Industrial Engineering Letters                                                                 www.iiste.orgISSN 2224-6096...
Industrial Engineering Letters                                                                 www.iiste.orgISSN 2224-6096...
Industrial Engineering Letters                                                                  www.iiste.orgISSN 2224-609...
Industrial Engineering Letters                                           www.iiste.orgISSN 2224-6096 (print) ISSN 2225-058...
Industrial Engineering Letters                                                               www.iiste.orgISSN 2224-6096 (...
Industrial Engineering Letters                                                               www.iiste.orgISSN 2224-6096 (...
Industrial Engineering Letters                                                               www.iiste.orgISSN 2224-6096 (...
Industrial Engineering Letters                                                               www.iiste.orgISSN 2224-6096 (...
The Name of the Journal of the Journal                                                                                    ...
The Name of the Journal of the Journal                                                                  www.iiste.orgISSN ...
The Name of the Journal of the Journal                                                        www.iiste.orgISSN 2222-XXXX ...
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Dg source allocation by fuzzy and sa in distribution system for loss reduction and voltage improvement

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Dg source allocation by fuzzy and sa in distribution system for loss reduction and voltage improvement

  1. 1. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011DG Source Allocation By Fuzzy and SA in Distribution System for Loss Reduction and Voltage Improvement M.Padma Lalitha (Corresponding author) Professor & HOD,Department of Electrical & Electronics Engineering, Annamacharya Institute of Techonology & Sciences, Rajampet, A.P. Tel# +9848998643, e-mail:padmalalitha_mareddy@yahoo.co.in V.C.Veera Reddy Professor & HOD,Electrical & Electronics Engineering Dept , S.V.U.C.E,S.V.University,Tirupathi, e-mail:veerareddy_vc@yahoo.com N.Sivarami Redy Professor & HOD,Department of Mechanical Engineering, Annamacharya Institute of Techonology & Sciences, Rajampet, A.P. Tel# +9848998645, e-mail:siva.narapureddy@gmail.comAbstractDistributed Generation (DG) is a promising solution to many power system problems such as voltageregulation, power loss, etc. This paper presents a new methodology using Fuzzy and SimulatedAnnealing(SA) for the placement of Distributed Generators(DG) in the radial distribution systems toreduce the real power losses and to improve the voltage profile. A two-stage methodology is used for theoptimal DG placement . In the first stage, Fuzzy is used to find the optimal DG locations and in the secondstage, Simulated Annealing algorithm is used to find the size of the DGs corresponding to maximum lossreduction.. The proposed method is tested on standard IEEE 33 bus test system and the results arepresented and compared with different approaches available in the literature. The proposed method hasoutperformed the other methods in terms of the quality of solution and computational efficiency.Keywords: DG placement, Meta heuristic methods, Simulated Annealing, Genetic Algorithm, lossreduction, radial distribution system1. IntroductionDistributed or dispersed generation (DG) or embedded generation (EG) is small-scale power generationthat is usually connected to or embedded in the distribution system. The term DG also implies the use ofany modular technology that is sited throughout a utility’s service area (interconnected to the distribution orsub-transmission system) to lower the cost of service (Pica 2001). The benefits of DG are numerous(J.Morrison 2001)and the reasons for implementing DGs are an energy efficiency or rational use of energy,deregulation or competition policy, diversification of energy sources, availability of modular generatingplant, ease of finding sites for smaller generators, shorter construction times and lower capital costs ofsmaller plants and proximity of the generation plant to heavy loads, which reduces transmission costs. Alsoit is accepted by many countries that the reduction in gaseous emissions (mainly CO 2) offered by DGs ismajor legal driver for DG implementation (P. Chiradeja et al 2004).The distribution planning problem is to identify a combination of expansion projects that satisfy loadgrowth constraints without violating any system constraints such as equipment overloading (R.E. Brown etal 1997). Distribution network planning is to identify the least cost network investment that satisfies loadgrowth requirements without violating any system and operational constraints. Due to their high efficiency,54 | P a g ewww.iiste.org
