Flows Split in Closed Loops Expending Least Energy

Arora, Madan

doi:10.1061/jyceaj.0004520

Cited by 8 publications

(4 citation statements)

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“…The literature on solving the nonconvex WFP as well as other related problem formulations is rich and briefly summarized next. The main classical approaches to solve the WFP are based on Hardy-Cross [13], Newton-Raphson [14]- [16], linearization [17], [18], optimization [19], [20], gradientbased [21], and more recently, fixed-point methods [22], [23]. All of these methods are iterative algorithms developed to solve a set of linear and nonlinear equations to obtain the physical status of WDNs, i.e., the flow through each pipe or the head at each node.…”

Section: A Literature Reviewmentioning

confidence: 99%

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Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

Wang

Taha

Gatsis

et al. 2020

IEEE Trans. Control Netw. Syst.

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Optimal, network-driven control of water distribution networks (WDNs) is very difficult: valve and pump models form non-trivial, combinatorial logic, hydraulic models are nonconvex, water demand patterns are uncertain, and WDNs are naturally large-scale. Prior research on control of Water Distribution Network (WDN)s addressed major research challenges, yet either (i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or (ii) used mixed-integer, nonconvex optimization to solve WDN control problems.The objective of this paper is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints-all while only using convex, continuous optimization. Specifically, we propose new Geometric Programming (GP)-based Model Predictive Control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls-pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. Under demand uncertainty, the proposed approach is tested using a 126-node network with many valves and pumps and shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results are all included on Github.

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Section: A Literature Reviewmentioning

confidence: 99%

“…where the closed form expression of f GP (•) is given in Appendix B. The WDN constraints (19) can be rewritten as Constraints-GP:…”

Section: Abstract Gp Modelmentioning

confidence: 99%

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

Wang

Taha

Gatsis

et al. 2020

IEEE Trans. Control Netw. Syst.

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“…Inspired by this idea, we can apply the inverse operation to WFP-GP (25), and generate an LP for the WFP. After applying the log function on both sides of GP form of the mass balance equation (17), the result would be the original linear form of the mass balance equation (4). It means the linear modeling is converted back from GP modeling.…”

Section: Lp Modeling Derived From Gp Modelingmentioning

confidence: 99%

“…The literature of solving the WFP as well as other related problem formulations is rich and briefly summarized next. The main approaches for solving the WFP are based on Hardy-Cross [5], Newton-Raphson [6]- [10], linearization [11]- [16], optimization [17], [18], gradient-based [4], [10], graph decomposition [19]- [22] and more recently, fixed-point methods [23], [24]. These methods can be classified as primarily relying on iterative updating, decomposition methods, or optimization-based formulations, and differ in terms of their modeling limitations and complexity, handling non-linearities, and convergence speed, as discussed in the following paragraphs.…”

Section: Introductionmentioning

confidence: 99%

A New Derivative‐Free Linear Approximation for Solving the Network Water Flow Problem With Convergence Guarantees

Wang

Taha

Sela

et al. 2020

Water Resources Research

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Addressing challenges in urban water infrastructure systems, including aging infrastructure, supply uncertainty, extreme events, and security threats, depends highly on water distribution networks modeling emphasizing the importance of realistic assumptions, modeling complexities, and scalable solutions. In this study, we propose a derivative‐free, linear approximation for solving the network water flow problem. The proposed approach takes advantage of the special form of the nonlinear head loss equations, and, after the transformation of variables and constraints, the water flow problem reduces to a linear optimization problem that can be efficiently solved by modern linear solvers. Ultimately, the proposed approach amounts to solving a series of linear optimization problems. We demonstrate the proposed approach through several case studies and show that the approach can model arbitrary network topologies and various types of valves and pumps, thus providing modeling flexibility. Under mild conditions, we show that the proposed linear approximation converges. We provide sensitivity analysis and discuss in detail the current limitations of our approach and suggest solutions to overcome these. All the codes, tested networks, and results are freely available on Github for research reproducibility.

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Design of Water Distribution Network by a Noniterative Two-Stage Optimization

Gupta

Bhave

2006

ISH Journal of Hydraulic Engineering

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The authors have suggested a two-stage methodology: (l) stage I to obtain the optimal flow distribution by linear programming (LP); and (2) stage 2 to obtain the optimal solution by LP for the flow distribution obtained in stage I .The authors have made different statements for optimal flow distribution. On p. 21, initially they state " ... global optimal solution can be achieved only when the sum of the carrying capacity of the links is minimum." They have neither explained this statement further nor described any method of obtaining it. Later, on the same page they state "The first stage is based on the concept that the flow follows the path of least resistance. The flow distribution is such that the total energy loss in the system is minimum." This is true for any network, and not only for the optimal network. Arora ( 1976) stated that "Flows in the pipes of a hydraulic network adjust so that the expenditure of the system energy is minimum." They used this concept to provide an optimality-based method of network analysis-to obtain the flows in different pipes of looped networks. They minimized system energy SE = I.iKQxhxl in which K = appropriate constant; Qx = discharge in pipe x; hx = head loss in pipe x; and the summation sign covers all pipes of the network (Bhave, 1991 ). Later, the authors claim that the linear optimization model of Eqs. ( 1) and (2) provides the optimal flow distribution. This may not be true as shown later.By treating the pipe diameter as a continuous variable, the total cost of a gravity network is by (Bhave, 1978;Maidamwar et al., 2000; Bhave, 2003). C.= ~ K Km/ r Ll+ml rQpm/ rh -m/,. I £... 2 I X X X

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Flows Split in Closed Loops Expending Least Energy

Cited by 8 publications

References 0 publications

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

A New Derivative‐Free Linear Approximation for Solving the Network Water Flow Problem With Convergence Guarantees

Design of Water Distribution Network by a Noniterative Two-Stage Optimization

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