Bacteria foraging based algorithm for optimum economic load dispatch with non-convex loads

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Bacteria foraging based algorithm for optimum economic load dispatch with non-convex loads

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Abstract

An algorithm based on Bacteria Foraging (BF) was developed to solve the problem of finding the optimum load allocation amongst the committed units in power system with non-convex loads. The performance of the proposed algorithm is evaluated on a test case of 15 units. The performance of the algorithm is compared with floating point genetic algorithm (FPGA) with optimum parameters. In addition, the BF algorithm is evaluated with and without swarming effect. Results demonstrate that the performance of the BF algorithm is far better than FPGA algorithm in terms of convergence rate and solution quality. BF algorithm with swarming effect proves to be more efficient as compared to that without swarming. Economic load dispatch (ELD) in electric power system is the optimum allocation of load amongst the committed generating units subject to satisfaction of the constraints. Most of the conventional classical dispatch algorithms, like lambda-iteration method, base point and participation factors method, and the gradient method [1], [2] are gradient based methods and hence, cannot tackle the non-convexity well.

Abstract
Introduction
Bacterial foraging algorithm (BFA)
1. Chemotaxis
2. Swarming
3. Reproduction
4. Elimination and dispersal
5. BFA algorithm in brief
ELD problem formulation
Numerical tests
Conclusion
References

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[...] Wollenberg, Power Generation, Operation and Control, second edition, New York, USA, Wiley K. P. Wong, and Y. W. Wong, “Thermal generator scheduling using hybrid genetic/simulated annealing approach,” IEE Proc. Part-C, Vol.142, No.4, pp.372-380, July D. C. Walter, and G. B. Sheble, “Genetic algorithm solution of economic dispatch with valve point loading,” IEEE Trans. on Power Systems, Vol.8, No.3, pp.1325-1332, August A. Petridis V. Bakirtzis, and S. Kazarlis, S., “Genetic algorithm solution to the economic dispatch problem,” IEE Proc. Part-D, Vol No pp. 377–382, July G. B. Sheble, and K. [...]

[...] For each elimination-dispersal event each bacterium in the population is subjected to elimination-dispersal with probability ped. To keep the number of bacteria constant, if we eliminate a bacterium, simply disperse one to a random location in the optimization domain. The flowchart of the bacterial foraging algorithm is shown in Fig.1. E. BFA Algorithm in brief: Step Initialization First following variables must be chosen. Number of bacteria to be used in the search. Number of parameters to be optimized. Ns: Swimming length. [...]

[...] Huang, “Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions,” IEEE Trans. on Power Systems, Vol.11, No.1, pp.112-118, February X. Yao, Y. Liu, and G. Lin, “Evolutionary programming made faster,” IEEE Trans. Evolutionary Computation, Vol pp. 82–102, July Nidul Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary programming techniques for economic load dispatch,” IEEE Trans. on Evolutionary Computation, Vol.7, No.1, pp.83-94, February Nidul Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Fast Evolutionary programming techniques for short-term hydrothermal scheduling,” IEEE Trans. [...]

[...] The performance of BFA algorithms in both forms is better than FPGA C st o ) x Generations Fig The convergence nature of FPGA on the test case x 10 BFA with swarming 3 Cost 2.5 BFA without swarming Chamotectic steps Fig.3: The convergence nature of BFA with swarming and without swarming. Table-2. Statistical test results of 10 runs with different initial solutions (with non-smooth cost curves) for the test case. Method Average cost (Rs.) 34131 Maximum cost 34540 Minimum cost (Rs.) 33523 FPGA BFA (without swarming) BFA (with swarming) V. CONCLUSION Algorithms based on FPGA, BFA (swarming) and BFA (without swarming) are developed in Matlab and their performances are tested on a test case of 15 units for non-convex economic load dispatch problems with valve point loading effects. [...]

[...] (iii) To investigate into the performance of the algorithm with swarming as well as without swarming on the same problem. II. BACTERIAL FORAGING ALGORITHM (BFA) The idea of foraging under BFA is based on the fact that natural selection tends to eliminate animals with poor foraging strategies and favour those having successful foraging strategies. After many generations, poor foraging strategies are either eliminated or reshaped into good ones. The E. coli bacteria that are present in our intestines have a foraging strategy governed by four processes, namely, chemotaxis, swarming, reproduction, and elimination and dispersal [28]. [...]

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