68 results found
Ulusoy A-J, Pecci F, Stoianov I, 2020, A MINLP-based approach for the design-for-control of resilient water supply systems, IEEE Systems Journal, Vol: 14, Pages: 4579-4590, ISSN: 1932-8184
The improvement in resilience of water supplysystems by increasing their redundancy, either in energyor in connectivity, is a common priority when doing rehabilitation and expansion. This however can come at thecost of other aspects of network performance, such asleakage management. In this work, we consider the designfor-control problem of adding new connections (from a predefined set of candidate pipes) to water supply systems toimprove their resilience to failure events while minimizingthe impact on leakage management under normal operatingconditions. We present a mixed-integer non-linear programming formulation of the problem of optimal link additionfor the minimization of average zone pressure, a surrogatemeasure of pressure dependent leakage. We implement amethod based on spatial branch-and-bound to solve theproblem on a case study network from the literature andan operational network part of an urban water system inthe UK. Finally, we validate the improvement in networkresilience resulting from the addition of new connectionsby performing an a posteriori critical link analysis, usingthe hydraulic resilience measure of reserve capacity.
Konstantinou C, Stoianov I, 2020, A comparative study of statistical and machine learning methods to infer causes of pipe breaks in water supply networks, URBAN WATER JOURNAL, Vol: 17, Pages: 534-548, ISSN: 1573-062X
Pecci F, Parpas P, Stoianov I, 2020, Sequential convex optimization for detecting and locating blockages in water distribution networks, Journal of Water Resources Planning and Management, Vol: 146, ISSN: 0733-9496
Unreported partially/fully closed valves or other type of pipe blockages in water distribution networks result in unexpected energy losses within the systems, which we also refer to as faults. We investigate the problem of detection and localization of such faults. We propose a novel optimization-based method, which relies on the solution of a non-linear inverse problem with l1 regularization. We develop a sequential convex optimization algorithm to solve the resulting non-smooth non-convex optimization problem. The proposed algorithm enables the use of non-smooth terms within the problem formulation, and exploits the sparse structure inherent in water network models. The performance of the developed method is numerically evaluated to detect and localize blockages in a large water distribution network using both simulated and experimental data. In all experiments, the sequential convex optimization algorithm converged in less than three seconds, suggesting that the proposed fault detection and localization method is suitable for near real-time implementation. Furthermore, we experimentally validate the developed method for near real-time fault diagnosis in a large operational water network from the UK. The method is shown to successfully detect and localize blockages, with real system modelling uncertainties.
Waldron A, Pecci F, Stoianov I, 2020, Regularisation of an inverse problem for parameter estimation in water distribution networks, Journal of Water Resources Planning and Management, Vol: 146, ISSN: 0733-9496
An accurate hydraulic model of a water distribution network (WDN) is a critical prerequisite for a multitude of operational, optimisation and planning tasks. The accuracy of a hydraulic model can only be maintained through its periodic calibration and validation with acquired pressure and flow data from a WDN. It is important that this process is robust and computationally efficient. This paper describes the regularisation of an inverse problem to deal with data uncertainties and ill-posedness of parameter estimation problems in WDNs. A novel data driven strategy is presented for tuning the regularisation hyper-parameter for the inverse problem and also for validating the results on an independent set of operational hydraulic data. A limited-memory quasi-Newton method (L-BFGS19 B) is implemented for solving the resulting regularised nonlinear inverse problem. Furthermore, the implemented method utilises either the Darcy-Weisbach or Hazen-Williams head loss formulae, and is investigated both with and without pipe grouping. An extensive experimental programmewas carried out to acquire unique hydraulic data from an operational WDN in order to investigate the robustness of the proposed parameter estimation method. The hydraulic model of the operational WDN and the acquired hydraulic data are provided as supplementary data to enable the comparisonof hydraulic model calibration methods with operational data and encourage reproducible research
Nerantzis D, Pecci F, Stoianov I, 2020, Optimal control of water distribution networks without storage, European Journal of Operational Research, Vol: 284, Pages: 345-354, ISSN: 0377-2217
The paper investigates the problem of optimal control of water distribution networks without storage capacity. Using mathematical optimization, we formulate and solve the problem as a non-convex NLP, in order to obtain optimal control curves for both variable speed pumps and pressure reducing valves of the network and thus propose a methodology for the automated control of real operational networks. We consider both single-objective and multi-objective problems with average zonal pressure, pump energy consumption and water treatment cost as objectives. Furthermore, we investigate global optimality bounds for the calculated solutions using global optimization techniques. The proposed approach is shown to outperform state-of-the-art global optimization solvers. The described procedure is demonstrated in a case study using a large size operational network.
Blocher C, Pecci F, Stoianov I, 2020, Localizing leakage hotspots in water distribution networks via the regularization of an inverse problem, Journal of Hydraulic Engineering, Vol: 146, Pages: 04020025-1-04020025-13, ISSN: 0733-9429
The ill-posed inverse problem for detecting and localizing leakage hotspots is solved using a novel optimization-based method which aims to minimize the difference between hydraulic measurement data and simulated steady states of a water distribution network. Regularization constrains the set of leak candidate nodes obtained from a solution to the optimization problem. Hydraulic conservation laws are enforced as nonlinear constraints. The resulting nonconvex optimization problem is solved using smooth mathematical optimization techniques. The solution identifies leakage hotspot areas, which can then be further investigated with alternative methods for precise leak localization. A metric is proposed to quantitatively assess the performance of the developed leak localization approach in comparison with a method that uses the sensitivity matrix. In addition, we propose a strategy to select the regularization parameter when large-scale operational networks are considered. Using two numerical case studies, we demonstrate that the proposed approach outperforms the sensitivity matrix method, with regards to leak isolation, in most single leak scenarios. Moreover, the developed method enables the localization of multiple simultaneous leaks.
