Hidraulički proračun mreža pod pritiskom primenom TRIBAL-∆Q metode

Abstract

Za potrebe modeliranja mreža pod pritiskom u praksi se najĉešće koristi EPANET softver, globalno priznat kao pouzdan i robustan. EPANET koristi formulaciju osnovnih jednaĉina koje opisuju teĉenje u mrežama pod pritiskom poznatu kao metoda ĉvorova, za ĉije rešavanje se primenjuje metoda globalnog gradijenta (Global Gradient Algorithm – GGA). Alternativna formulacija metodi ĉvorova jeste formulacija metode prstenova (ΔQ metoda). Osnovna prednost formulacije metode prstenova je znaĉajno manji broj nepoznatih veliĉina, što proizilazi iz ĉinjenice da realne mreže imaju znatno manje prstenova nego ĉvorova. Osnovni nedostatak je neophodna identifikacija prstenova u mreži koja nije jednoznaĉna. U ovom radu je predstavljena nova metoda za hidrauliĉki proraĉun mreža pod pritiskom (TRIBAL–ΔQ), zasnovana na novom algoritmu za brzu identifikaciju prstenova u mreži (TRIBAL) i efikasnoj implementaciji ΔQ metode za rešavanje osnovnih jednaĉina sistema. Cilj predstavljene metode je da iskoristi oĉigledne prednosti formulacije metode prstenova i prevaziĊe poteškoće procesa identifikacije prstenova postojećih metoda baziranih na istoj formulaciji. TRIBAL–ΔQ metoda je testirana na ĉetiri primera realnih mreža razliĉite topologije i složenosti. Poseban akcenat je dat poreĊenju brzine proraĉuna TRIBAL–ΔQ metode sa GGA metodom implementiranom u EPANET. Rezultati ilustruju da, iako zahteva veći broj iteracija za konvergenciju, nova TRIBAL–ΔQ metoda ostvaruje istu preciznost proraĉuna uz bolju numeriĉku stabilnost sa znaĉajnom uštedom raĉunarskog vremena.

The most popular software for hydraulic analysis of pressurized water distribution networks nowadays is EPANET, globally recognized as reliable and robust. EPANET uses node-based formulation of governing equations and employs Global Gradiet Algorithm (GGA) to solve hydraulics of the network. Alternative formulation to the node-based one is the loop-flow formulation of governing equations, also known as the ΔQ method. Main advantage of the loop-flow formulation is significantly lower number of unknowns to solve for, coming from the fact that real-sized networks typically have far less loops than nodes. Main drawback is the need to identify loops in the network, a task with multiple alternative solutions and proven to be cumbersome. This paper presents new TRIBAL-ΔQ method for hydraulic simulation in pressurized water distribution networks, based on the new algorithm for identification of loops in the network (TRIBAL) and more efficient implementation of loop-flow method for hydraulic simulation (ΔQ). Main goal of presented method is to exploit obvious advantages of the loopflow method and overcome main drawbacks identified in similar researches. TRIBAL-ΔQ method is tested on four networks varying in topology and complexity. Focus of research is on a comparison of computational efficiency of TRIBAL-ΔQ based solver with GGA based solver implemented in EPANET. Results indicate that TRIBAL-ΔQ based solver is significantly computationally faster than GGA based one, equally accurate and has slightly better numerical stability