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Artificial Bee Colony Optimization for Short-Term Hydrothermal Scheduling

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Abstract

Artificial bee colony optimization is applied to determine the optimal hourly schedule of power generation in a hydrothermal system. Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The algorithm is tested on a multi-reservoir cascaded hydroelectric system having prohibited operating zones and thermal units with valve point loading. The ramp-rate limits of thermal generators are taken into consideration. The transmission losses are also accounted for through the use of loss coefficients. The algorithm is tested on two hydrothermal multi-reservoir cascaded hydroelectric test systems. The results of the proposed approach are compared with those of differential evolution, evolutionary programming and particle swarm optimization. From numerical results, it is found that the proposed artificial bee colony optimization based approach is able to provide better solution.

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Abbreviations

a si , b si , c si , d si , e si :

Cost curve coefficients of ith thermal unit

C 1j , C 2j , C 3j , C 4j , C 5j , C 6j :

Power generation coefficients of jth hydro unit

I hjt :

Inflow rate of jth reservoir at time t

k :

Index of prohibited zones of a hydro unit

N s :

Number of thermal generating units

N h :

Number of hydro generating units

n j :

Number of prohibited zones for hydro unit j

P sit :

Output power of ith thermal unit at time t

P min si , P max si :

Lower and upper generation limits for ith thermal unit

P Dt :

Load demand at time t

P Lt :

Transmission loss at time t

P hjt :

Output power of jth hydro unit at time t

P min hj , P max hj :

Lower and upper generation limits for jth hydro unit

Q hjt :

Water discharge rate of jth reservoir at time t

Q min hj , Q max hj :

Minimum and maximum water discharge rate of jth reservoir

Q L hj,k , Q U hj,k :

Lower and upper bounds of kth prohibited zones of hydro unit j

R uj :

Number of upstream units directly above jth hydro plant

S hjt :

Spillage of jth reservoir at time t

t, T :

Time index and scheduling period

UR i , DR i :

Ramp-up and ramp-down rate limits of the ith thermal unit

V hjt :

Storage volume of jth reservoir at time t

V min hj , V max hj :

Minimum and maximum storage volume of jth reservoir

τ lj :

Water transport delay from reservoir l to j

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Author information

Authors and Affiliations

  1. Department of Power Engineering, Jadavpur University, Kolkata, India

    M. Basu

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  1. M. Basu
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Corresponding author

Correspondence to M. Basu.

Appendix

Appendix

Table 7 Cost curve coefficients, ramp-rate limits and operating limits of thermal generators
Full size table
Table 8 Load demand
Full size table

Transmission loss coefficients are given below:

$$ B = 10^{ - 4} \times \left[ {\begin{array}{*{20}r} \hfill {0. 3 4} & \hfill {0. 1 3} & \hfill {0.0 9} & \hfill { - 0.0 1} & \hfill { - 0.0 8} & \hfill { - 0.0 1} & \hfill { - 0.0 2} \\ \hfill {0. 1 3 } & \hfill {0. 1 4} & \hfill {0. 10} & \hfill {0.0 1} & \hfill { - 0.0 5} & \hfill { - 0.0 2} & \hfill { - 0.0 1} \\ \hfill {0.0 9} & \hfill {0. 10} & \hfill {0. 3 1} & \hfill {0.00} & \hfill { - 0. 1 1} & \hfill { - 0.0 7} & \hfill { - 0.0 5} \\ \hfill { - 0.0 1} & \hfill {0.0 1} & \hfill {0.00} & \hfill {0. 2 4} & \hfill { - 0.0 8} & \hfill { - 0.0 4} & \hfill { - 0.0 7} \\ \hfill { - 0.0 8} & \hfill { - 0.0 5} & \hfill { - 0. 1 1} & \hfill { - 0.0 8} & \hfill { 1. 9 2} & \hfill {0. 2 7} & \hfill { - 0.0 2} \\ \hfill { - 0.0 1} & \hfill { - 0.0 2} & \hfill { - 0.0 7} & \hfill { - 0.0 4} & \hfill {0. 2 7} & \hfill {0. 3 2} & \hfill {0.00} \\ \hfill { - 0.0 2} & \hfill { - 0.0 1} & \hfill { - 0.0 5} & \hfill { - 0.0 7} & \hfill { - 0.0 2} & \hfill {0.00} & \hfill { 1. 3 5} \\ \end{array} } \right]{\text{ per MW}} $$
$$ B0 = 10^{ - 6} \times \left[ {-0. 7 500 \, -0.0 600 \, 0. 7000 \, -0.0 300 \, 0. 2 700 \, -0. 7 700 \, -0.0 100} \right] $$
$$ B00 \, = \, 0.55{\text{ MW}} $$

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Basu, M. Artificial Bee Colony Optimization for Short-Term Hydrothermal Scheduling. J. Inst. Eng. India Ser. B 95, 319–328 (2014). https://doi.org/10.1007/s40031-014-0119-7

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