  2. 2. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011small size, low investment cost, modularity and ability to exploit renewable energy sources, areincreasingly becoming an attractive alternative to network reinforcement and expansion. Numerous studiesused different approaches to evaluate the benefits from DGs to a network in the form of loss reduction,loading level reduction (E. Diaz-Dorado et al 2002 M. Mardaneh et al 2004 and Silvestri et al 1994).Naresh Acharya et al (2006) suggested a heuristic method in to select appropriate location and to calculateDG size for minimum real power losses. Though the method is effective in selecting location, it requiresmore computational efforts. The optimal value of DG for minimum system losses is calculated at each bus.Placing the calculated DG size for the buses one by one, corresponding system losses are calculated andcompared to decide the appropriate location. More over the heuristic search requires exhaustive search forall possible locations which may not be applicable to more than one DG. This method is used to calculateDG size based on approximate loss formula may lead to an inappropriate solution.In the literature, genetic algorithm and PSO have been applied to DG placement (G.Celli etal 2005 andC.L.T.Borges et al 2006) In all these works either sizing or location of DGs are determined by thesemethods. This paper presents a new methodology using Simulated Annealing algorithm (Kirkpatrick, S.,1984, Metropolis, N 1956 and Pincus, M., 1970) for the placement of DG in the radial distributionsystems. The advantage of this algorithm is that it does not require external parameters such as selection,cross over rate and mutation rate as in case of genetic algorithm and differential evolution and it is hard todetermine these parameters in prior. The other advantage is that the global search ability in the algorithm isimplemented by introducing hyper mutation which differs from mutation in GA in two ways. One is themutation rate is very high that every solution is mutated here and the second one is the mutation is not asingle bit mutation.In this paper, the optimal locations of distributed generators are identified based on the Fuzzymethod(M.Padma Lalitha et al 2010) and Simulated Annealing technique which takes the number andlocation of DGs as input has been developed to determine the optimal size(s) of DG to minimize real powerlosses in distribution systems. The advantages of relieving SA method from determination of locations ofDGs are improved convergence characteristics and less computation time. Voltage and thermal constraintsare considered. The effectiveness of the proposed algorithm was validated using 33-Bus DistributionSystem [19].To test the effectiveness of proposed method, results are compared with different approachesavailable in the literature. The proposed method has outperformed the other methods in terms of the qualityof solution and computational efficiency.2. Theoretical Background 2The total I R loss (P ) in a distribution system having n number of branches is given by: L n PLt   I i2 Ri (1) i 1 thHere I is the magnitude of the branch current and R is the resistance of the i branch respectively. The i ibranch current can be obtained from the load flow solution. The branch current has two components, activecomponent (I ) and reactive component (I ). The loss associated with the active and reactive components of a rbranch currents can be written as: n PLa   I ai Ri 2 (2) i 1 n PLr   I ri Ri 2 (3) i 1Note that for a given configuration of a single-source radial network, the loss P associated with the active Lacomponent of branch currents cannot be minimized because all active power must be supplied by thesource at the root bus. However by placing DGs, the active component of branch currents arecompensated and losses due to active component of branch current is reduced. This paper presents amethod that minimizes the loss due to the active component of the branch current by optimally placing theDGs and thereby reduces the total loss in the distribution system. A two stage methodology is applied here.In the first stage optimum location of the DGs are determined by using fuzzy approach and in the second55 | P a g ewww.iiste.org
