Optimal methods and its application of large pumping station operation

2011 3 29 2 Mar 2011 Vol 29 No 2 doi 10 3969 /j issn 1674-8530 2011 02 008 225127 GA PSO SA - PSO PSO GA Matlab SA - PSO 0 99% ~ 4 22% GA PSO 0 22% ~ 2 80% 0 02% ~ 0 40% 3 30 52 25 s SA - PSO S277 9 TV675 A 1674-8530 2011 02-0127 - 06 Optimal methods and its application of large pumping station operation Feng Xiaoli Qiu Baoyun Yang Xingli Shen Jian Pei Bei School of Energy and Power Engineering Yangzhou University Yangzhou Jiangsu 225127 China Abstract In order to master modern optimal methods which are suitable for solving large pumping station optimal operation with multivariables Basic principles of genetic algorithms GA particle swarm optimization PSO and simulated annealing-particle swarm optimization SA - PSO were introduced and the similarities and differences were analyzed It is concluded that PSO is more simple and efficient than GA Taking Jiangdu pumping station system in Eastern Route of South-to-North Water Transfer Project as an example under the circumstances of certain pump assembly head selecting the number of running pump units and blade setting angles of water pumps as variables optimal mathematical models for pumping station operation schemes were established aiming at the least operation cost meeting the constraint conditions such as total pumping discharge allowed discharge of single pump and the number of running pump units GA PSO and SA - PSO were applied to solve the models respectively to determine the number of running pump units operation duties of pump units and daily operation cost of each pumping station Constraint conditions were used to deal with feasible rules and calculating procedure was programmed with Matlab The results indicate that the operation costs of the optimum 2010-08 - 07 2007B41 2008048 1982 fxlyzdx821@ sina com 1962 yzdxqby@ sohu com

128 29 schemes by adjusting pump blade setting angles with SA - PSO are 0 99% - 4 22% less than that of the conventional schemes under design blade angles and among the three optimum schemes the operation cost of the optimum scheme based on SA - PSO is about 0 22% - 2 80% 0 02% - 0 40% less than that based on GA and PSO respectively Computing times of the three optimizing algorithms are 30 52 and 25 s respectively Therefore SA - PSO is more suitable for solving large pumping station operation optimization problems Key words large pumping stations operation schemes optimization methods genetic algorithms particle swarm optimization simulated annealing-particle swarm optimization 1 2-3 4-7 1 2 PSO 8 GA n PSO SA - k X k = x k1 x k2 x kn V k = v k1 v k2 v kn t = p k1 p k2 p kn P g 1 P k 1 1 GA Darwin Mendel V k t + 1 = wv k t + c 1 r 1 P k t - X k t + c 2 r 2 P g t - X k t 1 X k t + 1 = X k t + V k t + 1 2 w c 1 c 2 r 1 r 2 0 1 V k j v kj j = 1 2 n v max 10% ~ 20% 2 2 t + 1 - t 1 3 9 SA 1 2 Holland

2 129 1 P a PSO f x x x' x ΔE = f x' f x x' x = min 1 exp - ΔE /θ θ P a f x' < f x P a = 1 1 PSO f x' > f x P a 0 ~ 1 3 GA 1 PSO GA PSO 4 PSO GA Metropolis PSO SA - PSO 2 2 1 GA PSO 1 GA m 3 /s 0 829 / kw h PSO 4 2 GA 3 4 7 m 4 m 350 1 M 2 Q T P T H s 1 3 GA Tab 1 Performance parameters of pump units in Jiangdu PSO pumping station M / Q T / P T / H s / m 3 s - 1 kw m 4 1 75ZLQ - 7 8 80 8 000 7 8 1 75ZLQ - 7 8 80 8 000 7 8 2000ZLQ13 5-7 8 10 135 16 000 7 8 2900ZLQ30-7 8 7 210 23 800 7 8 5 6 3 1 Q z 2 2 GA PSO 1 GA

130 29 1 F = min [ 4 2 j = 1 ( i = 1 ρgq i H z m i + P 1 000η zi η dri η zni + ΔP te1 mot i ) i + ΔP bj + ΔP te2 ] t y e 10-4 3 - f max - f min /ln 0 1 0 92 0 01 F ρ kg /m 3 g m /s 2 H z { m i w = w min + w max - w min f - f min f f f av - f av min Q i i w max f > f av m 3 /s m i i η zi i 5 η moti i w max w min w η dri i P zni 1 5 0 01 f f av f min f max kw ΔP te1i kw j ΔP bj j kw ΔP te2 kw t y { h e / kw h c 1 = c 1min - c 1max G + c G 1max max 2 4 c 2 = c 6 2max - c 2min G + c Q i n i = Q z G 2min max i = 1 c 1min c 1max c 2min c 2max c 1 c 2 Q i min Q i Q i max 4 c 1max = c 2max = 2 5 c 1min = c 2min = α i min α i α i max 0 5 G G max m i M i 3 2 i Q i m i 3 Q z m 3 /s Q i min Q i max i 2 3 H z F m 3 /s α i i t c m α α i min α i max i M i i 2 50 GA PSO SA - PSO Matlab 3 200 300 50 2 SA - PSO PSO SA - PSO w 5 GA PSO SA - PSO PSO 1 c 1 c 2 6 10 3 0 θ 0 =

2 131 4 3 Tab 2 2 Daily operation cost of Jiangdu pumping station system based on different optimal methods F / t c /s 7 GA 65 720 6 66 304 5 67 712 5 0 394 6 52 PSO 65 592 6 65 816 5 66 296 0 0 153 1 25 SA - PSO 65 578 2 65 681 1 66 157 8 0 104 7 30 4 GA 44 454 7 45 686 8 48 109 7 0 844 4 52 PSO 43 385 3 44 543 7 45 963 1 0 540 2 25 SA - PSO 43 210 1 43 858 9 44 828 5 0 369 3 30 Tab 3 3 Optimal operation schemes of Jiangdu pumping station system based on different optimal methods F / 7 GA 2-1 19 4 0 99 3-0 99 7-0 57 65 720 6 PSO 4 1 00 6-0 47 0 7-0 15 65 592 6 SA - PSO 4-0 04 6-0 04 0 7-0 09 65 578 2 4 GA 7-0 20 5-3 06 3-0 65 4-0 30 44 454 7 PSO 8-3 06 7-2 86 0 5-2 62 43 385 3 SA - PSO 8-4 00 8-4 00 0 5-3 32 43 210 1 Tab 4 4 Operation schemes of Jiangdu pumping station system at design pump blade angles F / 7 5 91 0 5 91 0 6 51 0 3 96 0 66 233 5 4 4 88 0 4 88 0 5 52 0 3 41 0 45 112 5 0 22% ~ 2 80% 0 02% ~ 0 40% 5 F 1 F 2 F 3 GA 7 m 4 m PSO SA - PSO 66 233 5 45 112 5 F 4 0 99% ~ 3 SA - PSO 4 22% SA - PSO GA PSO Tab 5 5 Comparison on operation cost of Jiangdu pumping station system based on different optimal methods 4 GA PSO SA - PSO /% F 4 / F 1 / F 2 / F 3 / F 1 - F 3 /F 1 F 2 - F 3 /F 2 F 4 - F 3 /F 4 7 65 720 6 65 592 6 65 578 2 66 233 5 0 215 0 021 0 988 4 44 454 7 43 385 3 43 210 1 45 112 5 2 800 0 404 4 217 3

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