Optimal Reorganization and Extension of an Existing Water Distribution Network Using the Thevenin Equivalent Network
Publication: World Environmental and Water Resources Congress 2023
ABSTRACT
A water distribution network (WDN) costs more than 60% of the total cost of a water supply system. It is indeed crucial to optimize a WDN for its economical design. Due to rapid urbanization and population growth, a particular portion of the existing network must be reorganized or extended to new zones. For the purpose of optimal reorganization, the new zone or the portion of the existing network can be identified as the sub-network. The optimal design of the sub-network demands high computational effort as the entire network needs to be simulated multiple times. To improve computational efficiency, the sub-network is separated from the large network, and the remaining network is replaced with its equivalent network with a minimum number of elements using the Thevenin theorem. The theorem can replace an extensive network with its equivalent, having a single reservoir connected in series with an equivalent pipe. The optimal design of the sub-network uses the derived Thevenin equivalent network connected with the sub-network. As the overall network size becomes considerably small, the computational effort also reduces exponentially. The probability of getting the most optimal solution is also improved as the search space is reduced. The proposed methodology is demonstrated with the help of a realistic WDN, and computational efficiency is investigated for various sets of pipe diameters. The network reduction method is found to be enormously helpful for hydraulic engineers in designing and optimizing a sub-network for reorganization and extension.
Get full access to this article
View all available purchase options and get full access to this chapter.
REFERENCES
Alexander, C., and Sadiku, M. (2000). Fundamentals of Electric Circuits,2000. McGraw-Hill.
Anderson, E. J., and Al-Jamal, K. H. (1995). “Hydraulic-network simplification.” J. Water Resour. Plan. Manage.,121(3). https://doi.org/10.1061/(ASCE)0733-9496(1995)121:3(235).
Bahadur, R., Johnson, J., Janke, R., and Samuels, W. B. (2006). “Impact of model skeletonization on water distribution model parameters as related to water quality and contaminant consequence assessment.” 8th Annual Water Dis. Sys. Anal. Sym., CIncinati, Ohio, USA.
Balireddy, R., Chakravorty, A., Bhallamudi, S. M., and Kuiry, S. N. (2021). Applications of the single-port linear Thevenin theorem for focused and efficient analysis of a sub-network connected with a large existing pipe network. Urban Water Journal, 18(9), 681–698.
Balireddy, R., Chakravorty, A., Bhallamudi, S. M., and Kuiry, S. N. (2022). Simplification of water distribution networks using non-linear Thevenin theorem and its application for maximum power transfer. Journal of Hydroinformatics.
Benzi, M., Golub, G. H., and Liesen, J. (2005). Numerical solution of saddle point problems. Acta numerica, 14, 1–137. https://doi.org/10.1017/S0962492904000212.
Broad, D., Maier, H. R., and Dandy, G. C. (2009). “Optimal operation of complex water distribution systems using metamodels.” J. Water Resour. Plan. Manage., 136(4), 433–443. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000052.
Chua, L. O. (1969). Introduction to nonlinear network theory. McGraw-Hill.
Cross, H. (1936). Analysis of flow in networks of conduits or conductors. University of Illinois at Urbana Champaign, College of Engineering. Engineering Experiment Station.
Desa, U. (2018). World urbanization prospects 2018. United Nations Department for Economic and Social Affairs.
Deuerlein, J. W. (2008). “Decomposition model of a general water supply network graph.” J. Hyd. Eng., 134(6), 822–832. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(822).
Eggener, C. L., and Polkowski, L. B. (1976). “Network models and the impact of modeling assumptions.” J. American Water Works Asso., 68(4), 189–196.
Eliades, D. G., Kyriakou, M., Vrachimis, S., and Polycarpou, M. M. (2016, November). EPANET-MATLAB toolkit: An open-source software for interfacing EPANET with MATLAB. In Proc. 14th international conference on computing and control for the water industry (ccwi) (Vol. 8).
Elhay, S., Simpson, A. R., Deuerlein, J., Alexander, B., and Schilders, W. H. (2014). Reformulated co-tree flows method competitive with the global gradient algorithm for solving water distribution system equations. Journal of Water Resources Planning and Management, 140(12), 04014040.
Epp, R., and Fowler, A. G. (1970). Efficient code for steady-state flows in networks. Journal of the hydraulics division, 96(1), 43–56.
Jeppson, R. W. (1982). “Equivalent hydraulic pipe for parallel pipes.” J. Hyd. Div., 108(1), 35–45.
