Abstract
The economic emission dispatch (EED) assumes a lot of significance to meet the clean energy requirements of the society and simultaneously minimizes the cost of generation. The biogeography based optimization (BBO), inspired from the geographical distribution of biological species, has some features that are common to genetic algorithm and particle swam optimization; and searches for optimal solution through the migration and mutation operators. This paper presents an effective BBO strategy for obtaining the robust solution of EED problem. The feasibility of the proposed approach is evaluated through three test systems and the results are presented to highlight its suitability for practical applications.
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Abbreviations
- \( a_{i} \;b_{i} \;c_{i} \) :
-
Fuel cost coefficients of the \( i{\text{th}} \) generator
- \( B\;B_{o} \;B_{oo} \) :
-
Loss coefficients
- BBO:
-
Biogeography based optimization
- \( d_{i} \;e_{i} \; \) :
-
Coefficients of valve point effects of the \( i{\text{th}} \) generator
- \( E \) :
-
Maximum possible emigration rate
- EED:
-
Economic emission dispatch
- ELD:
-
Economic load dispatch
- \( E_{i} \left( {P_{Gi} } \right) \) :
-
Emission cost function of the \( i{\text{th}} \) generator in ton/h
- \( F_{i} \left( {P_{Gi} } \right) \) :
-
Fuel cost function of the \( i{\text{th}} \) generator in \( \$ /{\text{h}} \)
- \( h_{i} \) :
-
Price penalty factor of the \( i{\text{th}} \) generator in \( \$ /{\text{ton}} \)
- \( I \) :
-
Maximum possible immigration rate
- \( Iter^{\hbox{max} } \) :
-
Maximum number of iterations for convergence check
- \( k \) :
-
Number of species in \( k{\text{th}} \) island
- \( K_{1} \;\,K_{2} \) :
-
Weight constants
- MED:
-
Minimum emission dispatch
- \( n \) :
-
Maximum number of species
- \( nd \) :
-
Number of decision variables
- \( ng \) :
-
Number of generators
- \( ni \) :
-
Number of islands
- \( nei \) :
-
Number of elite islands
- PM:
-
Proposed method
- \( P_{Gi} \) :
-
Real power generation at \( i{\text{th}} \) generator
- \( P_{Gi}^{\hbox{min} } \& \,\;P_{Gi}^{\hbox{max} } \) :
-
Minimum and maximum generation limits of \( i{\text{th}} \) generator respectively
- \( P_{D} \) :
-
Total power demand
- \( P_{L} \) :
-
Net transmission loss
- \( P^{\bmod } \) :
-
Island modification probability
- \( P_{m} \) :
-
Mutation probability
- \( S^{\hbox{max} } \) :
-
Maximum species count
- \( SIV \) :
-
Suitability index variable
- \( SI \) :
-
Suitability index
- \( w \) :
-
Trade-off parameter in the range of [0, 1] \( \alpha_{i} \;\,\beta_{i} \) \( \gamma_{i} \) \( \xi {}_{i} \) and \( \delta_{i} \) emission coefficients of \( i{\text{th}} \) generator
- λ :
-
Immigration rate
- μ:
-
Emigration rate
- \( \Upphi \) :
-
Objective function to be minimized
- \( \Uppsi \) :
-
Augmented objective function to be minimized
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Acknowledgments
The authors gratefully acknowledge the authorities of Annamalai University for the facilities offered to carry out this work.
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Rajasomashekar, S., Aravindhababu, P. (2013). Biogeography Based Optimization Technique for Economic Emission Dispatch. In: Malathi, R., Krishnan, J. (eds) Recent Advancements in System Modelling Applications. Lecture Notes in Electrical Engineering, vol 188. Springer, India. https://doi.org/10.1007/978-81-322-1035-1_41
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DOI: https://doi.org/10.1007/978-81-322-1035-1_41
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