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A Hybrid Big Bang–Big Crunch optimization algorithm for solving the different economic load dispatch problems

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Abstract

In this paper, we applied a Hybrid Big Bang–Big Crunch optimization technique for solving the different types of economic load dispatch (ELD) problems in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and non-smooth cost functions are considered using the proposed method in practical generator operation. The proposed method is tested on three different systems (six-unit system considering losses, 15 units: ED considering transmission loss, large system: 40 generating units with valve-point loading effects). Furthermore, results are compared with other optimization approaches proposed in the recent literature, showing the feasibility of this technique to highly nonlinear and different ELD problem.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Biskra, Biskra, Algeria

    Yacine Labbi

  2. Department of Electrical Engineering, University of El-Oued, El-Oued, Algeria

    Yacine Labbi & Djilani Ben Attous

Authors
  1. Yacine Labbi
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  2. Djilani Ben Attous
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Correspondence to Yacine Labbi.

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Appendix

Appendix

β matrices of 15 generating units:

$$\begin{aligned} \beta_{ij} & = \left[ {\begin{array}{*{20}l} {0.0014} \hfill & {0.0012} \hfill & {0.0007} \hfill & { - 0.0001} \hfill & { - 0.0003} \hfill & { - 0.0001} \hfill & { - 0.0001} \hfill & { - 0.0001} \hfill & {0.0003} \hfill & {0.0005} \hfill & { - 0.0003} \hfill & { - 0.0002} \hfill & {0.0004} \hfill & {0.0003} \hfill & { - 0.0001} \hfill \\ {0.0012} \hfill & {0.0015} \hfill & {0.0013} \hfill & {0.0000} \hfill & { - 0.0005} \hfill & { - 0.0002} \hfill & {0.0000} \hfill & {0.0001} \hfill & { - 0.0002} \hfill & { - 0.0004} \hfill & { - 0.0004} \hfill & { - 0.0000} \hfill & {0.0004} \hfill & {0.0010} \hfill & { - 0.0002} \hfill \\ {0.0007} \hfill & {0.0013} \hfill & {0.0076} \hfill & { - 0.0001} \hfill & { - 0.0013} \hfill & { - 0.0009} \hfill & { - 0.0001} \hfill & {0.0000} \hfill & { - 0.0008} \hfill & { - 0.0012} \hfill & { - 0.0017} \hfill & { - 0.0000} \hfill & { - 0.0026} \hfill & {0.0111} \hfill & { - 0.0028} \hfill \\ { - 0.0001} \hfill & {0.0000} \hfill & { - 0.0001} \hfill & {0.0034} \hfill & { - 0.0007} \hfill & { - 0.0004} \hfill & {0.0011} \hfill & {0.0050} \hfill & {0.0029} \hfill & {0.0032} \hfill & { - 0.0011} \hfill & { - 0.0000} \hfill & {0.0001} \hfill & {0.0001} \hfill & { - 0.0026} \hfill \\ { - 0.0003} \hfill & { - 0.0005} \hfill & { - 0.0013} \hfill & { - 0.0007} \hfill & {0.0090} \hfill & {0.0014} \hfill & { - 0.0003} \hfill & { - 0.0012} \hfill & { - 0.0010} \hfill & { - 0.0013} \hfill & {0.0007} \hfill & { - 0.0002} \hfill & { - 0.0002} \hfill & { - 0.0024} \hfill & { - 0.0003} \hfill \\ { - 0.0001} \hfill & { - 0.0002} \hfill & { - 0.0009} \hfill & { - 0.0004} \hfill & {0.0014} \hfill & {0.0016} \hfill & { - 0.0000} \hfill & { - 0.0006} \hfill & { - 0.0005} \hfill & { - 0.0008} \hfill & {0.0011} \hfill & { - 0.0001} \hfill & { - 0.0002} \hfill & { - 0.0017} \hfill & {0.0003} \hfill \\ { - 0.0001} \hfill & {0.0000} \hfill & { - 0.0001} \hfill & {0.0011} \hfill & { - 0.0003} \hfill & { - 0.0000} \hfill & {0.0015} \hfill & {0.0017} \hfill & {0.0015} \hfill & {0.0009} \hfill & { - 0.0005} \hfill & {0.0007} \hfill & { - 0.0000} \hfill & { - 0.0002} \hfill & { - 0.0008} \hfill \\ { - 0.0001} \hfill & {0.0001} \hfill & {0.0000} \hfill & {0.0050} \hfill & { - 0.0012} \hfill & { - 0.0006} \hfill & {0.0017} \hfill & {0.0168} \hfill & {0.0082} \hfill & {0.0079} \hfill & { - 0.0023} \hfill & { - 0.00036} \hfill & {0.0001} \hfill & {0.0005} \hfill & { - 0.0078} \hfill \\ { - 0.0003} \hfill & { - 0.0002} \hfill & { - 0.0008} \hfill & {0.0029} \hfill & { - 0.0010} \hfill & { - 0.0005} \hfill & {0.0015} \hfill & {0.0082} \hfill & {0.0129} \hfill & {0.0116} \hfill & { - 0.0021} \hfill & { - 0.0025} \hfill & {0.0007} \hfill & { - 0.0012} \hfill & { - 0.0072} \hfill \\ { - 0.0005} \hfill & { - 0.0004} \hfill & { - 0.0012} \hfill & {0.0032} \hfill & { - 0.0013} \hfill & { - 0.0008} \hfill & {0.0009} \hfill & {0.0079} \hfill & {0.0116} \hfill & {0.0200} \hfill & { - 0.0027} \hfill & { - 0.0034} \hfill & {0.0009} \hfill & { - 0.0011} \hfill & { - 0.0088} \hfill \\ { - 0.0003} \hfill & { - 0.0004} \hfill & { - 0.0017} \hfill & { - 0.0011} \hfill & {0.0007} \hfill & {0.0011} \hfill & { - 0.0005} \hfill & { - 0.0023} \hfill & { - 0.0021} \hfill & { - 0.0027} \hfill & {0.0140} \hfill & {0.0001} \hfill & {0.0004} \hfill & { - 0.0038} \hfill & {0.0168} \hfill \\ { - 0.0002} \hfill & { - 0.0000} \hfill & { - 0.0000} \hfill & { - 0.0000} \hfill & { - 0.0002} \hfill & { - 0.0001} \hfill & {0.0007} \hfill & { - 0.0036} \hfill & { - 0.0025} \hfill & { - 0.0034} \hfill & {0.0001} \hfill & {0.0054} \hfill & { - 0.0001} \hfill & { - 0.0004} \hfill & {0.0028} \hfill \\ {0.0004} \hfill & {0.0004} \hfill & { - 0.0026} \hfill & {0.0001} \hfill & { - 0.0002} \hfill & { - 0.0002} \hfill & { - 0.0000} \hfill & {0.00001} \hfill & {0.0007} \hfill & {0.0009} \hfill & {0.0004} \hfill & { - 0.0001} \hfill & {0.0103} \hfill & { - 0.0101} \hfill & {0.028} \hfill \\ {0.0003} \hfill & {0.0010} \hfill & {0.0111} \hfill & {0.0001} \hfill & { - 0.0024} \hfill & { - 0.0017} \hfill & { - 0.0002} \hfill & {0.00005} \hfill & { - 0.0012} \hfill & { - 0.0011} \hfill & { - 0.0038} \hfill & { - 0.0004} \hfill & { - 0.0101} \hfill & {0.0578} \hfill & { - 0.0094} \hfill \\ { - 0.0001} \hfill & { - 0.00002} \hfill & { - 0.0028} \hfill & { - 0.0026} \hfill & { - 0.0003} \hfill & {0.0003} \hfill & { - 0.0008} \hfill & { - 0.0078} \hfill & { - 0.0072} \hfill & { - 0.0088} \hfill & {0.0168} \hfill & {0.0028} \hfill & {0.0028} \hfill & { - 0.0094} \hfill & {0.1283} \hfill \\ \end{array} } \right] \\ \beta_{oi} & = \left[ { - 0.0001 \, - 0.0002 \, 0.0028 \, - 0.0001 \, 0.0001 \, - 0.0003 \, - 0.0002 \, - 0.0002 \, 0.0006 \, 0.0039 \, - 0.0017 \, - 0.0000 \, - 0.0032 \, 0.0067 \, - 0.0064} \right] \\ \beta_{oo} & = \, 0.055. \\ \end{aligned}$$

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Labbi, Y., Attous, D.B. A Hybrid Big Bang–Big Crunch optimization algorithm for solving the different economic load dispatch problems. Int J Syst Assur Eng Manag 8, 275–286 (2017). https://doi.org/10.1007/s13198-016-0432-4

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