18meee15.pptx

Artificial bee colony optimization for multi-area economic dispatch Author: m. basu Presented by:

PRANAY M. SEN(18MEEE15)

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CONTENTS • • • • • •

Abstract/Introduction Problem formulation Artificial bee colony optimization(ABCO) Implementation of ABCO Simulation Conclusion

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Abstract/Introduction • Artificial bee colony optimization for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. • Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees.

• The effectiveness of the proposed algorithm has been verified on different test systems and compared with Differential evolution (DE), evolutionary programming (EP) and real coded genetic algorithm (RCGA). 3

Problem formulation Constraints used: 1. Real power balance constraints 𝑀𝑖

෍ 𝑃𝑖𝑗 = 𝑃𝐷𝑖 + 𝑃𝐿𝑖 + ෍ 𝑗=1

𝑘,𝑘≠𝑖

2. Tie line capacity constraints 𝑚𝑎𝑥 𝑚𝑎𝑥 −𝑇𝑖𝑘 ≤ 𝑇𝑖𝑘 ≤ 𝑇𝑖𝑘 3. Real power generation capacity constraints 𝑃𝑖𝑗𝑚𝑖𝑛 ≤ 𝑃𝑖𝑗 ≤ 𝑃𝑖𝑗𝑚𝑎𝑥 4. Prohibited operating zone 𝑙 𝑃𝑖𝑗𝑚𝑖𝑛 ≤ 𝑃𝑖𝑗 ≤ 𝑃𝑖𝑗,1 𝑢 𝑙 𝑃𝑖𝑗,𝑚−1 ≤ 𝑃𝑖𝑗 ≤ 𝑃𝑖𝑗,𝑚 𝑢 𝑚𝑎𝑥 𝑃𝑖𝑗,𝑛 ≤ 𝑃 ≤ 𝑃 𝑖𝑗 𝑖𝑗 𝑖𝑗

𝑇𝑖𝑘

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Problem formulation (contd.) The objective of MAED is to minimize the total production cost of supplying loads to all areas while satisfying different constraints. MAED problems considered:

1. MED with quadratic cost function, prohibited operating zones and transmission losses (MAEDQCPOZTL) 𝑀𝑖 𝑀𝑖 𝑁 𝑁 𝐹𝑡 = σ𝑖=1 σ𝑗=1 𝐹𝑖𝑗 𝑃𝑖𝑗 = σ𝑖=1 σ𝑗=1 𝑎𝑖𝑗 +𝑏𝑖𝑗 𝑃𝑖𝑗 +𝑐𝑖𝑗 𝑃𝑖𝑗2 2. MAED with valve point loading (MAEDVPL) 𝑀𝑖 𝑁 𝐹𝑡 = σ𝑖=1 σ𝑗=1 𝐹𝑖𝑗 𝑃𝑖𝑗 = 𝑀𝑖 𝑚𝑖𝑛 2 σ𝑁 σ 𝑎 +𝑏 𝑃 +𝑐 𝑃 +|𝑑 ∗ sin 𝑒 ∗ 𝑃 − 𝑃𝑖𝑗 | 𝑖𝑗 𝑖𝑗 𝑖=1 𝑗=1 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗

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Problem formulation (contd.) 3. MAED with valve point loading multiple fuel sources and transmission losses (MAEDVPLMFTL) 𝐹𝑖𝑗 𝑃𝑖𝑗 = 𝑎𝑖𝑗𝑚 +𝑏𝑖𝑗𝑚 𝑃𝑖𝑗 +𝑐𝑖𝑗𝑚 𝑃𝑖𝑗2 +|𝑑𝑖𝑗 ∗ sin 𝑒𝑖𝑗 ∗ 𝑃𝑖𝑗𝑚𝑖𝑛 − 𝑃𝑖𝑗 | 𝑚𝑖𝑛 𝑚𝑎𝑥 If 𝑃𝑖𝑗𝑚 ≤ 𝑃𝑖𝑗 ≤ 𝑃𝑖𝑗𝑚 for fuel type m

𝐹𝑡 = 𝐹𝑖𝑗 𝑃𝑖𝑗

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Artificial bee colony optimization

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Implementation of ABCO for MAED problem •

Initialization

pn= [(P11,P12,…,P1m1),…, (Pi1,Pi2,…,Pim1),…, (PN1,PN2,…, 𝑃𝑁𝑀𝑁 ),…, (T12,T13,…,T1N), (T23,T24,…,T2N),…,(T(N-1)N)] •

Evaluation of fitness 1 fitness = Ft

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Selection of initial population

Select m best solutions on the basis of highest fitness for neighborhood search 8

Implementation of ABCO for MAED problem • Generation of neighborhood solution (nb) 𝑃𝑟𝑖𝑗 =𝑃𝑛𝑖𝑗 + 𝑚𝑢𝑙𝐺 ∗ 𝑁 0,1 ∗ (𝑃𝑖𝑗𝑚𝑎𝑥 − 𝑃𝑖𝑗𝑚𝑖𝑛 ) 𝑚𝑎𝑥 𝑚𝑎𝑥 𝑇𝑟𝑖𝑘 =𝑇𝑛𝑖𝑘 + 𝑚𝑢𝑙 𝑇 ∗ 𝑁 0,1 ∗ (𝑇𝑖𝑘 − (−𝑇𝑖𝑘 )) • Selection Select the best solution from nb * m • Termination The search process is stopped as the count of generations reaches Nmax otherwise select best m solutions to generate neighborhood solutions. 9

Simulation Result 1

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Simulation Result 2

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Simulation Result 2

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Simulation Result 3

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Simulation Result 3

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CONCLUSION • In this paper, ABCO has been successfully implemented to solve MAED problems.

• The effectiveness of the proposed method is illustrated by using three different test systems and the test results are compared with the results obtained from DE, EP and RCGA. • It is seen from the comparison that the proposed ABCO has the ability to converge to a better quality solution than DE, EP and RCGA. 15

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