  3. 3. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011stage SA method is used to determine sizes of the DGs for maximum real loss reduction.3. Identification Of Optimal DG Locations Using Fuzzy ApproachThis paper presents a fuzzy approach to determine suitable locations for DG placement. Two objectives areconsidered while designing a fuzzy logic for identifying the optimal DG locations. The two objectives are:(i) to minimize the real power loss and (ii)to maintain the voltage within the permissible limits. Voltagesand power loss indices of distribution system nodes are modeled by fuzzy membership functions. A fuzzyinference system (FIS) containing a set of rules is then used to determine the DG placement suitability ofeach node in the distribution system. DG can be placed on the nodes with the highest suitability.For the DG placement problem, approximate reasoning is employed in the following manner: when lossesand voltage levels of a distribution system are studied, an experienced planning engineer can chooselocations for DG installations, which are probably highly suitable. For example, it is intuitive that a sectionin a distribution system with high losses and low voltage is highly ideal for placement of DG. Whereas alow loss section with good voltage is not ideal for DG placement. A set of fuzzy rules has been used todetermine suitable DG locations in a distribution system.In the first step, load flow solution for the original system is required to obtain the real and reactive powerlosses. Again, load flow solutions are required to obtain the power loss reduction by compensating the totalactive load at every node of the distribution system. The loss reductions are then, linearly normalized into a[0, 1] range with the largest lossthreduction having a value of 1 and the smallest one having a value of 0.Power Loss Index [18]value for i node can be obtained using equation 4. ( Lossreduction (i)  Lossreduction (min)) PLI (i)  (4) ( Lossreduction (max)  Lossreduction (min))These power loss reduction indices along with the p.u. nodal voltages are the inputs to the FuzzyInference System (FIS), which determines the nodes that are more suitable for DG installation.3.1. Implementation of Fuzzy methodIn this paper, two input and one output variables are selected. Input variable-1 is power loss index (PLI)and Input variable-2 is the per unit nodal voltage (V). Output variable is DG suitability index (DSI). PowerLoss Index range varies from 0 to 1, P.U. nodal voltage range varies from 0.9 to 1.1 and DG suitabilityindex range varies from 0 to 1.Five membership functions are selected for PLI. They are L, LM, M, HM and H. All the five membershipfunctions are triangular as shown in fig.1. Five membership functions are selected for Voltage. They are L,LN, N, HN and H. These membership functions are trapezoidal and triangular as shown in fig.2. Fivemembership functions are selected for DSI. They are L, LM, M, HM and H. These five membershipfunctions are also triangular as shown in fig.3.For the DG allocation problem, rules are defined to determine the suitability of a node for DG installation.Such rules are expressed in the following form:IF premise (antecedent), THEN conclusion (consequent). For determining the suitability of DG placementat a particular node, a set of multiple-antecedent fuzzy rules has been established. The inputs to the rulesare the voltage and power loss indices and the output is the suitability of capacitor placement. The rules aresummarized in the fuzzy decision matrix in Table-1. In the present work 25 rules are constructed.56 | P a g ewww.iiste.org
  4. 4. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011 Fig .1: Membership function plot for PLI. Fig.2: Membership function plot for voltage Fig.3: Membership function plot for DSI Table1 :Fuzzy Decision Matrix57 | P a g ewww.iiste.org
  5. 5. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011 Voltage AND LL LN NN HN HH L LM LM L L L LM M LM LM L L DSI M HM M LM L L HM HM HM M LM L H H HM M LM L4. Identification Of Optimal DG Sizes By SA Algorithm4.1. Introduction to Simulated AnnealingAs its name implies, Simulated Annealing (SA) exploits an analogy between the way in which a metalcools and freezes into a minimum energy crystalline structure (the annealing process) and the search for aminimum in a more general system. The algorithm is based upon that of Metropolis et al. (1953) which wasoriginally proposed as a means of finding the equilibrium configuration of a collection of atoms at a giventemperature. The connection between this algorithm and mathematical minimization was first noted byPincus (1970), but it was Kirkpatrick et al (1984) who proposed that it form the basis of an optimizationtechnique for combinatorial (and other) problems.SA’s major advantage over other methods is that an ability to avoid becoming trapped at local minima. Thealgorithm employs a random search which not only accepts changes that decrease objective function f, butalso some changes that increase it. The latter is accepted with a probability. The implementation of the SAalgorithm is remarkably easy. In order to get a better idea of how a general SA algorithm works, we willlook at an example. First, we