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M is the set of switches belong to the same mesh with switch d. The second loop limits the number of open switches to the number of meshes. The modified BPSO procedure is as follows:

1.	Set population size (m), maximal iteration number and stop criterion. 2.	Randomly select in feasible solutions x, compute p for each x, p8 is the minimum in all pi, the initial values of v; are zero, 3.	Using (2) to calculate vi for particle i. 4.	Using (7) to update xL 5.	Calculate feeder load balancing index. 6.	If the fitness value of particle i is better than the previous pi, the value is set to pi. If the best p is better than p,, the value is set to pB 7.	If stop criterion is satisfied, p8 is the optimal solution, otherwise, go to Step 3. When the stop criterion is satisfied or the maximal iteration number is reached, the procedure is ended. B. Inertia Weight w The inertia weight w plays the role of balancing the global search and local search [6]. It can be a positive constant or a positive liner or nonlinear function of time. When w is small the PSO is more like a local search algorithm. When w is large (> 1.2), the PSO is more like a global search method and even more it always tries to exploit the new areas. The bigger the inertia weight w is, the less dependent on initial population the solution is, and the more capable to exploit new areas the PSO is. The range [0.9, 1.2] is a good area to choose w from. The PSO with w in this range will have a bigger chance to find the global optimum within a reasonable number of iterations. We defined the inertia weight was a decreasing function of time instead of a fixed constant. It started with a large value 1.4 and linearly decreased to 0.4 when the iteration number reached 100. We also take w as fixed constant (0.4, 0.8, 1.2, 1.6, and 2.0) as comparison.

C. No-hope/Re-hope System We also need a mechanism to prevent the swarm from getting stuck in local optima. This mechanism is called the no-hope/re-hope system and is used, among others, by [8].We

use a different approach to get the search going again. When a certain particle has not changed its fitness over a predefined number of times, it is moved to a new random position in the search space. No-hope for a particle thus means that it is not moving any more or it has been wandering around on a plateau in the search space. An application of the no-hope mechanism leaves the best position for the particle unchanged.

VI. TEST RESULTS The test system, as show in Fig. 2, includes 13 distribution transformers and 16 branches. The network is supplied by three substations and each branch has been considered with a switch Thus we can use it to represent a simplified large-scale distribution network. The electrical data can be found in [ 1 ].

The network has three meshes: branch 3, 4, 5 and 6; branch 7, 8 and 9; branch 10, 11, 12, 13 and 14. For each group of branch, only one switch on one of the branches can be opened, in order to maintain the radial structure. As branch 15 does not belong to any mesh, it must be closed to keep it connected with the source.

(11)	(12) Distribution (	) Branch number Fig. 2. Test system In this test, dimension size is 16, the population size is set to 100, maximum number of iteration is set to 100, cr=2.0, c2=2.0. Since the algorithm are based on random number generators that may create different sequences of random numbers, to show average performance, 10 run were executed. They all converged to the same solution: switches on branch 5, 7 and 12 are open. It is the same with the result in [11. On average, the optimal solutions can be obtained in 4-7 iterations. The modified BPSO has a good perform in searching for better feeder reconfiguration for load balancing.

TABLE I OPEN SWrrCHES AND LOAD BALANCING MEX BEFORE AND AFTER FEEDER RECONFIGURATION Open switches	Load balancing index Initial condition	4, 8, 12	6.537 Final solution	5, 7, 12	6.062

TABLE II AVERAGE ITERATION TIME FOR DIFFERENT INERTIA WEIGHT inertia weight (w)	Average iteration time 0.4	5.82 0.8	5.4 1.2	5.3 1.6	5.7 2.0	6.16 1.40.4	4.8 As shown in table II, the decreasing inertia weight w has better result than fixed constant.

VII. CONCLUSION A modified binary particle swarm optimization algorithm is proposed in this paper to configure distribution network to keep load balancing. A novel model is used to simplify the distribution network. The problem is formulated as a non-linear optimization problem with an objective function of minimizing load balancing index subject to security constraints. Test results have shown that using the modified BPSO method, the feeder reconfiguration problem can be solved efficiently and the load balancing index is decreased by reconfiguration.

VIII. REFERENCES 1.	Augugliaro, A.; Dusonchet, L.; Ippolito, M.G.; Sanseverino, E.R.; "Minimum losses reconfiguration of MV distribution networks through local control of tie-switches," Power Delivery, IEEE Transactions on, Volume: 18, Issue: 3, July 2003 Pages:762 - 771 2.	Papadopoulos, M.P.; Peponis, G.J.; Boulaxis, N.G.; Drossos, N.X.;'Heuristic methods for the optimisation of MV distribution networks operation and planning," Electricity Distribution. Part 1. Contributions. 14th International Conference and Exhibition on (TEE Conf. Publ. No. 438), Volume: 6, 2-5 June 1997 Pages:911 - 915 vo1.6 3.	Chang, R.F.; Lu, C.N.; "Feeder reconfiguration for load factor improvement," Power Engineering Society Tinter Meeting, 2002. IEEE ,Volume: 2, 27-31 Jan. 2002 Pages:980 - 984 vol.2 4. 	Kennedy, J.; Ebe hare, R.;'Particle swarm optimization," Neural Networks, 1995. Proceedings„ IEEE International Conference on, Volume: 4 , 27 Nov.-l Dec. 1995 Pages:1942 - 1948 vol.4 5.	Kennedy, J.; Eberbart, R.C.; "A discrete binary version of the particle swarm algorithm," Systems, Man, and Cybernetics, 1997. 'Computational Cybernetics and Simulation'., 1997 IEEE International Conference on, Volume: 5, 12-15 Oct 1997 Pages-.4104 - 4108 vol.5 6. 	Shi, Y.; Eberhart, R.; "A modified particle swarm optimizer," Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence, The 1998 IEEE International Conference on, 4-9 May 1998 Pagee69 - 73 7.	Juan Liu; Bi Pengxiang; Zhang Yanging; Wu Xiaomeng; 'Power flow analysis on simplified feeder modeling.' Power Delivery, IEEE Transactions on, Volume: 19, Issue: 1, Jan. 2004 Pages:279 - 287 8. 	Schoofs, L.; Naudts, B.; "Swarm intelligence on the binary constraint satisfaction problem," Evolutionary Computation, 2002. CEC '02. Proceedings of the 2002 Congress on, Volume: 2 , 12-17 May 2002 Pages: 1444 -1449

IX. BIOGRAPHIES Xiaoling An received the bachelor's degree in Electrical Engineering in 2001 at Shandong University, China. She is now working on PhD at Shandong University. Her research interest includes distribution network automation. Jranguo Zhao is presently a professor at Shandong University. His research interest includes power system operation and control Ying Sun is presently a professor at Shandong University. His research interest includes power system operation and control. Kejun Li is presently a lecturer at Shandong University. His research interest includes FACTS. Boqin Zhang is presently an assistant engineer at Huangtai electrical power station.