EVALUATION OF THE SUITABILITY OF GLOBAL GRADIENT ALGORITHM AND INVERSE MATRIX METHOD FOR STEADY-STATE ANALYSIS OF WATER DISTRIBUTION NETWORKS

Yıl 2018, Cilt: 7 Sayı: 1, 23 - 33, 31.01.2018

Selami Demir

https://doi.org/10.28948/ngumuh.383777

Cited By: 1

Öz

   Two methods
for steady-state analysis of water distribution networks (WDNs) were evaluated
in this paper: Global Gradient Algorithm (GGA) and inverse matrix method (IMM).
Both methodologies are based on the solution of nonlinear system of equations
formed by mass and energy balances within a WDN. A number of WDNs were solved
using both methods. Results showed that GGA solves the WDNs in around 70 to 75%
less number of iterations than IMM. Besides, single GGA solution of a WDN takes
less time compared to IMM solution (about 57% faster for a network of 31
elements). In contrast, single iteration takes 127 to 552 μs with IMM while it
takes 235 to 773 μs with GGA depending on the number of network elements.
Evaluations are based on the speed, the accuracy, and ease of handling the
iteration procedures and it was concluded that, although GGA provides faster
solutions, both methods are fast enough and IMM, with its simpler iteration
procedure, could be beneficial if employed for teaching WDNs in engineering
education.

Anahtar Kelimeler

Water distribution networks, systems of nonlinear equations, global gradient algorithm, inverse matrix method

İÇME SUYU ŞEBEKELERİNİN KARARLI DURUM ANALİZİ İÇİN KÜRESEL GRADYEN ALGORİTMASI VE TERS MATRİS YÖNTEMİNİN UYGUNLUĞUNUN DEĞERLENDİRİLMESİ

Öz

   Bu çalışmada içme suyu şebekelerinin kararlı
akım analizi için kullanılabilen iki yöntem değerlendirilmiştir: Küresel
Gradyen Algoritması (KGA) ve ters matris yöntemi (TMY). Her iki yöntem de
şebeke için yazılan kütle ve enerji korunum denklemlerinden oluşan, doğrusal
olmayan denklem sisteminin çözümüne dayanmaktadır. Bu çalışmada her iki yöntem
de kullanılarak bir dizi şebeke çözümü yapılmıştır. Sonuçlar, KGA’nın TMY’ye
göre yaklaşık %70 ile %75 oranında daha az iterasyonla sonuca ulaştığını
göstermiştir. Ayrıca, KGA ile tek şebeke çözümü, TMY’ye göre daha az zaman
almaktadır (31 elemanlı bir şebeke için yaklaşık %57 oranında daha hızlı). Buna
karşın, şebekedeki eleman sayısına bağlı olmak üzere TMY’de tek iterasyon 127
ile 552 µs’de tamamlanırken KGA’da 235 ile 773 µs sürmektedir. Değerlendirmeler
metotların hızı, doğruluğu ve iterasyon prosedürlerinin kolaylığına göre
yapılmış olup, KGA daha hızlı çözümler üretmesine karşın her iki yöntemin de
yeteri kadar hızlı olduğunu söylemek mümkündür ve iterasyon prosedürleri çok
daha kolay olduğu için TMY’nin mühendislik eğitiminde içme suyu şebekelerini
öğretmek için kullanılması KGA’ya göre daha avantajlı olabilir.

Anahtar Kelimeler

İçme suyu şebekeleri, doğrusal olmayan denklem sistemleri, küresel gradyen algoritması, ters matris yöntemi

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