Optimal methods and its application of large pumping station operation

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1 Mar 2011 Vol 29 No 2 doi /j issn GA PSO SA - PSO PSO GA Matlab SA - PSO 0 99% ~ 4 22% GA PSO 0 22% ~ 2 80% 0 02% ~ 0 40% s SA - PSO S277 9 TV675 A 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 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 B fxlyzdx821@ sina com 1962 yzdxqby@ sohu com

2 schemes by adjusting pump blade setting angles with SA - PSO are 0 99% % 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% % 0 02% % less than that based on GA and PSO respectively Computing times of the three optimizing algorithms are 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 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 w c 1 c 2 r 1 r V k j v kj j = 1 2 n v max 10% ~ 20% 2 2 t t SA 1 2 Holland

3 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 GA PSO 1 GA m 3 /s / kw h PSO 4 2 GA m 4 m 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 ZLQ ZLQ ZLQ ZLQ Q z 2 2 GA PSO 1 GA

4 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 f max - f min /ln 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 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 SA - PSO PSO SA - PSO w 5 GA PSO SA - PSO PSO 1 c 1 c θ 0 =

5 Tab 2 2 Daily operation cost of Jiangdu pumping station system based on different optimal methods F / t c /s 7 GA PSO SA - PSO GA PSO SA - PSO Tab 3 3 Optimal operation schemes of Jiangdu pumping station system based on different optimal methods F / 7 GA PSO SA - PSO GA PSO SA - PSO Tab 4 4 Operation schemes of Jiangdu pumping station system at design pump blade angles F / % ~ 2 80% 0 02% ~ 0 40% 5 F 1 F 2 F 3 GA 7 m 4 m PSO SA - PSO F % ~ 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

6 m 4 m Yan Bipeng Cheng Li Optimal operation of water-sup- ply pumping station by chaos J Journal of Drainage 0 99% ~ 4 22% SA - PSO and Irrigation Machinery Engineering in Chinese 5 Pulido-Calvo I Gutiérrez-Estrada J C Asensio-Fern ndez R Optimal design of pumping stations of inland SA - PSO intensive fishfarms J Aquacultural Engineering 2006 References 6 Zecchin A C Simpson A R Maier H R et al Applica- 1 tion of two ant colony optimisation algorithms to water J distribution system optimisation J Mathematical and Computer Modelling / Chen Yuanyuan Wu Xiance Ji Rongliang Application 7 Ostfeld A Tubaltzev A Ant colony optimization for of dynamic programming theory in optimized operation of least-cost design and operation of pumping water distri- pump station over west-south oil product pipeline J Oil & Gas Storage and Transportation in Chinese 2 Feng Xiaoli Qiu Baoyun Cao Haihong et al Optimal operation for Baoying pumping station in East Route Project of South-to-North Water Transfer J Chinese Journal of Mechanical Engineering Xin Kunlun Liu Suiqing Tao Tao et al Application of pseudo-parallel genetic algorithm in optimal operation of multisource water supply network C Proceedings of the 8th Annual Water Distribution Systems Analysis Symposium Cincinnati Ohio USA 163 Reston ASCE J bution systems J Journal of Water Resources Planning and Management Kennedy J Eberhart R Particle swarm optimization C Proceedings of IEEE International Conference on Neural Networks Piscataway IEEE Service Center 1995 IV M Ratnaweera A Halgamuge S K Watson H C Self-organizing hierarchical particle swarm optimizer with timevarying acceleration coefficients J IEEE Transaction on Evolutionary Computation