Application of Teaching Learning Based Optimization for Size and Location Determination of Distributed Generation in Radial Distribution System.

Application of Teaching Learning Based Optimization for Size and Location Determination of Distributed Generation in Radial Distribution System. Khyati Mistry Electrical Engineering Department. Sardar Vallabhbhai National Institute of Technology Surat p@eed.svnit.ac.in Ranjit Roy Electrical Engineering Department. Sardar Vallabhbhai National Institute of Technology Surat rr@eed.svnit.ac.in Abstract Distributed generator (DG) placement in distribution system is one of the important tass for better operation of distribution system. Distribution system has high r/x ratio and high operating current resulting into higher power loss and higher voltage drop. The main objective of this paper is to minimize the active power loss and to improve voltage profile of overall system by optimal sizing and siting of DG. This paper presents application of three different optimization techniques namely Particle swarm optimization (PSO), Craziness based particle swarm optimization (CRPSO) and Teaching-learning based optimization (TLBO) algorithm for optimal placement of distributed generators. The methods have been tested with two IEEE standard test cases, 16-node radial distribution networ and 33-node radial distribution networ, and the results obtained by three different algorithms are competitive with each other. Keywords- Active power loss, Distributed Generation (DG), Optimization Technique, Radial distribution networ, Voltage profile. D I. INTRODUCTION ISTRIBUTED generation (DG) has gained more attention as it uses renewable and non-renewable small energy sources. Distributed generators (DG) can be 1) renewable energy sources, such as: Wind turbines, Solar photovoltaic, Biomass energy sources or 2)non- renewable energy sources such as: Diesel generator, Small turbines. Distributed generators are neither centrally placed nor dispatchable. It is scattered within the distribution system at or near load centre. Incorporation of DGs in distribution system results in increase in the capacity of the feeder, higher reliability, lowers system losses, improves voltage profile and improves voltage stability of the system and lowers the pea demand resulting into increase in the life of system equipment and hence more number of customers can be served. To avail these merits one has to find out the appropriate capacity and location of DG, otherwise higher DG capacity results into higher power losses and increase of system voltage. The size of DG should be such that it is equal to the total load of the system plus the total system losses. Higher capacity of DG results into reverse power flow from substation to the source node. In the literature three methods are adopted to find the optimum size of DG, they are: analytical, heuristic and optimization techniques. Analytical method requires repetitive derivation of current and voltage after placement of DG,which requires more time. Heuristic methods are simple but the results obtained from heuristic algorithms are not guaranteed to be optimal. Optimization techniques can give the best solution within short duration of time for a given distribution networ. Combined genetic algorithm (GA) and particle swarm optimization (PSO) are presented in [1] for optimal location and sizing of DG. Multi objective function [2] is developed to determine the optimal locations of DG in distribution system to minimize active power losses of the system and to enhance the reliability and improves voltage profile through dynamic programming. Two new methodologies [3] of DG placement are presented in an optimum power flow based wholesale electricity maret. Optimal placement and size is identified for social welfare as well as profit maximization problem. The candidate location for DG placement is identified on the basis of locational marginal price (LMP). A genetic algorithm [4] is developed for simultaneous power quality improvement, optimal placement and sizing of fixed capacitor bans in radial distribution