need to decide a start and stop temperature. At any given time during thealgorithm, the temperature, T, will be between the starting and stopping temperatures. This is importantbecause temperature T, is used in the probability equation. The probability equation, as defined byMetropolis, is P= e-(E2-E1)/kT, (10) where k is Boltzmann constant that is chosen to suit the specificproblem, E2 is the new configuration, and E1 is the current configuration. This probability equation can bechanged to suit a specific problem. Whatever the probability, this equation ends up being used to determinewhether a new configuration is accepted or not. If a new configuration has a smaller cost, and therefore isbetter than the current configuration, it will be accepted automatically.SA starts by choosing some random configuration that solves the problem. There is an objective functionthat determines the cost of the given configuration. It is this function that is being minimized (ormaximized depending on what the optimal solution is). The cost of the original, randomly chosenconfiguration is then computed. Considering we are still at the original temperature, SA generates n newconfigurations one at a time, where n is some number chosen by the user before SA begins. Each newconfiguration is derived from the old configuration. The costs of the two configurations are then compared.If the new configuration is better than the current configuration it is automatically accepted. If the newconfiguration is worse than the current one it is then accepted or not based on the outcome of theprobability equation, where E1 is the cost of the current configuration and E2 is the cost of the newconfiguration. After this process of finding a new configuration, comparing it to the current configuration,and either accepting or rejecting it is done n times, the temperature changes. The rate of change for thetemperature is also based on the specific problem and the amount of time for which the user wants SA torun. The number of iterations, n, is also chosen this way. This process then repeats until the stoppingtemperature is reached. As the temperature cools, the probability for selecting a new configuration becomesless, just as the molecules in a piece of metal are not moving around as much.4.2. SA to find the DG sizes at desired locations58 | P a g ewww.iiste.org
  6. 6. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011 Step 1. Read the system data. Set the initial temperature, final temperature, annealing schedule and solution generator. Step 2. Initially generate a solution randomly which represents the sizes of the DG units at given locations. Step 3. Evaluate energy value of this solution by using the formula Energy = 1/(1+Real Power Loss) (11) Step 4. From current solution, generate a random successor solution. Step 5. Evaluate energy value of new solution by using equation 11. Step 6. If the fitness value of new solution is less than current solution set the new solution as current solution and go to step 8. Step 7. Otherwise generate a number r randomly between 0 and 1. If r is less than the probability given by equation 10 the solution is accepted and set that solution as current solution. Step 8. Adjust temperature as per cooling schedule. If the stopping criterion is met stop and print results. Step 9. Otherwise with the current solution go to step 3.4.3. Assigned Values for Various Parameters of SAThe assigned values for various parameters of SA method are as follows.  Initial temperature =1  Final temperature = 1e-8  Annealing Schedule = 0.8*T  Maximum rejections iterations = 1000  maximum Iterations = 10000  maximum Success Iterations = 30  Boltzmann Constant (k) = 1.65. Results And DiscussionFirst load flow is conducted for IEEE 33 bus test system (M. E. Baran et al 1989). The power loss due toactive component of current is 136.9836 kW and power loss due to reactive component of the current is66.9252 kW. Optimal DG locations are identified based on the DSI values. For this 33 bus system, Fouroptimal locations are identified. The candidate locations with their DSI values are given in Table 2.The locations determined by Fuzzy method for DG placement are 6,15,25,32.With these locations, sizesof DGs are determined by using SA Algorithm described in section 4. The sizes of DGs are dependent onthe number of DG locations. Generally it is not possible to install many DGs in a given radial system.Here 4 cases are considered. In case I only one DG installation is assumed. In case II two DGs, in case IIIthree DGS and in the last case four DGs are assumed to be installed. DG sizes in the four optimal locations,total real power losses before and after DG installation for four cases are given in Table 3. Table 2: Buses with DSI values Bus No. DSI 32 .92 30 .7982 31 .75 18 .75 Table 3: Results of IEEE 33 bus system.59 | P a g ewww.iiste.org
