE 14 bus system. The one line diagram of an IEEE-14 bus system is shown in Fig.1. The System data is taken from IEEE PES Society and discussed in Appendix A. In this system five generators placed at bus numbers 1,2,3,6 and 8. Trans- formers are placed in between buses 4-7; 4-9; 5-9. IEEE 14 bus system is benchmark system selected for the case study. The system is also graphically represented and tabulated in Appendix A. In short, this network consists of 14 buses, 20 branches, and 12 loads , IJIRAE- All Rights Reserved Page -47

6 TABLE 1: SYSTEM DESCRIPTION BUSES 14 BRANCHES 20 GENERATORS 5 POWER GRIDS 0 LOADS 12 Figure 3: IEEE 14 bus system III. LOAD FLOW ANALYSIS FOR IEEE 14 BUS SYSTEM During load Flow study, this research work is carried out for the system as it is for evaluation of power factor, capacity of transmission line, voltage profile and other parameters. As this research is oriented for optimal capacitor placement, the existing fixed capacitors in the network is removed first and then load flow is carried out before capacitor placement as well as with capacitor placement. TABLE 2: LINE DATA FROM LOAD FLOW IN ETAP ID RATING RATE KV KW KVAR AMP % PF % LOADING V TERMAL BUS SHUNT KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA LOAD KVA , IJIRAE- All Rights Reserved Page -48

7 TABLE 3:GENERATOR DATA FOR LOAD FLOW IN ETAP ID RATING RATED KV MW MVAR AMP % PF % GENE RATION GEN_ MW GEN_2 40 MW GEN_3 0 MW GEN_6 0 MW GEN_8 0 MW LOAD FLOW OF IEEE 14 BUS ETAP based load flow study is carried out using ETAP and given in Table 2 Fig. 3 shows IEEE 14 bus system. The details of this system is also illustrated in Appendix A. OCP-PSO software initialize with ETAP based load flow data. Necessary information relating to bus and line is passed through OCP treatment in two modules. First module simulates objective function without capacitor and second module introduces PSO treatment with capacitor placement with Local and Global minima. IV. ETAP SIMULATION PROCESS FOR LOAD FLOW Figure 4: IEEE 14 bus system Load Flow Analysis Table 2 shows bus data simulations for bus voltage in per unit, rated voltage, active and reactive power loading and ampere loading on every bus. Table 3 indicates load data information regarding active and reactive power drawn by load, power factor load current, percentage loading and terminal voltage. All these information is essential in OCP simulation process which is developed in dot net framework. Table 2 shows load data without capacitor while Table 3 represents generator data. This useful data is then provided as input to OCP software module. Five generators are connected to bus 1, 2, 3,6, 8. Generator 1 is connected to swing bus and rated with MW as shown in Table 5.5. This generator is running with 100 % generation with MW, MVAr with leading power factor. Generator 2 is producing 40MW active and MVAr reactive powers. Whereas genera tors placed at buses 3,6, 8 are standby and used to absorb reactive power. IEEE 14 bus line data is shown in Table 2 with line number, active and reactive power flow, current flow, voltage drop in line and active and reactive power losses due to resistance and inductance of transmission line or transformer device. This line data is provided to OCP software for further evaluation process through two treatments in the module, one without capacitor and other with capacitor placement module. V. OCP MODULE IN ETAP Optimal Capacitor Placement module in ETAP consist, Optimal location & bank size Minimize installation & operation costs Individual source or average energy cost Voltage & power factor objectives Minimum, maximum, & average loading Branch capacity release & cost savings Review capacitor impact on the system Capacitor control method To place shunt capacitors in power systems , IJIRAE- All Rights Reserved Page -49

