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Economic Load Dispatch Using Hybrid MpBBO-SQP Algorithm

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Nature-Inspired Computation in Engineering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 637))

Abstract

Solving economic load dispatch (ELD) problems of electric power systems means finding the optimal output of the generating units, so that the load demand can be satisfied with the lowest possible operating cost, and without violating any design constraint. Recently, many nature-inspired algorithms have been successfully used to solve these highly constrained non-linear and non-convex ELD problems without facing much efforts as regularly happens with the conventional optimization algorithms. Biogeography-based optimization (BBO) algorithm is a new population-based evolutionary algorithm (EA). As per the conducted studies in the literature, BBO has good exploitation, but it lacks exploration. In this study, the poor exploration level of BBO is enhanced by hybridizing it with the Metropolis criterion of the simulated annealing (SA) algorithm in order to have more control on the migrated individuals; and hence the first phase of this proposed algorithm is called Metropolis BBO (in short MpBBO). The second hybridization phase is done by combining the strength of the Sequential Quadratic Programming (SQP) algorithm with MpBBO to have a new superior algorithm called MpBBO-SQP, where the best solutions per each generation of MpBBO phase is fine-tuned by SQP phase. The performance of MpBBO-SQP is evaluated using three test cases with five different cooling strategies of SA. The results obtained show that MpBBO-SQP outperforms different BBO models as well as many other competitive algorithms presented in the literature.

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Notes

  1. 1.

    The mechanisms of most algorithms are inspired by nature; or, in a more specific, from biology, physics and chemistry sciences [15].

  2. 2.

    It is important to note that the solution of this analytical technique becomes valid only if \(P_1\) passes some restrictions, like: located between lower and upper limits, positive and real, satisfies prohibited operating zones, satisfies downward and upward ramp rates, etc.

  3. 3.

    This statement becomes invalid if ramp rate limits, prohibited operating zones and transmission losses \(P_L\) are considered.

  4. 4.

    SQP is skipped because it is very popular and detailed explanation can be easily found in many mathematical optimization books; like [30].

  5. 5.

    In the literature, different cooling strategies are proposed for this purpose.

  6. 6.

    Biogeography is a branch of biology science, and it is a synthetic discipline, relying heavily on theory and data from ecology, population biology, systematics, evolutionary biology, and the earth sciences [34]. Biogeography seeks to describe, analyze and explain the geographic patterns and changing distributions of ecosystems and fossil species of plants (flora) and animals (fauna) through geological space and time [35, 36].

  7. 7.

    In island biogeography, the word “island” could be aquatic island, desert oasis, individual plants, caves, lakes or ponds, mountain-tops (sky-islands), microcosms or even patches of terrestrial ecosystems [39, 40].

  8. 8.

    The emigration and immigration rates can be modeled as exponential, logistic, linear, etc. [34, 41, 42]. Also, the maximum emigration and immigration rates can be unequal (i.e., \(I\ne E\)) [38, 42]. Moreover, the equilibrium location \(\hat{S}\) can be shifted to the right or left side based on the type of rate functions, the area of island and/or the distance or isolation between the recipient island and the source island or mainland [34, 38, 43].

  9. 9.

    Biotic factors: predation, competition, interactions, etc. Abiotic factors: wind, water, sunlight, temperature, pressure, soil, etc. [46].

  10. 10.

    The blended BBO, given in [49], has the ability to avoid this duplication phenomenon.

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  1. Electrical and Computer Engineering, Dalhousie University, 1459 Oxford Street, Halifax, NS, B3H 4R2, Canada

    Ali R. Al-Roomi & Mohamed E. El-Hawary

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  1. Ali R. Al-Roomi
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  2. Mohamed E. El-Hawary
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Correspondence to Ali R. Al-Roomi .

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  1. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

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Al-Roomi, A.R., El-Hawary, M.E. (2016). Economic Load Dispatch Using Hybrid MpBBO-SQP Algorithm. In: Yang, XS. (eds) Nature-Inspired Computation in Engineering. Studies in Computational Intelligence, vol 637. Springer, Cham. https://doi.org/10.1007/978-3-319-30235-5_11

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  • DOI: https://doi.org/10.1007/978-3-319-30235-5_11

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