Johnson, D. H. (2003). “Origins of the equivalent circuit concept: the voltage-source equivalent.” Proc. IEEE, 91(4), 636–640.
Jung, B., Boulos, P. F., and Wood, D. J. (2007). “Impacts of skeletonization on distribution system hydraulic transient models.” World Env. Water Res. Cong. 2007: Restoring Our Natural Habitat, 1–10.
Kumar, S. M., Narasimhan, S., and Bhallamudi, S. M. (2008). “State estimation in water distribution networks using graph-theoretic reduction strategy.” J. Water Resour. Plan. Manage., 134(5), 395–403. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:5(395).
Larock, B. E., Jeppson, R. W., and Watters, G. Z. (1999). Hydraulics of pipeline systems. CRC press.
Martínez Alzamora, F., Ulanicki, B., and Salomons, E. (2014). Fast and practical method for model reduction of large-scale water-distribution networks. Journal of Water Resources Planning and Management, 140(4), 444–456.
Ostfeld, A. “Reliability analysis of regional water distribution systems.” Urban Water 3, no. 4 (2001): 253–260. https://doi.org/10.1016/S1462-0758(01)00035-8.
Perelman, L., and Ostfeld, A. (2011). “Water-distribution systems simplifications through clustering.” J. Water Resour. Plan. Manage., 138(3), 218–229.
Piller, O., and Brémond, B. (2002). “A stochastic model for peak period analysis of pipe networks.” ASCE Env. Water Res. Sys. Anal. (EWRSA).
Qiu, M., Elhay, S., Simpson, A. R., and Alexander, B. (2019). Benchmarking study of water distribution system solution methods. Journal of Water Resources Planning and Management, 145(2), 04018098.
Rao, Z., and Alvarruiz, F. (2007). “Use of an artificial neural network to capture the domain knowledge of a conventional hydraulic simulation model.” J. Hydroinf, 9(1), 15–24.
Saldarriaga, J., Ochoa, S., Rodriguez, D., and Arbeláez, J. (2008). “Water distribution network skeletonization using the resilience concept.” Water Dis. Sys. Anal. 2008, 1–13.
Sarbu, I., and Ostafe, G. (2016). Optimal design of urban water supply pipe networks. Urban Water Journal, 13(5), 521–535.
Schafer, A., and Victor, D. G. (2000). The future mobility of the world population. Transportation research part a: policy and practice, 34(3), 171–205.
Simpson, A. R., Elhay, S., and Alexander, B. (2014). Forest-core partitioning algorithm for speeding up analysis of water distribution systems. J. Water Resour. Plan. Manage., 140(4), 435–443. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000336.
Todini, E. (2000). “Looped water distribution networks design using a resilience index based heuristic approach.” Urban water, https://doi.org/10.1016/S1462-0758(00)00049-2.
Todini, E., and Pilati, S. (1988). A gradient algorithm for the analysis of pipe networks. In Computer applications in water supply: vol. 1---systems analysis and simulation (pp. 1–20).
Van Valkenburg, M. E. (1964). Network analysis, Vol. 3. Prentice-Hall Englewood Cliffs, NJ.
Walski, T. M., Chase, D. V., Savic, D. A., Grayman, W., Beckwith, S., and Koelle, E. (2003). Advanced water distribution modeling and management. Haestad press.
Wood, D. J., and Charles, C. O. (1972). Hydraulic network analysis using linear theory. J. Hyd. div., 98(7), 1157–1170. https://doi.org/10.1061/JYCEAJ.0003348.
Alcocer-Yamanaka, V. H., Tzatchkov, V. G., and Arreguin-Cortes, F. I. (2012). “Modeling of drinking water distribution networks using stochastic demand.” Water res. Manage., https://doi.org/10.1007/s11269-012-9979-2.
Yang, S.-L., Hsu, N.-S., Louie, P. W. F., and Yeh, W. W. G. (1996). “Water distribution network reliability: Stochastic simulation.” J. infra. Sys., 2(2), 65–72, https://doi.org/10.1061/(ASCE)1076-0342(1996)2:2(65).
Information & Authors
Information
Published In
History
Published online: May 18, 2023
ASCE Technical Topics:
- Analysis (by type)
- Benefit cost ratios
- Business management
- Design (by type)
- Economic factors
- Engineering fundamentals
- Financial management
- Hydraulic design
- Infrastructure
- Practice and Profession
- System analysis
- Urban and regional development
- Water and water resources
- Water management
- Water supply
- Water supply systems
- Water use
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.