K. Valipour 1 E. Dehghan 2 M.H. Shariatkhah 3

Transcription

1 International Research Journal of Applied and Basic Sciences 2013 Available online at ISSN X / Vol, 4 (7): Science Explorer Publications Optimal placement of Capacitor Banks and Distributed Generation for Losses Reduction and Voltage THD Improvement in Distribution Networks Based on BBO Algorithm K. Valipour 1 E. Dehghan 2 M.H. Shariatkhah 3 1, 2. Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil, Iran, 3. ETD-Lab, Electrical Eng. Dept. Tarbiat Modares University, Tehran, Iran, * Corresponding Author esdehghan@gmail.com ABSTRACT: This paper presents a new approach based on Biogeography based optimization (BBO) algorithm for the simultaneous power quality improvement and optimal placement and sizing of capacitor banks and distributed generation (DGs) in the presence of voltage harmonic in radial distribution networks. The optimization aims at minimizing the power losses and voltage profils and THD improvement by DGs and capacitor banks placement for radial distribution system. Constraints include voltage limits and locations of installed DG and capacitors number/size, limit candidate buses. Biogeography based optimization is a novel evolutionary algorithm that is based on the mathematics of biogeography. In the BBO model, problem solutions are represented as islands, and the sharing of features between solutions is represented as immigration and emigration between the islands. A numerical application on a 33-bus bar network was performed. For effectiveness of the proposed procedure, the results obtained by BBO are compared with the genetic algorithm (GA). Keywords: Optimal Placement, Capacitor Banks, Distributed Generation, Biogeography-Based Optimization, Distribution Networks. INTRODUCTION Optimal allocation of DG and capacitor banks can lead to a increase the feeder capacity, reduction in losses, power factor correction, and improve the voltage profile in radial distribution networks. The optimal capacitor placement is a non-convex problem and thus the achievement of the global optimum may be impaired by the presence of local optima. Additionally a large number of alternative solutions may be obtained due to the discrete nature of the problem, which will demand high computational costs (Grainger et al 1981), (Lee et al 1981). In today s nonlinear devices and loads appear in power systems, special attention should be paid to the placement of capacitors banks in such distribution systems. This is due to the possibility of unwanted over-voltages that may be caused by harmonic resonance. This problem is recognised and discussed in (Varilone et al 2). Proper placement and sizing of shunt capacitor banks in distorted networks can result in reactive power compensation, improved voltage regulation, power factor correction, power/energy loss reduction, as well as power quality improvement (Masoum 4). In recent years, DGs, as clean natural energy generation and cogeneration system of high thermal efficiency, has increased due to the problems of global warming and exhaustion of fossil fuels. The general capacitor placement and distributed generation problem consists mainly of determining the optimal location and size of the installed capacitors, DG such that the maximum yearly benefit due to peak power and energy loss reduction against the cost of installation of capacitors is achieved (Samahy et al 4). In the present work optimal placement and sizing of capacitor banks and DGs in radial distribution networks based on biogeography based optimization (BBO) algorithm with simultaneous for system power loss, energy losses and voltage THD improvement. The methods are presented to find optimal size and bus location for placing DG and Capacitor banks in a networked system based on bus admittance, generation information and load distribution of the system.

2 Problem Formulation The main goal of the proposed algorithm is to determine the best locations for new DG and Capacitor banks by minimizing different function, related to project aims; for instance, consider the following: Optimal power flow for losses reduction system. Optimal for improved system power factor. Optimisation of generator parameters to enhance its efficiency. Minimization of design costs and maximization of efficiency and etc. Figure 1 shows the single line diagram of the 33-bus radial distribution system considered in this work. Figure 1. Single line diagram IEEE 33-bus of the studied distribution system Optimal placement and sizing of DGs is formulated as a nonlinear optimization problem. Every engineering system is expressed with a set of quantities that some of them the set of variables in the design process as design or decision variables appear. The variables with the set of design variables for design vector is presented. In this work three case considered, that including; optimal placement capacitor, DGs and simultaneous DG and capacitor. A- Case 1: Optimal capacitor placement only providing reactive power. This type can improve the voltage profile and system power factor. Control variable is given as:!! (1) " # $ Where $ %&' number of capcitor that installation corresponding to the bus. Q is the total reactive power that provided with capacitor banks. B- Case 2: Optimal DGs placement able to provided real power with variable power factors. Control variable is given as: ( )* )*,-,-,- )*.!/!)* (2) " # 0 Where $ 12 number of DGs that installation corresponding to the bus )*. P is the total real power that generated with DGs and pf is power factor of DGs. C- Case 3: Optimal capacitor and DGs placement have been considered at this state. Control variable are given as: )* %&' %&' %&' )*!3! )* 4! 5 (3) " # 6 12 %&' Where $ 12, $ %&' number of DGs and capacitor that instalation corresponding to the bus )* and respectively. P is the total real power that generation with DGs and Q is the total reactive power that provided with capacitor. In the capacitor and DG selection process, the following constraints must be taken into account: 7 89 : 7 : 7 8&; (4) <=>? : <=> 8&; (5) Where V min, V max, and THD max represent the allowed minimum rms, maximum rms, and maximum THD of node voltages.@7 is the overall rms voltage at the i th bus can be evaluated BC D7 A 9 D 9E (6) THD (%) is the total harmonic diritortion which is defined by: 1664

