Geometric Programming-Based Control for Nonlinear, DAE-Constrained Water Distribution Networks

IEEE Trans. Control Netw. Syst.

Gatsis

et al. 2020

Self Cite

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.

Section: B Paper Contributionsmentioning

confidence: 99%

Section: Control-oriented Modeling Of Wdnsmentioning

confidence: 99%

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

IEEE Trans. Control Netw. Syst.

Gatsis

et al. 2020

Self Cite

“…In this section, we introduce the modeling of WDNs. 1) Tanks and Reservoirs: The water hydraulic dynamics in the i th tank can be expressed by a discrete-time difference equation [16] h TK i pk`1q"h TK i pkq`∆ t A TK i¨ÿ jPN in i q ji pkq´ÿ jPN out i q ij pkq‚ . (7) where h TK i , A TK i respectively stand for the head, cross-sectional area of the i th tank, and ∆t is sampling time; q ji pkq, j P N in i is inflow, while q ij pkq, j P N out i is outflow of the j th neighbor.…”

Section: A Modeling Wdnsmentioning

confidence: 99%

“…Using this technique, we can convert some problems with negative feasible regions into a new problem with a positive feasible region, and then solve it by using modern optimization solvers. This technique has been successfully applied to solve the control of WDNs in our recent work [16]. The SE problem here is similar to the control problem of WDNs; however, in the current paper, we convert the SE problem (12) into an LP or QP problem instead of a GP, which provides more elegant-and computationally more efficient-solutions.…”

Section: A Geometric Program and A New Optimization Techniquementioning

confidence: 99%

“…‚ A new optimization technique is introduced to solve the nonconvex SE problem through a tractable computational algorithm for a general WDN topology. The proposed research builds on our recent work on pump control of WDNs using GP [16], but offers a different approach through LP formulation, in comparison with our prior work.…”

Section: Introduction and Paper Contributionsmentioning

confidence: 99%

See 1 more Smart Citation

State Estimation in Water Distribution Networks through a New Successive Linear Approximation

2019 IEEE 58th Conference on Decision and Control (CDC)

Sela

et al. 2019

Self Cite

State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonlinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and pressure measurements. This paper proposes a new, scalable successive linear approximation to solve the SE problem in WDNs. The approach amounts to solving either a sequence of linear or quadratic programs-depending on the operators' objectives. The proposed successive linear approximation offers a seamless way of dealing with valve/pump model nonconvexities, is different than a first order Taylor series linearization, and can be incorporated into with robust uncertainty modeling. Two simple test-cases are adopted to illustrate the effectiveness of proposed approach using head measurements at select nodes.

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

Water Resources Research

Sela

et al. 2020

Self Cite

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.