## 2A Systems modelling

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## Bogumil Ulanicki

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## Multiple Abnormality Function and Detection Scheme for a Simple Pipeline System

Sanghyun Kim

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Authors:

Sanghyun Kim

This work presents a platform for efficient formulation of general abnormality (multiple leakages and multiple partial blockages) in a reservoir pipeline valve system. Leakage detection algorithms had been focused to calibrate the locations and quantities and blockage detection schemes explored to predict the locations and sizes of partial blockages using pressure variation induced from each abnormality. Formulations for leakage and blockage were combined to obtain the general abnormality matrix in the frequency domain. To delineate the feasible expression for complicated analytical formulas of multiple leakages and multiple partial blockages, an alternative formula (the multiple abnormality function), is proposed for use in a reservoir pipeline valve system. The unsteady friction impacts for laminar and turbulent flow conditions were considered in its development using 2D frequency dependent model and 1D acceleration based model, respectively. The validity of the alternative formula was checked by comparing impedance distributions produced by it, with those of existing approaches. The new formula was tested in terms of model parsimony, computational accuracy, and efficiency. Its robustness was evaluated for its abnormality implementation sequence, and for its capability to identify any abnormality impact of pipeline systems (pressure response to waterhammer).

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## Hydraulic modelling and calibration of the water distribution network of Reguengos de Monsaraz, Portugal

Paulo Chaveiro

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Authors:

Paulo Chaveiro and Jorge Isidoro

Access to drinking water is essential for any and every population. As such, an efficient management of water distribution networks becomes mandatory for management authorities. This work presents the hydraulic modeling and calibration of the water distribution network of Reguengos de Monsaraz, Portugal. Hydraulic modeling and calibration were carried out using EPANET 2.0. A pressure measurement campaign undertaken specifically for the purpose of this study allowed to obtain the temporal pressure distribution at 20 representative locations. Reguengos de Monsaraz is a small municipality in the Central Alentejo region, district of Évora, Portugal with 7261 habitants. Length of the water distribution network is of 75.86 km of pipes, 46% in asbestos-cement (transit) and 54% in PVC, with 4156 branches built of which only 3300 are currently active. The Reguengos de Monsaraz City Hall is the managing authority of the municipal water supply system. The water distribution network show signs of aging, with inoperative check valves, frequent leakage and low-pressure issues. Also, different pressure levels cause spatial and temporal variability of the comfort pressure in the city. The topology and characteristics of pipes, valves and fittings were obtained from a georeferenced register (project SIGREDES), duly updated. This set of information was exported to the input data format to be used in EPANET 2.0. The calibrated hydraulic model allows to simulate new network managing solutions, e.g., by designing and testing district metered areas (DMAs), with the ultimate goal of reducing physical water losses. The authors intend this study may contribute not only to the improvement of the economic and sustainability indices of the water supply system of the city of Reguengos de Monsaraz, but also to show that it is possible to improve these indices is many small cities without the need of big expenditures or state-of-the-art models.

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## Combining genetic algorithms and graph theory to consider engineering aspects in WDN partitioning

Enrico Creaco

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Authors:

Enrico Creaco

This abstract explores the combination of graph theory and genetic algorithms in the context of water distribution network (WDN) partitioning into district metered areas (DMAs). This combination is proposed to reply to the need of improving the solutions obtained by applying traditional WDN partitioning algorithms. In fact, since these algorithms are typically based on graph-theory concepts, they may produce solutions that fail to account explicitly for engineering aspects. The WDN partitioning algorithm used for the two works is the fast-greedy partitioning algorithm (FGPA) based on the concept of modularity, which is a topological index that describes the possibility of identifying communities in a network. Starting from a configuration in which each node is a DMA of its own, FGPA operates by aggregating nodes sequentially, while maximizing the increment of modularity at each step, until the target number of DMAs has been reached. In a first application, FGPA is embedded into a multi-objective genetic algorithm that modulates the weight of WDN links. This results in the possibility to account for the structure of WDN segments and to explore the trade-off between engineering objectives typically considered in WDN partitioning, such as number of boundary pipes laying between DMAs and demand uniformity over DMAs. In a second application, FGPA is embedded into a multi-objective genetic algorithm that proposes control valve installations and isolation valve closure in the WDN. Iterated Linear Programming is used for optimizing the hourly settings of control valves in the typical day of WDN operation. This combination of three algorithms enables optimizing control valve installation and DMA creation for reducing leakage in WDNs, that is for exploring the trade-off between the following three objective functions, cost of installed control valves, demand uniformity over DMAs and daily leakage volume.

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## Flow Data Based DMA Characterisation

Ramon Perez

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Authors:

Sergi Grau and Ramon Perez

Data in water companies have been collected since sensors (level, pressure, flow, Temperature, chlorine concentration, etc.) have been gradually introduced. Supervision and control of processes were the first drivers of this introduction. In the last decade the evolution of sensors, communications, data management and data analysis suggest the revolution of industry 4.0 that has its counterpart in utilities 4.0. The first challenge of such revolution for assuming the utility is to adapt the cutting edge methodologies to the existing technologies in its system. This work focusses in the analysis of the existing sensors, in particular flow sensors, in order to use them intensively for a more intelligent water network management. Flow sensors are abundant in a water network. Their purposes are not unique and using the data, produced by themselves, can be helpful for characterising them. Once the sensors are characterised the data received from them can be more easily validated and reconstructed.

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## Tight convex relaxations for optimal design and control problems in water supply networks

Filippo Pecci

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Authors:

Filippo Pecci, Edo Abraham and Ivan Stoianov

We study convex relaxations for optimisation problems arising in the framework of water supply networks. The non-convexity of the considered optimisation problems is due to the absolute power functions representing frictional energy losses within the system. We define polyhedral relaxations of these non-convex constraints, and propose a tailored domain reduction procedure to tighten the relaxations. In order to evaluate the proposed convex relaxation approach, we consider the problem of optimal valve placement and operation in water supply networks, where the objective is to minimise average zone pressure. The problem formulation includes flow across network links, hydraulic heads at nodes, and valves control settings as continuous decision variables. Moreover, binary variables are introduced to model the placement of valves. Mass and energy conservation laws are enforced as optimisation constraints, resulting in a non-convex mixed integer nonlinear program (MINLP). The considered MINLP has been often studied using meta-heurstic approaches, based on genetic algorithms. However, such approaches do not provide theoretical guarantee on the global optimality of the computed valve configurations. In this work, we show that the developed convex relaxation methods enable the implementation of a branch and bound algorithm to obtain certified bounds on the optimality gap of the solutions. The developed methods are numerically evaluated using case studies, including an operational water network from the UK. The branch and bound algorithm converged to good quality feasible solutions in all instances, with bounds on the optimality gap comparable to the level of uncertainty usually experienced in water network models.