3 <=>? F GG DH K BC IJD 9L (7) D7 9 D Where n; is the harmonic order is the fundamental rms voltage at l-th level. The capacitor size is given by: M N OP! Q6RST (8) In which j=0,1,,8. The selection of capacitor size is limited to standard sizes of Q c ={150,,450,600,750,900,1050,1} KVar. The selection of DGs size is limited of P DG (P i,pf j )={(0,500) kw, (-0.9,0.9)}. In which i=0,1,2,3,4. And j=5,6,7,8. Power loss The power losses in the distribution system depend on the line resistance and currents and are usually called thermal losses. In a distribution system with n number of branches, the total real power losses can be calculated as (Hawary et al 2). +?UVV C9 WX N! DY N D NE Z (9) Where, I j and R J are the magnitude of current and the resistance of the branch j, respectively. Biogeography Theory Biogeography Based Optimization (BBO) approach has been developed based on the theory of biogeography. The idea of BBO was first proposed in 8 by Dan Simon. It is an example of natural process that can be modeled to solve general optimization problems. In BBO, each individual is considered as an island (or a habitat), and the sharing of features between individuals are represented as emigration and immigration figure 2. Each solution feature is called a suitability index variable (SIV). Geographical areas that are well suited as residences for biological species are said to have a high habitat suitability index (HSI) (Wesche et al 1987). Where a high HSI of an island means good performance on the optimization problem and a low HSI means bad performance on the optimization problem. Intensification the population is the way to solve problems in heuristic algorithms. The method to generate the next generation in BBO is by immigrating solution features to other islands, and receiving solution features by emigration from other islands. Then mutation is performed for the whole population in a manner similar to mutation in GAs. emigrating islands (individuals) I E Immigratio Rate Emigration immigrating island (individual) Figure 2. Emmigration of species and new island. S 0 Species count S max Figure 3. Species model of a single habitat In BBO, each individual has its own immigration rate, denoted by, and emigration rate, denoted by [. A good solution has higher [; hence, it has a very high chance of borrowing features from other solutions, helping it to improve for the next generation Fig. 3. Note that emigration in BBO does not mean that the emigrating island loses a feature [9]. Mathematically the concept of emigration and immigration can be represented by a probabilistic model. Further suppose that, consider the probability P s that the habitat contains exactly S species at t. changes from time t to time t+t as follows: ( t + t) = ( t)(1 λs t µ s t) + 1λ s 1 t + + 1µ s+ 1 t (10) If time t is small enough so that equation (1) as t 0gives the following equation; 1665

4 ( λs + µ s) + µ s , S = 0 P = ( λs + µ s) + λs µ s , 1 S Smax 1 ( λs + µ s) + λs 1 1, S = Smax (11) These relationships are shown in Fig. 2. as straight lines but, in general, they might be more complicated curves. The values of emigration and immigration rates are given as: µ Ek k = n (12) k λk = I(1 ) n (13) where I is the maximum possible immigration rate; E is the maximum possible emigration rate; K is the number of species of the k-th individual and n is the number of species. Now, consider the special case E=I Figure 4. In this case; λ k + µ k = E (14) E=I Immigration Emigration Rate Worst Solution Species count Best Solution Figure 4. Illustration of two candidate solutions to some problem. Biogeography-Based Optimization Suppose that we have a problem and a population of candidate solutions that are represented as vectors. Further suppose that we have some way of assessing the goodness of the solutions. Good solutions are analogous to islands with a high island suitability index (ISI), and poor solutions are analogous to islands with a low ISI Island H Island H Island H a) Before migration Island H a) Before inverse mutation Island H Island H b) After inverse mutation Figure 6. The mutation operator in BBO b) After migration Figure 5. The migration operator in BBO. Note that ISI is the same as fitness in other population based optimization algorithms. BBO mainly works based on the two mechanisms. These are migration and mutation figures 5,

