外文翻譯-- 擴(kuò)展的粒子群算法與經(jīng)典優(yōu)化算法的比較（英文）

1、 Comparison of Enhanced-PSO and Classical Optimization Methods: a case study for STATCOM placement Yamille del Valle and Ronald G. Harley Department of Electrical and Computer engineering Georgia Institute of Techno

2、logy Atlanta, GA 30332 USA yamille.delvalle@gatech.edu, rharley@ece.gatech.edu Ganesh K. Venayagamoorthy Department of Electrical and Computer Engineering Missouri University of Science and Technology Rolla, MO 6540

3、9 USA gkumar@ieee.org Abstract—This paper validates the effectiveness of an enhanced particle swarm optimizer (Enhanced-PSO) method in solving the problem of optimal allocation of FACTS devices in a power system. The

4、 performance of the Enhanced-PSO method is compared with classical optimization approaches using a simple but realistic case study of optimal allocation of STATCOM devices, considering steady state and economic criter

5、ia. This paper also discusses the concepts and details about the optimization process that tend to be overlooked in the literature since the selection of an optimization algorithm highly depends on them. Index Terms—

6、 FACTS devices, classical optimization, Benders’ decomposition, branch and bound, evolutionary computation techniques, particle swarm optimization. I. INTRODUCTION HE topic of optimal allocation of FACTS (Flexible AC

7、Transmission System) devices is still in a relatively early stage of investigation. Currently, there is no widely accepted method and many researchers claim their methods to be “better” than others. Considering the pr

8、esent state-of-the-art in this area, a comparison of different methods, particularly between classical and metaheuristic approaches, has been difficult because each study focuses on different problem formulations, sy

9、stem sizes and operating conditions. This paper provides a common background for comparing the performance of classical and metaheuristic optimization algorithms. In particular between Bender’s decomposition and Branc

10、h-and-bound (B therefore an exhaustive manual search can be performed to find the global optimum, (ii) the problem has a reduced, scattered and non convex feasible region, and (iii) only a steady state criterion is c

11、onsidered to avoid possible discrepancies if a transient analysis was also to be included [20]. A. Objective Function Two goals are considered: (i) to minimize voltage deviations in the system and (ii) to minimize the

12、cost. Thus, two metrics J1 and J2 are defined as in (1) and (3). ∑ ? =Nk V J12 1 ) 1 ((1) where J1 is the voltage deviation metric, Vk is the p.u. value of the voltage at bus k and N is the total number of buses. The t

13、otal cost function, Ctotal, consists of two components: a fixed cost per unit that is installed in the system and a variable cost that is a linear function of each unit size: ∑ = ? + ? =Mp p v f total C M C M C1 ) ( η

14、 (2) where M is the number of units to be allocated, Cf is the fixed cost per unit, Cv is the cost per MVA, and ηp is the size in MVA of unit p. Since Cf >> Cv, it is convenient to normalize each term of the c

15、ost function prior to its inclusion in the objective function: MVA Max MMM CCM CM C JMp pvMp p vff _1max max max1max2 ∑ ∑ = = + = ? ??+ ?? =ηηη(3) where J2 is the cost metric, Mmax is the maximum number of STATCOM unit

16、s to be allocated, and ηmax is the maximum size in MVA of each STATCOM unit. The multi-objective optimization problem can now be defined using the weighted sum of both metrics J1 and J2 to create the overall objectiv

17、e function J shown in (4). 2 2 1 1 J J J ? + ? = ω ω(4) The weight for each metric is adjusted to reflect the relative importance of each goal. In this case, considering the maximum magnitudes of J1 and J2, it is decid

18、ed to assign values of ω1 = 1 and ω2 = 0.5, such that both metrics have equal importance. B. Decision Variables The decision variables are the location of the STATCOM units and their sizes. These variables can be arra

19、nged in a vector as: [ ] M M i x η λ η λ ... 1 1 =(5) where λp, p=1...M, is the location (bus number) of STATCOM unit p. All components of the decision vector are integer numbers, thus xi ∈ Z2M. C. Constraints There a

20、re several constraints in this problem regarding the characteristics of the power system and the desired voltage profile. Each constraint represents a limit in the search space, which in this particular case correspon

21、ds to: Generator buses are omitted from the search process since they have voltage regulators to regulate the voltage. ? Bus numbers are limited to {1, 2,…, N}. ? Only one unit can be connected at each bus. ? The number

22、 of units: 1≤ M ≤ 5. ? The size of each unit: 0≤ ηp ≤ 250 MVA. ? The desired voltage profile requires N additional restrictions defined as: { } N k Vk ,..., 2 , 1 , 05 . 1 95 . 0 ∈ ? ≤ ≤(6) Each solution that does not s