Optimal control of water distribution systems by network flow theory

Abstract

e e d b a c k c o n t r o l a r o u n d t h e o p e r a t i n g p o i n t s , which absorbs estimate e r r o r and s m a l l v a r i a t i o n i n consumption. The scheme has been realized by a minicomputer system and i s p r e s e n t l y i n o p e r a t i o n . 1. I n t r o d u c t i o n Owing t o i n c r e a s i n g u r b a n i z a t i o n , s c a r c i t y o f w a t e r r e s o u r c e s h a s become a s e r i o u s p r o b l e m i n u r b a n areas. Minimizing of water waste i s u r g e n t l y n e e d e d . Consumers want t o r e c e i v e w a t e r w i t h h i g h p r e s s u r e , b u t e x c e s s p r e s s u r e c a u s e s w a t e r l e a k a g e f r o m p i p e j u n ct i o n s . It i s g e n e r a l l y t h o u g h t t h a t 20% of a l l t h e w a t e r i n t h e d i s t r i b u t i o n s y s t e m i s l o s t t h r o u g h l e a k a g e . F o r t h i s r e a s o n , p r e s s u r e m u s t b e r e g u l a t e d o r d i s t r i b u t i o n s y s t e m s h a v e b e e n s t u d i e d . However, t h e s e s t u d i e s [l-41 have not aimed a t r e g u l a t i n g p r e s s u r e , b u t r a t h e r a t s c h e d u l i n g t h e o p e r a t i o n s o f r e s e r v o i r s and pumping devices for economical dispatch. For the purpose, i t is n o t n e c e s s a r y t o d e a l w i t h p r e c i s e p r e s s u r e , l i n e a r i t y c a n s o m e t i m e s b e assumed ( s e e [ 2 ] ) , and r e d u c t i o n o f t h e c o m p u t a t i o n a l time i s n o t c r i t i c a l . T h i s p a p e r p r e s e n t s a modelling technique and c o n t r o l s c h e m e f o r p r e s s u r e ( a s w e l l a s f l o w ) r e g u l at i o n w h i c h s o l v e s t h e a b o v e -m e n t i o n e d l a r g e -s c a l e nonl i n e a r p r o b l e m . A system model must be realized in minimum o r d e r f o r c o n t r o l p u r p o s e s . The net:--ork aggregation method makes s u c h m o d e l l i n g p o s s i b l e . To overcome n o n l i n e a r i t y , a two-level control scheme i s i n t r o d u c e d , w h i c h c o n s i s t s of t h e s e t t i n g o f o p e r a t i n g p o i n t s a n d t h e f e e d b a c k c o n t r o l a r o u n d them. A very f a s t o p t i m i z a t i o n t e c h n i q u e t o d e t e r m i n e o p e r a t i n g p o i n t s i s derived from network flow theory, making onl i n e c o n t r o l p o s s i b l e . T h e f o l l o w i n g s e c t i o n s d e s c r i b e t h e m o d e l l i n g t e c h n i q u e and t h e c o n t r o l scheme a l o n g w i t h some implementation experience. This scheme has been CH1788-9/82/0000-0362$00.75@ 1982 IEEE 362 r e a l i z e d by a minicomputer system with telemetry d e v i c e s and i s p r e s e n t l y i n o p e r a t i o n . 2 . Modelling of Distribution Systems 2 . 1 System Equations A w a t e r d i s t r i b u t i o n s y s t e m is a n e t w o r k , t h e a r c s of which are pipes and the nodes of which a r e r e s e r v o i r s , c o n s u m p t i o n p o i n t s a n d p i p e j u n c t i o n s . Pressure and flow on t h e n e t w o r k a r e...

GPU-Accelerated Stochastic Predictive Control of Drinking Water Networks

“…Dynamical models of drinking water networks have been studied in depth in the last two decades [11], [14], [32]. Flowbased models are derived from simple mass balance equations of the network which lead to the following pair of equations…”

“…Nowû i j , e i j , β i j are calculated from (30), (32) and (36b) respectively. Using our assumption that L is full-rank, we can see thatR is a positive definite and symmetric matrix, therefore, f is strongly convex.…”

Economics of Water Resources: From Regulation to Privatization

“…Numerous studies in the literature have examined various water-distribution designs using network programming and other mathematical programming techniques to find an efficient and minimum-cost distribution system (Miyaoka & Funabashi 1984, Ratcliffe 1986, Orth 1986, Todini & Pilati 1987, Germanopoulos 1988, lowitt & Xu 1990. Orth (1986), for instance, using pressure, pipe-diameter, material and other hydraulic-design constraints, has taken a mathematical programming approach to find the most efficient pipeline network to satisfy water demand.…”

Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks

“…These approaches employ computationally expensive meta-heuristics or suffer from inefficient coupling of gradient-based optimization with non-smooth simulation by existing network hydraulics software, such as EPANET [20]. Other topics in water management include network design [21][22][23][24], online control [25,26], state estimation [27], and contamination detection [28]. More loosely related recent work addresses modeling and optimization for networks of irrigation and sewage canals or for gas networks, see, e.g., [29][30][31][32][33][34][35].…”