5 A. Migration With probability P mod, known as habitat modification probability each solution can be modified based on other solutions. If a given solution S i is selected to be modified, then its immigration rate is used to probabilistically decide whether or not to modify each suitability index variable (SIV) in that solution. After selecting the SIV for modification, emigration rates [ of other solutions are used to select which solutions among the population set will migrate randomly chosen SIVs to the selected solution S i (MacArthur, Wilson 1967). B. Mutation In BBO species count probabilities are used to determine mutation rates. The probabilities of each species count can be calculated using the differential equation as mentioned in equation (11). Each population member has an associated probability, which indicates the likelihood that it exists as a solution for a given problem. If the probability of a given solution is very low then that solution likely to mutate to some other solution. Similarly if the probability of some other solution is higher then that solution set has very little chance to mutate. Mutation rate of each set of solution can be calculated in terms of species count probability using the equation; \] \ 8&; W ^_` _ ab Z (15) Where m max is a user defined parameter. SIMULATION RESULTS The proposed BBO algorithm has been implemented on IEEE 33-Bus systems. The test networks a kv system with 32 buses and 4 feeders (M.A. Kashem et al 0). The following BBO parameters have been used, population size=, Habitat Modification Probability=1, Immigration Probability bounds per gene=[0,1], step size for numerical integration of probabilities=1, maximum and rates for each island=1 and Mutation Probability=0.05. This paper presents simulation studies are 3 state. Case 1 is optimal placement and sizing of capacitor banks and case 2 optimal placement and sizing DGs and final state is simultaneous optimal placement and sizing of capacitor banks and DGs. All harmonic sources are assumed to be in phase and their data, which follow the assumptions mentioned in section II, are given in TableIII. Figure 7 shows the final radial configuration of the system after compensation. Figure 8 is expressed Convergence characteristic of BBO and GA, the objective function is power losses. The analysis shows that the real power losses can be reduced by installation capacitor and DGs, and voltage profile and THD (%) improvement is obtained by capacitor and DG installation at each bus of system figures 9, 10. Moreover, the simulation results of the proposed algorithm and GA for different trials in terms of the solution, have been shown in Tables I, II. Power Losses (Kw) BBO GA Figure 7. Single line diagram IEEE-33 bus system after compensation iter Figure 8.Convergence characteristic of BBO and GA 1667

6 Without Capasitor & DG with BBO Capasitor & DG with GA Voltage(KV) Bus number Figure 9. Voltage profile before and after DG and Capacitor at each bus of system Without Capasitor & DG with BBO Capasitor & DG with GA THD(%) Bus number Figure 10. THD(%) before and after DG and Capacitor installation at each bus of system TABLE I. Power losses reduction and (%) saving System Method Case Optimal Placement Power Loss (KW) % Saving Load flow analysis Base case Case 1 Capacitor BBO Case 2 DG bus Case 3 DG & Capacitor Case 1 DG GA Case 2 Capacitor Case 3 DG & Capacitor

7 TABLE II. Present the best results achieved by the BBO and GA algorithms System Case Heuristic Search Bus No. Capacitor Placement (KVar) Bus No. (KVar) Bus No. DG Placement + )* (KW) + )*,- )* V min (pu) Old V min (pu) V min (pu) New THD max (%) THD max (%) Old THD ma x (%) New BBO Case GA BBO Bus Case GA BBO Case GA TABLE III. Harmonics data Harmonic order W CONCLUSIONS In this paper a BBO method has been implemented to solve both optimal placement and sizing of capacitor and DGs in order to decreasing radial distribution system losses, improving voltage profile and THD (%) problems. It is clear from the results obtained by different trials that the proposed BBO method can obtain better quality solution. The analysis shows that the real power losses can be reduced by capacitor and DG installation at each bus of system. Voltage profile and THD (%) improvement is obtained by new capacitor and DG installation at each bus of system. The other benefits of DGs and capacitor as well as economics of it can be considered in future research work. REFERENCES J.J. Grainger, S.H. Lee, Mar. 1981, Optimum Size and Location of Shunt Capacitors for Reduction of Losses on Distribution Feeders, IEEE Transactions Power Apparatus Systems, Vol. PAS-, No. 3. S.H. Lee, J.J. Grainger, Jan. 1981, Optimum Placement of Fixed and Switched Capacitors on Primary Distribution, IEEE Transactions Power Apparatus Systems, Vol. PAS-, No

8 J.J. Grainger, S.H. Lee, May 1982, Capacity Release by Shunt Capacitor Placement on Distribution Feeders a New Voltage Dependent, IEEE Transactions Power Apparatus Systems, Vol. PAS-101, No. 5. P. Varilone, G. Carpinelli, A. Abur, June 2, Capacitor Placement in Unbalanced Power Systems, Proc. 14th Power System Computations Conference, Seville, Spain. M.A.S. Masoum, October 4, Optimal Placement, Replacement and Sizing of Capacitor Banks in Distorted Distribution Networks by Genetic Algorithms, IEEE Transaction on Power Delivery, Vol. 19, No. 4, pp LEI-Samahy, E.F.El-Saadany, 4, The Effect of Harmonics on the Optimal Capacitor Placement Problem, IEEE Transactions, pp Hawary, S.A. Soliman, M.A. Moustafa, M.M. Mansour, New Heuristic Strategies for Reactive Power Compensation of Radial Distribution Feeders, 2, IEEE Transactions Power Delivery, Vol. 17, pp T. Wesche, G. Goertler, W. Hubert, 1987, Modified Habitat Suitability Index Model for Brown Trout in Southeastern Wyoming, North Amer. J. Fisheries Manage., Vol. 7, pp D. Simon, Biogeography-Based Optimization, IEEE Transactions on Evolutionary Computation, Vol. 12, No. 6, pp , December 8. R. MacArthur, E. Wilson, 1967, The Theory of Biogeography, Princeton, NJ: Princeton University Press. M.A. Kashem, V. Ganapathy, G.B. Jasmon, M.I. Buhari, 4-7 April 0, A Novel Method for Loss Minimization in Distribution Networks, International Conference on Electric Utility, Deregulation and Restructuring and Power Technologies 0, London, pp