Optimal Pressure Management for Large-Scale Water Distribution Systems Using Smoothing Model
Main Article Content
Abstract
Optimal pressure management in water distribution systems (WDSs) is one of the most efficient approaches to control water leakage for water utilities worldwide. The optimal pressure management can be accomplished through regulating operations of pressure reducing valves (PRVs) to ensure that the excessive pressure in the WDS is minimized. This engineering task can be casted into a nonlinear program problem (NLP) with non-smooth constraints. Until now, the non-smooth constraints have been approximated by the smoothing function of Chen Harker-Kanzow-Smale (CHKS). In this paper, instead of using the CHKS function, we propose to apply the uniform smoothing function for formulation of the NLP. Numerical simulations using two smoothing functions will be carried out for optimal pressure managements of a benchmark WDS and a real-world WDS in Thainguyen City, in Vietnam. The comparison results reveal that the NLP formulated with the uniform smoothing function outperforms the existing NLP formulated with the CHKS in terms of optimal solution accuracy.
Keywords
Leakage reduction, nonlinear optimization, water distribution systems
Article Details
References
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[2] Araujo, L. S., Ramos, H., & Coelho, S. T. Pressure control for leakage minimisation in water distribution systems management. Water resources management, 20(1) (2006) 133-149.
[3] Ulanicki, B., et al. Open and closed loop pressure control for leakage reduction. Urban Water 2(2) (2000) (1998) 105-114.
[4] Vairavamoorthy, K., & Lumbers, J. Leakage reduction in water distribution systems: Optimal valve control. Journal of hydraulic Engineering, 124(11) (1998) 1146-1154.
[5] Ulanicki, B., AbdelMeguid, H., Bounds, P., & Patel, R. Pressure control in district metering areas with boundary and internal pressure reducing valves, In Water Distribution Systems Analysis (2008) 1-13.
[6] Rossman, L.A. EPANET2-User’s Manual, U.S. Environmental Protection Agency, Cincinnati, Ohio, (2001).
[7] AbdelMeguid, Hossam, and Bogumil Ulanicki, Pressure and leakage management in water distribution systems via flow modulation PRVs, Water Distribution Systems Analysis 2010 (2010) 1124-1139.
[8] De Paola, F., Galdiero, E. and Giugni, M., Location and setting of valves in water distribution networks using a harmony search approach. Journal of Water Resources Planning and Management, 143(6) (2017) 04017015.
[9] Wright, Robert, et al., Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming, Water Resources Research 51(12) (2015) 9925-9941.
[10] Ghaddar, B., Claeys, M., Mevissen, M., & Eck, B. J., Polynomial optimization for water networks: Global solutions for the valve setting problem, European Journal of Operational Research, 261(2) (2017) 450-459.
[11] Dai, Pham Duc, and Pu Li, Optimal pressure regulation in water distribution systems based on an extended model for pressure reducing valves, Water resources management 30(3) (2016) 1239-1254.
[12] Gopal, Vipin, and Lorenz T. Biegler, Nonsmooth dynamic simulation with linear programming based methods. Computers & chemical engineering 21(7) (1997) 675-689.
[13] Chen, X., Smoothing methods for nonsmooth, nonconvex minimization. Mathematical programming, 134(1) (2012) 71-99.
[14] Sterling M, Bargiela, A. Leakage reduction by optimised control of valves in water networks. Transactions of the Institute of Measurement and Control 6(6) (1984) 293-298.
[15] Wächter, A., & Biegler, L. T., On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming, 106(1) (2006) 25-57.