8 It is necessary to determine bank size in kvar, determine connection location, determine a control method and determine a connection type. The capacitor size and the appropriate location for voltage support and power factor correction can be determined in different ways. A common method applies rules of thumb techniques, and then runs multiple load flow studies to fine-tune the size and location. Unfortunately, this method may not yield the optimal solution and it can also be very time consuming and impractical for large systems. A. KEY FEATURES OF ETAP Calculate the most cost-effective installation locations and best bank size Minimize total installation and operation cost Consider voltage support and power factor correction Evaluate Capacitor control method Allow review of capacitor impact on the system Employ most advanced optimum techniques Figure 5: IEEE 14 bus system optimal capacitor placement B. FLEXIBLE OPERATION Show available locations Apply user-selected load categories Utilize individual and global constraints Handle unlimited network configurations Use only user selected installation locations Constrain maximum capacitors installed at a location to user specified quantity C. CAPABILITY OF ETAP OCP MODULE Advanced graphic user interface User friendly input and output Instantly view new capacitors Speed and precision control Integrated load flow results Standard Crystal reports D. PLOTTING IN ETAP Loss reduction savings during the planning period Capacitor operation cost during the planning period Profit during the planning period , IJIRAE- All Rights Reserved Page -50

9 E. REPORTING Capacitor properties Capacitor locations and sizes Load flow results for maximum, average and minimum loads Branch capacity release Cost summary VI. CALCULATION METHOD ETAP currently utilizes the genetic algorithm for optimal capacitor placement. The genetic algorithm is an optimization technique based on the theory of natural selection. A genetic algorithm starts with a generation of solutions with wide diversity to represent characteristics of the whole search space. By mutation and crossover, good characteristics are selected and carried to the next generation. The optimal solution can be reached through repeated generations. OCP uses the present worth method to perform alternative comparisons. It considers initial installation and operating costs, which include maintenance, depreciation, and loss reduction savings. OBJECTIVE FUNCTION OF OCP IN ETAP The objective of optimal capacitor placement is to minimize the cost of the system. This cost is measured in four ways: Fixed capacitor installation cost Capacitor purchase cost Capacitor bank operating cost (maintenance and depreciation) Cost of real power losses Cost can be represented mathematically as: minf = xic0i + QciC1i + BiC2iT + C2 TlPLi Nbus - No of bus candidate Xi - 0/1,0 means no cap installed at bus i C0i - Installation cost C1i - per kvar cost of capacitor bank Qci - Capacitor bank size in KVAr Bi - Number of capacitor banks C2i - Operating cost of per bank, per year T - Planning period(years) C2 - Cost of each kwh loss in Rs/kWh L - Load levels, maximum, average and minimum Tl - Time duration, in hours, of load level lpli - Total system loss at load level l Constraints The main constraints for capacitor placement are to meet the load flow constraints. In addition, all voltage magnitudes of load (PQ) buses should be within the lower and upper bars. Load Power Factor (PF) should be greater than the minimum. It may be a maximum power factor bar at unity. The constraints can be represented mathematically as: Vmin < V < Vmax PFmin PF VTHD V max THD Qci Bi KVAR ETAP based optimal capacitor placement for IEEE 14 bus system is studied. VII. SIMULATION AND RESULTS For this research work, a case study of IEEE 14 bus system is selected to implement optimal capacitor placement. ETAP has different module for reliability and optimal capacitor placement. This research work is carried out for ETAP based optimal capacitor placement for IEEE 14 bus. Adding KVAr through capacitor placement can/may improve voltage profile, modify power factor, decrease losses, improve reliability indices, decrease cost associated to reliability and lot of benefits. Most importantly capacitor placement should be profit oriented in addition to above benefits. all above parameters which modifies as number of capacitor increases while placing capacitor is evaluated. All these parameters are then compared with the results when no capacitor is placed. This comparison study is required to take decision whether to place a capacitor or not. This study includes voltage constraint, power factor constraint and both constraint separately At the same time, voltage constraint is studied for two different limits (i) 0.95 < V < 1.05 and (ii) 0.9 < V < 1.1 for 10 cases for this study. In ETAP software, OCP and reliability is evaluated separately and cost function is added such that the objective function developed should match with objectives of genetic algorithm technique used in ETAP. Before optimal capacitor placement in ETAP following parameters are set as bus constraints , IJIRAE- All Rights Reserved Page -51