  7. 7. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011 bus DG Total losses before loss after DG saving/Case Saving locations sizes(Mw) Size(MW) DG installation installation DG size (Kw) (Kw) (Kw) I 32 1.2931 1.2931 203.9088 127.0919 76.817 59.405 32 0.3836 II 1.5342 203.9088 117.3946 86.5142 56.39 30 1.1506 32 0.2701 III 30 1.1138 1.5342 203.9088 117.3558 86.553 56.41 31 0.1503 32 0.2701 30 0.8233 IV 1.8423 203.9088 90.292 113.6166 61.67 31 0.1503 18 0.5986The last column in Table 3 represents the saving in kW for 1 MW DG installation. The case with greaterratio is desirable. As the number of DGs installed is increasing the saving is also increasing. In case4maximum saving is achieved but the number of DGs is four. Though the ratio of saving to DG size ismaximum of all cases which represent optimum solution but the number of DGs involved is four so it is noteconomical by considering the cost of installation of 4 DGs. But in view of reliability, quality and futureexpansion of the system it is the best solution.Table 4 shows the minimum voltage and % improvement in minimum voltage compared to base case for allthe four cases. In all the cases voltage profile is improved and the improvement is significant. The voltageprofile for all cases is shown in Figure 4. Table 4: Voltage improvement with DG placement case No. Bus No. Min % Voltage change Base case 18 0.9118 Case I 18 0.9314 2.149 Case II 18 0.9349 2.533 Case III 18 0.9349 2.533 Case IV 14 0.9679 6.153Table 5 shows % improvements in power loss due to active component of branch current, reactivecomponent of branch current and total active power loss of the system in the four cases considered. Theloss due to active component of branch current is reduced by more than 54% in least and nearly 79% at best.Though the aim is reducing the PLa loss, the PLr loss is also reducing due to improvement in voltageprofile. From Table 5 it is observed that the total real power loss is reduced by 38% in case 1 and 56% incase 4.60 | P a g ewww.iiste.org
  8. 8. Industrial Engineering Letters www.iiste.orgISSN 2224-6096 (print) ISSN 2225-0581 (online)Vol 1, No.2, 2011 Fig.4:Voltage profile with and without DG placement for all Cases Table 5 :Loss reduction by DG placement case % % % PLa (kW) PLr (kW) PLt (kW) No. Saving Saving Saving Base 136.9836 ---- 66.9252 ---- 203.9088 ---- case caseI 62.7085 54.22 64.3834 3.7979 127.0919 37.45 caseII 53.6323 60.847 63.7623 4.726 117.3946 42.43 caseIII 53.5957 60.874 63.7601 4.729 117.3558 42.45 caseIV 27.7143 79.768 62.5779 6.4957 90.292 55.72The convergence characteristics of the solution of SA algorithm for all the four cases are shown in figure5.Table 6 shows the minimum, average and maximum values of total real power loss from 100 trials ofSA algorithm. The average number of iterations and average CPU time are also shown.61 | P a g ewww.iiste.org
  9. 9. The Name of the Journal of the Journal www.iiste.orgISSN 2222-XXXX (Paper) ISSN 2222-XXXX (Online)Vol X, No.X, 2011 Case I Case II 105.12 91 105.1 Best Fitness Best Fitness 90.5 105.08 105.06 90 105.04 105.02 89.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Success Iterations Success Iterations Case III Case IV 79.3 76 79.29 74 Best Fitness Best Fitness 79.28 72 79.27 70 79.26 68 79.25 66 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Success Iterations Success Iterations Figure 5: Convergence characteristic of SA for 33 bus test system Table 6: Performance of SA algorithm for IEEE 33 Bus System Total real power loss (kW) Case I Case II Case III Case IV Min 104.813 89.752 79.012 66.029 Average 105.023 89.9619 79.2515 66.5892 Max 105.424 90.12 79.856 66. 759 Avg. No. of iterations 8.257 24.384 62.896 67.903 Average Time (Sec.) 1.563 9 21.25 28.93762 | P a g e
  10. 10. The Name of the Journal of the Journal www.iiste.orgISSN 2222-XXXX (Paper) ISSN 2222-XXXX (Online)Vol X, No.X, 20115.1.Comparison PerformanceTo demonstrate the validity of the proposed method the results of proposed method are compared with anexisting GA method(M.Padma Lalitha et al 2010). The comparison is shown in Table 7. Table 7: Comparison of results of IEEE 33-bus system by proposed method and other existing method. sizes(Mw) Total Size(Mw) saving(Kw) Case Bus locations SA GA SA GA SA GA I 32 1.2931 1.2931 1.1883 1.1883 76.8169 76.3619 32 0.3835 0.3836 II 1.416 1.416 86.5142 86.0246 30 1.1509 1.1506 32 0.2703 0.2701 III 30 1.1130 1.1138 1.416 1.416 86.5529 86.0628 31 0.1503 0.1503 32 0.2642 0.27006 30 0.8413 0.8432 IV 1.86176 1.86176 113.4292 113.4294 31 0.1508 0.1503 18 0.5992 0.5982From the above table it is clear that the proposed method is producing the results that matches with those ofexisting method or even slightly better