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...
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