networs with nonlinear loads and distributed generation (DG) imposing voltage current harmonics. At each bus optimum DG size [5] is found using a power flow algorithm assuming every bus has a DG source. It requires a large number of load flow computations. Priority-ordered constrained search technique [6] for optimal distributed generation (DG) allocation in radial distribution feeder systems is developed. The artificial bee colony (ABC), as a new meta-heuristic population-based algorithm, is adopted to verify the proposed technique efficiency. The heuristic optimization technique named Particle Swarm Optimization (PSO) [7] is utilized to search for an optimal solution of the DG placement problem. In this paper, DG is considered as an active power source. Optimum capacity and location of DG is found out with three different optimization techniques for minimization of active power loss and to improve voltage profile of the distribution system. In this wor, a novel optimization technique namely Teachnig-learning based optimization (TLBO) is applied to find out the optimum location and capacity of DG which is not reported in the literature yet. 1

Active power loss (MW) II. DG PLACEMENT DG is considered as a negative load on the system. The node where load is connected is considered to be the location of DG. For example consider 33-node radial distribution networ shown in Figure 1. The total active power load on the system is 3.715 MW and total active power loss of the system is 0.2026 MW. In this case, maximum DG capacity is assumed 5 MW. Let us considere DG is placed at node 2 and capacity of DG is varied from 0.1 MW to 5 MW in step 0.1. Figure 2. shows the plot of active power loss versus DG capacity for 33- node networ where DG is placed at node 2. From Figure 2, it is clear that if DG capacity increases from 0.1MW to 4.5 MW the overall system losses are reducing in nature. Afterwards, the losses increase due to increasing DG capacity. It is clear that the optimum DG capacity for node 2 lies between 4 MW to 4.5MW. The accurate optimum capacity of DG for each node is found out using three different optimization techniques. 0.206 0.204 0.202 0.2 0.198 0.196 0.194 Figure 1. 33-node radial distribution networ. 0.192 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 DG capacity(mw) Figure 2. Active power loss versus DG capacity for 33-node networ when DG is placed at node 2. III. PROBLEM FORMULATION The optimum size of DG can be found out with the equation (1) for each node where the load is connected. P i = P DGi P Di (1) where, P i = real power injection at node i. P DGi =real power generation by DG at node i. P Di = real power demanded at node i. The problem is formulated with the objective function, namely minimization of active power loss considering voltage constraint. The objective function is, Minimize total real power losses= n n 2 TLP = jj =1 LP (jj ) = jj=1 I jj r jj (2) subjected to: Voltage constraint: Voltage magnitude at each node must lie within their permissible ranges to maintain power quality: V min i V i V max i (3) where jj is the branch number, I jj represents the branch current, r jj stands for branch resistance. LP jj is the power loss of branch jj. V min i = Minimum voltage limit at node i. V max i = Maximum voltage limit at node i. The DG capacity is varied from minimum to maximum value. IV. SIMULATED TEST SYSTEMS The proposed method is tested with two test cases. The first test case is16-node radial distribution networ [8] and second test case is 33-node radial distribution networ [9]. For the load flow study, the following parameters are considered: For 16-node networ, substation voltage=11kv, base MVA=100, total active load =28.7 MW. The voltage limit is 0.95 p.u to 1.05 p.u. The DG capacity for this test case is assumed 30 MW. For 33-node networ, substation voltage=12.66 KV, base MVA=100, total active load =3.715 MW. The voltage limit is 0.95 p.u to 1.05 p.u. The DG capacity for this test case is assumed 5 MW. V. ASSUMPTION MADE FOR DG PLACEMENT DG is considered as negative load. DG injects only active power. The