10 TABLE 4 CONSTRAINTS APPLIED BUS ID %VOLTAGE (MIN) %VOLTAGE (MAX) P.F. (MIN) P.F. (MAX) BUS BUS BUS BUS BUS BUS BUS After applying these constraints ETAP proposed capacitor bank at following buses TABLE 5 CAPACITOR PLACEMENT AFTER OCP BUS NO CAPCITOR SIZE NO. OF CAPACITORS PLACED BUS 4 20 KVAR 8 BUS 5 20 KVAR 2 BUS 7 20 KVAR 14 BUS KVAR 100 BUS KVAR 37 BUS KVAR 11 BUS KVAR 88 Results are compared for loss reduction, p.f. improvement, capacity release in dissertation work before and after OCP implementation TABLE 6 BRANCH/CKT LOSS COMPARISON BEFORE OCP AND AFTER OCP BRANCH LOSSES BEFORE OCP LOSSES BEFORE OCP (KVAR) LOSSES AFTER OCP LOSSES AFTER OCP (KVAR) (KW) (KW) TOTAL TABLE 7 BUS % VTG COMPARISON BEFORE OCP AND AFTER OCP BUS NO. % VOLTAGE BEFORE OCP % VOLTAGE AFTER OCP BUS BUS BUS , IJIRAE- All Rights Reserved Page -52

11 BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS TABLE 8 BUS % P.F. COMPARISON BEFORE OCP AND AFTER OCP BUS NO % P. F. BEFORE OCP % P. F. AFTER OCP BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS BUS VIII. CONCLUSION In this paper, a new method for solving capacitor placement problem was described. It can provide specific location of fixed capacitors in order to reduce energy system's losses. The load variation, the energy cost and capacitors sizes easily found in market were considered in the model. The program developed can be used in radial systems with different topologies and load variation because it has flexible parameters. Also it can be used as an analysis tool to make planning studies or to take decisions about the convenience of a specific reactive compensation plan. Then is a powerful tool in the design of an electrical distribution system.so, the work presented is possible, cheap and reliable to find the optimal capacitor placement in a radial system. REFERENCES [1] Carpinelli, G. ; Celli, G. ; Mocci, S. ; Mottola, F.; Pilo, F.; Proto, D., Optimal Integration of Distributed Energy Storage Devices in Smart Grids, Smart Grid, IEEE Transactions on Volume: 4, Issue: 2 DOI: Year: 2013, [2] Biswas, S. ; Goswami, S.K. ; Chatterjee, A., Optimal distributed generation place- ment in shuntcapacitor compensated distribution systems considering voltage sag and harmonics distortions, Generation, Transmission & Distribution, IET Volume: 8, Is- sue: 5 Publication Year: 2014, [3] Hamid Reza Esmaeilian, Omid Darijany, Mohsen Mohammadian, Optimal place- ment and sizing of DG units and capacitors simultaneously in radial distribution networks based on the voltage stability security margin, Turkish Journal of Electrical Engineering & Computer Sciences, Published Online,2014, [4] Calderaro, V. ; Galdi, V. ; Piccolo, A. ; Conio, G. ; Fusco, R., Wind farm power plant: Optimal capacitor placement for reactive power compensation, Innovative Smart Grid Technologies Europe (ISGT EUROPE), th IEEE/PES Year: 2013, [5] Sathya Siva Chandan. G, Optimal Placement of Capacitor and Sizing in a Radial Distribution Network to Reduce Real Power Losses, International Journal of Scien- tific Engineering and Research (IJSER) ISSN (Online): Volume 2 Issue 9, September , IJIRAE- All Rights Reserved Page -53