**6. References**


Optimal Sizing of Harmonic Filters in Electrical Systems: Application of a Double Simulated Annealing Process 45

[3] Saric A.T, Calovic M.S, Djukanovic M.B (1997) Fuzzy optimisation of capacitors in distribution systems. IEE Proc. Generation Transmission Distribution, Vol. 144, n° 5, pp 415-422.

44 Simulated Annealing – Single and Multiple Objective Problems

**Table 10.** Parameters of the power transformers

*Department of Industrial Engineering and Maintenance, IUT Saint-Nazaire, University of Nantes, France* 

Distribution, Vol. 142, n° 1, pp 24-28.

**Author details** 

Patrick Guérin

**6. References** 

100, pp. 1105-1118.

Laurence Miègeville

Irms(A) 5 7 11 13

**Table 9.** Harmonic currents (A) injected by the non linear loads of the power system

*Department of Electrical Engineering, POLYTECH Nantes, University of Nantes, France* 

[1] Grainger J.J., Lee S.H (1981) Optimal size and location of shunt capacitors for reduction of losses in distribution feeders. IEEE Trans. on Power Application System, vol. PAS-

[2] Wu Z.Q, Lo K.L (1995) Optimal choice of fixed and switched capacitors in radial distributors with distorted substation voltage. IEE Proc. Generation Transmission

*Research Institute on Electrical Energy of Nantes Atlantique, St Nazaire, France* 

*Research Institute on Electrical Energy of Nantes Atlantique,St Nazaire, France* 

*MP\_BD* 0 0 53.7 38.8 *MP\_TD* 0 0 53.7 38.8 *MT\_BD* 46.5 24.7 14.4 9.75 *MT\_TD* 46.5 24.7 14.4 9.75 *UPS\_BD* 30.2 18.6 15.2 9.3 *UPS\_TD* 30.2 18.6 15.2 9.3 *Fluo\_ES* 5.4 0.8 0.4 0.4 *UPS4* 1.6 1.0 0.8 0.5 *Fluo\_BD* 8.9 1.3 0.6 0.6 *Fluo\_TB* 8.9 1.3 0.6 0.6 *UPS6* 1.6 1.0 0.8 0.5

ref. U1n (V) U2n (V) Sn (kVA) ucc (%) *TR3* 690 400 2000 5.5 *TR4* 690 400 2000 5.5 *TR5* 400 230 300 6 *TR6* 400 230 300 6 *TR8* 400 230 80 5.5

order h

	- [18] Thompson J, Dowsland KA (1995) General cooling schedules for a simulated annealing based timetabling system. Proceedings of the first International Conference on the practice and Theory of Automated timetabling, Napier University, Edinburgh.

**Chapter 3** 

© 2012 San-José-Revuelta, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 San-José-Revuelta, licensee InTech. This is a paper distributed under the terms of the Creative Commons

**Simulated Quenching Algorithm for Frequency** 

This chapter focuses on a specific application of two Natural Computation (NC)-based techniques: Simulated Quenching (SQ) and Genetic Algorithms (GA): the problem of channels' assignment to radio base stations in a spectrum efficient way. This task is known to be an NP-complete optimization problem and has been extensively studied in the last two decades. We have decided to include both SQ and GA in the chapter so as o give an academic

According to this point of view, our main interest is in describing and comparing the performances of these algorithms for solving the channel allocation problem (CAP). Therefore, the aim of our work is not the full theoretical description of SQ and GA. Surely,

There exists an important research activity in the field of mobile communications in order to develop sophisticated systems with increased network capacity and performance. A particular problem in this context is the assignment of available channels (or frequencies) to based stations in a way that quality of service is guaranteed. Like most of the problems that appear in complex modern systems, this one is characterized by a search space whose complexity increases exponentially with the size of the input, being, therefore, intractable for solutions using analytical or simple deterministic approaches (Krishnamachari, 1998; Lee, 2005). An important group of these problems −including the one we are interested in−

Simulated Quenching (SQ) belongs to the family of Simulated Annealing (SA)-like algorithms. Simulated Annealing is a general method for solving these kind of combinatorial optimization problems. It was originally proposed by (Kirkpatrick, 1983) and (Černy, 1985). Since then, it has been applied in many engineering areas. The basic SA algorithm can be considered a generalization of the local search scheme, where in each step

orientation to this work for readers interested in practical comparisons of NC methods.

**Planning in Cellular Systems** 

Additional information is available at the end of the chapter

some other chapters in this book will cover this issue.

belong to the class of NP-complete problems (Garey, 1979).

Luis M. San-José-Revuelta

http://dx.doi.org/10.5772/50566

**1. Introduction** 