maximum size of the DG is assumed to be total load demanded plus total loss of the system. The node at which load is connected considered as the possible location of DG. The source node is not to be considered as location for DG placement. VI. COMPUTATIONAL PROCEDURE Step 1: Run the load flow and find out total active power losses. Step 2: Place DG at each node and vary DG capacity from minimum to maximum value. Step 3: Store the size of DG corresponding to minimum loss obtained for each node. Step 4: Compare the loss for each node. Step 5: The node at which loss is minimum considered as the optimum location for DG placement. Step 6: Print the optimum capacity of DG corresponding to optimum location. Step 7: Run the load flow with optimum DG capacity to obtain the final results. VII. OPTIMIZATION TECHNIQUES EMPLOYED The optimization algorithm employed in this paper are Particle swarm optimization (PSO) [10], Craziness-based particle swarm optimization (CRPSO) [11], and Teachinglearning based optimization (TLBO) [12] to compute the optimum location and size of DG. 2

A. Particle Swarm Optimization The PSO was first introduced by Kennedy and Eberhart [13]. It is an evolutionary computational model, a stochastic search technique based on swarm intelligence such as fish schooling and bird flocing. PSO [10] is developed through simulation of bird flocing in multidimensional space. Each particle's present position is realized by the previous position and present velocity information. Bird flocing optimizes a certain objective function. Each agent nows its best value so far (pbest). This information corresponds to personal experiences of each agent. Moreover, each agent nows the best value so far in the group (gbest) among pbests. Namely, each agent tries to modify its position using the following information: * The current position vector x i * The current velocity vector v i * The distance between the current position and pbesti * The distance between the current position and gbest. Mathematically, velocities of the each particle are modified according to the following equation: Velocity updating equation: v v c r x c r x (4) 1 i i 1 1 p Best i i 2 2 gbest i where V i is the velocity of agent i at iteration ; c1 and c2 are the weighting factor; r1 and r2 are the random number between 0 and 1; x i is the current position of agent i at iteration. Position of each particle is updated by using equation: 1 1 xi xi vi (5) The first term of (4) is the previous velocity of the agent. The second and third terms are used to change the velocity of the agent. Without the second and third terms, the agent will eep on flying in the same direction until it hits the boundary. B. Craziness-based Particle Swarm Optimization The following modifications in velocity help to enhance the global search ability of PSO algorithm as observed in CRPSO [11]. (i) Velocity updating as proposed in [11] may be stated as in the following equation: 1 v r2v 1 r2c1 r1 p Best x i i i i (6) 1 r2 c2 1 r1 gbest x i Local and global searches are balanced by random number r2 as stated in (9). Change in the direction in velocity may be modeled as given in the following equation: 1 v i r2sign(r3) vi 1 r2c1 r1 (7) p Best x 1 r 2 c2 1 r1 gbest x i i i In (9), sign (r3) may be defined as 1 r3 0.05 sign( r3) = 1 r3 0.05 (ii) Inclusion of craziness: Diversity in the direction of birds flocing or fish schooling may be handled in the traditional PSO with a predefined craziness probability. The particles may be crazed in accordance with the following equation before updating its position. 1 1 craziness i i ( 4) ( 4) i v v Pr r sign r v (8) where Pr(r4) and sign(r4) are defined respectively as: r r 1 4 Pcraz Pr( r4) 0 4> Pcraz 1 r4 0.5 sign( r4) -1 r4<0.5 (9) (10) During the simulation of PSO, the best chosen maximum population size = 50, maximum allowed iteration cycles = 100, best Pcraz = 0.2 (chosen after several experiments). The choice of c1, c2 are very much vulnerable for PSO execution. craziness The best value of either c1 or c2 is 2.05. The value of v i lies between 0.25 and 0.35. C. Implementation of Teaching-learning based optimization The TLBO [12] method wors on the philosophy of teaching and learning. The output of learners (i.e. results or grades) is influenced by the teacher in a class. Students learn from teacher and interact between themselves. The teacher is considered as the highly learned person in the class. In this algorithm two main phases are considered: 1) Teacher phase and 2) Learner phase. 