results. To demonstrate the supremacy of the proposed method theconvergence characteristics are compared with that of GA as shown in Table 8. Both the number ofiterations and computation time are less for SA. The disadvantage of the GA method is, it is producingslightly different results for each run. Table 8: Comparison of results of Simulated Algorithm and GA Case I Case II Case III Case IV SA GA SA GA SA GA SA GA Swarm Size 50 50 50 50 50 50 50 50Avg. No. of iterations 8.257 123.48 24.384 126.97 62.896 141.29 67.903 149.31 Avg. time(sec.) 1.563 40.02 9 53.4 21.25 58.938 28.937 63.786. ConclusionsIn this paper, a two-stage methodology of finding the optimal locations and sizes of DGs for maximum lossreduction of radial distribution systems is presented. Fuzzy method is proposed to find the optimal DGlocations and a Simulated Annealing method is proposed to find the optimal DG sizes. Voltage and lineloading constraints are included in the algorithm.The validity of the proposed method is proved from the comparison of the results of the proposed methodwith other existing methods. The results proved that the proposed algorithm is simple in nature than GA63 | P a g e
  11. 11. The Name of the Journal of the Journal www.iiste.orgISSN 2222-XXXX (Paper) ISSN 2222-XXXX (Online)Vol X, No.X, 2011and PSO so it takes less computation time. By installing DGs at all the potential locations, the total powerloss of the system has been reduced drastically and the voltage profile of the system is also improved.Inclusion of the real time constrains such as time varying loads and different types of DG units and discreteDG unit sizes into the proposed algorithm is the future scope of this work.ReferencesPica (2001.) Innovative Computing For Power - Electric Energy Meets The Market. 22nd IEEE PowerEngineering Society International Conference, pp. 81-86.P.A. Daly, J. Morrison(2001), “Understanding the potential benefits of distributed generation on powerdelivery systems,” Rural Electri Power Conference, pp. A211 – A213.P. Chiradeja, R. Ramakumar,(2004) “An approach to quantify the technical benefits of distributedgeneration” IEEE Trans Energy Conversion, vol. 19, no. 4, pp. 764-773.“Kyoto Protocol to the United Nations Framework Convention on climate change”,http://unfccc.int/resource/docs/convkp/kpeng.htmlR.E. Brown, J. Pan, X. Feng, and K. Koutlev(1997) “Siting distributed generation to defer T&Dexpansion,” Proc. IEE. Gen, Trans and Dist, vol. 12, pp. 1151- 1159.E. Diaz-Dorado, J. Cidras, E. Miguez(2002), “Application of evolutionary algorithms for the planning ofurban distribution networks of medium voltage”, IEEE Trans. Power Systems , vol. 17, no. 3, pp. 879-884.M. Mardaneh, G. B. Gharehpetian(2004), “Siting and sizing of DG units using GA and OPF basedtechnique,” TENCON. IEEE Region 10 Conference, vol. 3, pp. 331-334, 21-24.Silvestri A.Berizzi, S. Buonanno(1999), “Distributed generation planning using genetic algorithms”Electric Power Engineering, Power Tech Budapest 99, Inter. Conference, pp.257.Naresh Acharya, Pukar Mahat, N. Mithulanathan(2006), “An analytical approach for DG allocation inprimary distribution network”, Electric Power and Energy Systems, vol. 28, pp. 669-678.G.Celli,E.Ghaini,S.Mocci and F.Pilo(2005), “A multi objective evolutionary algorithm for the sizing andsitting of distributed generation”,IEEE Transactions on power systems,vol.20,no.2,pp.750-757.C.L.T.Borges and D.M.Falcao(2006), “Optimal distributed generation allocation for reliability,losses andvoltage improvement”, International journal of power and energy systems,vol.28.no.6,pp.413-420.Kirkpatrick, S., (1984) “Optimization by Simulated Annealing — Quantitative Studies”, J. Stat. Phys. 34,975-986.Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller (1953) “Equations of StateCalculations by Fast Computing Machines”, J. Chem. Phys. 21, 1087-1092.Pincus, M., (1970) “A Monte Carlo Method for the Approximate Solution of Certain Types of ConstrainedOptimization Problems”, Oper. Res. 18, 1225-1228.Mrs. M.Padma Lalitha , Dr. V.C. Veera Reddy, Mrs. V. Usha Reddy(2010) “Application Of Fuzzy AndRCGA For DG Placement For Maximum Savings In Radial Distribution System” International Journal OfEmerging Technologies And Applications In Engineering, Technology And Sciences, Vol. 3, Issue 1, pp.447-453.M. E. Baran and F. F. Wu(1989), “ Network reconfiguration in distribution systems for loss reduction andload balancing”, IEEE Transactions on Power Delivery, Vol. 4, No 2, pp. 1401-1407.Mrs. M. Padma Lalitha , Dr.V.C. Veera Reddy, V. Usha Reddy(2010) “Optimal DG Placement ForMinimum Real Power Loss In Radial Distribution Systems Using PSO” Journal Of Theoretical AndApplied Information Technology ,Vol.13,No.2, pp.107-116.64 | P a g e

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