1) Teacher phase For initialization, the control variables are the mars obtained by learners in different subjects. For this problem, capacity of DG is considered as control variable which is denoted by g x. g x 0 =min+rand(1)*(max-min) (11) where, x varies from 1 to np, np being the number of population and min and max are the minimum and maximum values of DG capacity. A good teacher tries to improve the mean (mars/grades) of the class in terms of nowledge. As a result of the influence of the teacher, the g x variable is modified as: g new = g old + r g teacher T f M (12) where g teacher is the best solution among g x. In this case, best solution means the capacity of DG which yields minimum losses. T f is the teaching factor. Its value to be taen either 1 or 2. In this algorithm the value of T f is taen 1. M is the mean value of the population. r is the random number between 0 and 1. 2) Learner phase A learner learns from two different means: one through the teacher and other through interaction between learners. A learner interacts randomly with other learners as a group discussion, presentation, formal communication, etc. A learner learns from other learner who has more nowledge than him or her. Thus the g x variable is modified as: g new = g old + r g i g j, if f (g i ) f (g j ) (13) g new = g old + r g j g i, if f (g i ) f (g j ) (14) Provided i j. g j is selected randomly and it is given by g j =ceil(np*r) (15) where f(g i ) is the objective function which is defined in (2). r is the random number between 0 and 1. VIII. DISCUSSION ON RESULTS The objective of this paper is to find out optimum DG size and optimum location of DG which gives lowest possible total 3

Table I Total active power loss, minimum voltage magnitude for the base cases. Particulars 16-node networ 33-node networ Active power loss(kw) 511.398 202.6 Minimum Voltage magnitude (p.u) 0.9688 at node 12 0.9131 at node 18 Table II Optimal DG size, active power loss and minimum voltage magnitude at respective node of 16- node networ. Node Optimal DG Size (KW) Active power loss (KW) Minimum voltage magnitude (p.u) PSO CRPSO TLBO PSO CRPSO TLBO PSO CRPSO TLBO 4 8.5668 8.5477 8.5478 455.555 455.556 455.6 0.9706 at node 11 0.9688 at node 12 0.9688 at node 12 5 3.6737 5.6796 5.6794 460.239 460.238 460.2 0.9706 at node 11 0.9688 at node 12 0.9688 at node 12 6 5.7863 5.7812 5.7812 454.716 454.716 454.7 0.9706 at node 11 0.9688 at node 12 0.9688 at node 12 7 4.9840 4.9490 4.9488 459.797 459.794 459.8 0.9706 at node 11 0.9688 at node 12 0.9688 at node 12 8 15.3174 15.3266 15.3181 241.639 241.639 241.6 0.9848 at node 7 0.9848 at node 7 0.9848 at node 7 9 13.0019 13.0453 13.0411 168.484 168.481 168.5 0.9848 at node 7 0.9848 at node 7 0.9848 at node 7 10 8.2353 8.2456 8.2448 356.642 356.642 356.6 0.9784 at node 12 0.9848 at node 7 0.9785 at node 12 11 8.5797 8.6052 8.6029 279.021 279.019 279.0 0.9848 at node 7 0.9848 at node 7 0.9848 at node 7 12 10.5498 10.5392 10.5393 193.544 193.544 193.5 0.9848 at node 7 0.9848 at node 7 0.9848 at node 7 13 5.1333 5.1235 5.1237 482.194 482.194 482.2 0.9706 at node 11 0.9688 at node 12 0.9688 at node 12 14 3.2801 3.2797 3.2796 489.718 489.718 489.7 0.9688 at node 12 0.9688 at node 12 0.9688 at node 12 15 4.2479 4.2664 4.2664 476.313 476.312 476.3 0.9688 at node 12 0.9688 at node 12 0.9688 at node 12 16 3.8887 3.8889 3.8888 476.092 476.092 476.1 0.9688 at node 12 0.9688 at node 12 0.9688 at node 12 Table III Optimal DG size, active power loss and minimum voltage magnitude at respective node of 33- node networ. Node Optimal DG Size (MW) Active power loss (MW) Minimum voltage magnitude (p.u) PSO CRPSO TLBO PSO CRPSO TLBO PSO CRPSO TLBO 2 4.1260 4.1260 4.1260 0.1928 0.1928 0.1928 0.9157 at node 18 0.9157 at node 18 0.9156 at node 18 3 3.6297 3.6297 3.6296 0.1527 0.1527 0.1527 0.9276 at node 18 0.9277 at node 18 0.9277 at node 18 4 3.1594 3.1594 3.1594 0.1403 0.1403 0.1403 0.9337 at node 18 0.9337 at node 18 0.9337 at node 18 5 2.8916 2.8916 2.8916 0.1284 0.1284 0.1284 0.9394 at node 18 0.9395 at node 18 0.9395 at node 18 6 2.5752 2.5752 2.5752 0.9510 at node 18 0.9511 at node 18 0.9511 at node 18 7 2.4414 2.4413 2.4413 0.1050 0.1050 0.1050 0.9521 at node 18 0.9521 at node 18 0.9521 at node 18 8 2.0852 2.0851 2.0851 0.1096 0.1096 0.1096 0.9474 at node 33 0.9475 at node 33 0.9475 at node 33 9 1.7307 1.7307 1.7307 0.1162 0.1162 0.1162 0.9423 at node 33 0.9424 at node 33 0.9424 at node 33 10 1.5019 1.5019 1.5019 0.1202 0.1202 0.1202 0.9391 at node 33 0.9391 at node 33 0.9391 at node 33 11 1.4673 1.4673 1.4673 0.1209 0.1209 0.1209 0.9386 at node 33 0.9386 at node 33 0.9386 at node 33 12 1.4055 1.4055 1.4055 0.1223 0.1223 0.1223 0.9377 at node 33 0.9377 at node 33 0.9377 at node 33 13 1.2069 1.2069 1.2069 0.1274 0.1274 0.1274 0.9348 at node 33 0.9349 at node 33 0.9349 at node 33 14 1.1464 1.1464 1.1464 0.1292 0.1292 0.1292 0.9339 at node 33 0.9340 at node 33 0.9340 at node 33 15 1.0838 1.0838 1.0838 0.1319 0.1319 0.1319 0.9330 at node 33 0.9331 at node 33 0.9331 at node 33 16 1.0128 1.0128 1.0128 0.1352 0.1352 0.1352 0.9320 at node 33 0.9320 at node 33 0.9320 at node 33 17 0.9027 0.9027 0.9027 0.1411 0.1411 0.1411 0.9303 at node 33 0.9303 at node 33 0.9303 at node 33 18 0.8504 0.8504 0.8504 0.1442 0.1442 0.1442 0.9295 at node 33 0.9295 at node 33 0.9295 at node 33 19 1.7163 1.7163 1.7163 0.1979 0.1979 0.1979 0.9141 at node 18 0.9142 at node 18 0.9142 at node 18 20 0.4803 0.4803 0.4803 0.2001 0.2001 0.2001 0.9134 at node 18 0.9134 at node 18 0.9134 at node 18 21 0.4234 0.4234 0.4234 0.2002 0.2002 0.2002 0.9133 at node 18 0.9134 at node 18 0.9134 at node 18 22 0.3411 0.3411 0.3411 0.2005 0.2005 0.2005 0.9133 at node 18 0.9133 at node 18 0.9133 at node 18 23 2.4634 2.4634 2.4634 0.1618 0.1618 0.1618 0.9230 at node 18 0.9230 at node 18 0.9230 at node 18 24 1.7064 1.7064 1.7064 0.1657 0.1657 0.1657 0.9200 at node 18 0.9200 at node 18 0.9200 at node 18 25 1.2990 1.2990 1.2990 0.1712 0.1712 0.1712 0.9183 at node 18 0.9184 at node 18 0.9184 at node 18 26 2.4368 2.4368 2.4368 0.1058 0.1058 0.1058 0.9490 at node 18 0.9491 at node 18 0.9491 at node 18 27 2.2715 2.2715 2.2715 0.1081 0.1081 0.1081 0.9467 at node 18 0.9467 at node 18 0.9467 at node 18 28 1.8460 1.8460 1.8460 0.1136 0.1136 0.1136 0.9406 at node 18 0.9406 at node 18 0.9406 at node 18 29 1.6411 1.6411 1.6411 0.1158 0.1158 0.1158 0.9377 at node 18 0.9377 at node 18 0.9377 at node 18 30 1.5360 1.5360 1.5360 0.1176 0.1176 0.1176 0.9362 at node 18 0.9362 at node 18 0.9362 at node 18 31 1.3475 1.3475 1.3475 0.1236 0.1236 0.1236 0.9334 at node 18 0.9334 at node 18 0.9334 at node 18 32 1.2923 1.2923 1.2923 0.1259 0.1259 0.1259 0.9326 at node 18 0.9326 at node 18 0.9326 at node 18 33 1.2259 1.2259 1.2259 0.1296 0.1296 0.1296 0.9316 at node 18 0.9316 at node 18 0.9316 at node 18 4

Active power loss (MW) Active power loss(w) Active power loss (W) Active power loss (MW) Active power loss (W) Active power loss (MW) 178 0.1043 176 174 172 170 0.1042 0.1041 0.104 168 Figure 3.Active power loss of 16-node networ at node 9 using PSO 168.65 Figure 7.Active power loss of 33-node networ at node 6 using CRPSO 168.6 168.55 168.5 168.45 Figure 4.Active power loss of 16-node networ at node 9 using CRPSO Figure 8.Active power loss of 33-node networ at node 6 using TLBO 168.8 168.7 168.6 168.5 168.4 iteration cycles Figure 5.Active power loss of 16-node networ at node 9 using TLBO 0.107 Figure 9.Optimum DG size at each node for 16-node networ using three 0.106 0.105 0.104 0.103 Figure 6.Active power loss of 33-node networ at node 6 using PSO Figure 10.Active power loss at each node of 16-node networ using three 5

Figure 11.Optimum DG size at each node for 69-node networ using three power losses using three Table I shows the total active power loss and minimum voltage magnitude for base cases i.e. 16-node networ and 33- node networ. Table II shows the total active power loss, optimal DG capacity and minimum voltage magnitude for 16- node networ where DGs are placed one by one node where load is connected. Table III shows the optimal DG capacity, total active power loss and minimum voltage magnitude of 33- node networ. Figure 3, Figure 4 and Figure 5 shows the active power loss versus iteration cycle for 16-node networ using PSO, CRPSO and TLBO respectively. Figure 6,Figure 7 and Figure 8 shows the active power loss versus iteration cycle for 33-node radial distribution networ using PSO, CRPSO and TLBO respectively. Figure 9 shows the plot of optimum DG size at each node for 16-node networ. Figure 10 shows the plot of active power loss at each node of 16-node networ using three Figure 11 shows the plot of optimum DG size at respective node for 33-node networ. Figure 12 shows the plot of active power loss at each node of 33-node networ using different optimization techniques. IX. CONCLUSION This paper presents the optimum capacity of DG at various nodes using three The method is tested with two test cases i.e. 16-node radial distribution networ and 33-node radial distribution networs. The optimum location of DG is found out where overall active power losses are minimum. From the Table it is clear, that the optimal location of DG placement for 16-node networ is node 9 where total loss of the system is found to be minimum. Similarly for 33-node networ optimal location of DG is node 6. From the result it is also found that the minimum voltage magnitude of the networ is improved significantly compared to the case when DG is not placed in the networ. Figure 12.Active power loss at each node of 69-node networ using three X. REFERENCES [1] M.H.Moradi, M.Abedini, A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution system Electrical power and Energy systems, vol.34,pp.66-74,2012. [2] N.Khalesi., N.Rezaei.,M.R.Haghifarm. DG allocation with application of dynamic programming for loss reduction and reliability improvemnt Electric Power and Energy Systems, vol.33,pp.288-295,2011. [3] D.Gautam, N.Mithulananthan, Optimal DG placement in deregulated electricity maret, Electric Power System Research, vol.77, pp.1627-1636, 2007. [4] S.A.Taher.,M.Hasani.,A.Karimian., A novel method for optimal capacitor placement and sizing in distribution system with nonlinear loads and DG using GA, Common Nonlinear Sci Number Simulat, vol.16, pp.851-862, 2011. [5] N.S.Row, Y.H.Wan, Optimum location of resources in distributed planning, IEEE Trans. on PWRS, vol.4, pp.2014-2020, 1994. [6] F.S.Mounti, M.E.EI-Hawary, A priority-ordered constrined search technique for optimal distributed generation allocation in radial distribution systems 23 rd Canadian conference on Electrical and Computer Engineering (CCECE),2010. [7] B.Sooananta, W.Kuanprab, S.Hana, Determination of the optimal location and sizing of distributed generation using particle swarm optimization [8] R.Ranjan,D.Das, Simple and efficient computer algorithm to solve radial Distribution networs Electric Power Components and Systems, vol.31,pp.95-107,2003. [9] J.Z.Zhu, Optimal reconfiguration of electrical distribution networ using the refined genetic algorithm Electric Power Systems Research, vol.62,pp.37-42,2002. [10] R.Roy,S.P.Ghoshal, Evolutionary computation based comparative study of TCPS and CES control applied to automatic generation control Pow er System Technology and IEEE Power India Conference,POWERCON New Delhi,2008. [11] R. Roy, S.P. Ghoshal, "A novel crazy optimized economic load dispatch for various types of cost functions", Int. J. Electrical Power Energy Syst, vol. 30, no. 4, pp. 242 253, 2008. [12] R.V.Rao, V.J.Savsani, D.P.Vaharia, Teaching-learning based optimization: An optimization method for continuous non-linear large scale problrms, Int.J.Information Sciences, vol.183,pp.1-15,2012. [13] J.Kennedy.R.C.Eberhart, Particle swarm optimization in: Proceedings of IEEE International Conference on Neural Networs, Pearth, Australia, pp.1942-1948, 1995. 6