Scoular JM, Croft J, Ghail RC, et al., 2019, Limitations of persistent scatterer interferometry to measure small seasonal ground movements in an urban environment, Quarterly Journal of Engineering Geology and Hydrogeology, Vol: 53, Pages: 39-48, ISSN: 1470-9236
London Clay, which underlies the majority of Greater London, has a high shrink–swell potential that can result in damage to foundations and surface infrastructure due to seasonal expansion and contraction of the clay. Currently, surface movement as a result of shrink–swell is not monitored in London, meaning that the magnitude and cyclicity of these movements is poorly understood. Persistent Scatterer Interferometric (PSI) Synthetic Aperture Radar data provide high-precision line-of-sight displacement measurements at a high point density across urban areas, offering the possibility of routine shrink–swell monitoring across whole cities. To test this, PSI data derived from TerraSAR-X (TSX) observations for the period from May 2011 to April 2017 were analysed for shrink–swell patterns across three areas of London in Hammersmith, Muswell Hill and Islington. A consistent cyclicity and amplitude was detected at all sites and the number of cycles is comparable with those identified in rainfall data. The amplitude of these cycles is smaller than anticipated, most probably because of the resisting effect of roads and pavements. The Cranfield University Leakage Assessment from Corrosivity and Shrinkage (LEACS) database was used to subdivide the PSI data and the average velocity and amplitude of each class statistically tested for significant differences between classes. The results show that it is not possible to statistically isolate possible soil shrink–swell movement in TSX PSI data in London.
Changklom J, Stoianov I, 2019, Redundant flow estimation methods for robust hydraulic control in water supply networks, Journal of Hydroinformatics, Vol: 21, Pages: 571-592, ISSN: 1464-7141
The implementation of robust hydraulic control in water supply networks relies upon the utilisation of redundant flow estimation methods. In this paper, we propose a novel model-based flow estimation method for diaphragm actuated globe valves based on three pressure signals, namely the valve inlet pressure, valve outlet pressure and control chamber pressure (the 3P flow estimation method). The proposed flow estimation method relies upon the accurate determination of a valve stem position based on a force balance analysis for the diaphragm of a valve, the measured pressure differential across a valve and the flow coefficients of a valve (Cv, Kv). A novel stem position estimation model for diaphragm actuated globe valves has been formulated and experimentally validated. The non-linear parameterised valve stem position estimation model results in multiple solutions. We combine advances in signal processing with support vector machine classification to find a correct solution. We compare the proposed 3P flow estimation method with a method, which uses stem position sensor measurements of a valve and two pressure signals. A unique set of experimental data have been acquired for performance validation. We derive uncertainty bounds for the proposed flow estimation method and demonstrate its application for robust pressure control in water supply networks.
Pecci F, Abraham E, Stoianov I, 2019, Global optimality bounds for the placement of control valves in water supply networks, Optimization and Engineering, Vol: 20, Pages: 457-495, ISSN: 1389-4420
This manuscript investigates the problem of optimal placement of control valves in water supply networks, where the objective is to minimize average zone pressure. The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP). Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of the computed valve configurations. In our approach, we implement a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The algorithm relies on the solution of mixed integer linear programs, whose formulations include linear relaxations of the nonconvex hydraulic constraints. We investigate the implementation and performance of different linear relaxation schemes. In addition, a tailored domain reduction procedure is implemented to tighten the relaxations. The developed methods are evaluated using two benchmark water supply networks and an operational water supply network from the UK. The proposed approaches are shown to outperform state-of-the-art global optimization solvers for the considered benchmark water supply networks. The branch and bound algorithm converges to good quality feasible solutions in most instances, with bounds on the optimality gap that are comparable to the level of parameter uncertainty usually experienced in water supply network models.
Pecci F, Abraham E, Stoianov I, 2019, Model reduction and outer approximation for optimising the placement of control valves in complex water networks, Journal of Water Resources Planning and Management, Vol: 145, ISSN: 0733-9496
The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimisation frame work, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimisation framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimisation problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models.
Wilson RE, Stoianov I, OHare D, 2019, Continuous chlorine detection in drinking water and a review of new detection methods, Johnson Matthey Technology Review, Vol: 63, Pages: 103-118, ISSN: 2056-5135
Chlorination is necessary to prevent epidemics of waterborne disease however excess chlorination is wasteful, produces harmful disinfection byproducts, exacerbates corrosion and causes deterioration in aesthetic qualities, leading to consumer complaints. Residual chlorine must be continuously monitored to prevent both under- and over-chlorination and factors including pH, temperature and fouling must be considered as these also affect the disinfectant strength of residual chlorine. Standard methods used by water utility companies to determine residual chlorine concentration in drinking water distribution systems are appraised and found to be unsuitable for continuous monitoring. A selection of newly developed methods for residual chlorine analysis are evaluated against performance criteria, to direct research towards the development of chlorine sensors that are suitable for use in water systems. It is found that fouling tolerance in particular is generally not well understood for these selected sensor technologies and that long-term trials in real systems is recommended.
Ulusoy A, Stoianov I, Chazerain A, 2018, Hydraulically informed graph theoretic measure of link criticality for the resilience analysis of water supply networks, Applied Network Science, Vol: 3, ISSN: 2364-8228
Water Distribution Networks (WDN) are complex and highly interconnected systems. To maintain operation under failure conditions, WDNs should have built-in resilience based on topological and energy redundancy. There are various methods for analysing the resilience of WDNs based on either hydraulic models or surrogate network measures; however, not a single universally accepted method exists. Hydraulic modeling of disruptive operational scenarios suffer from combinatorial restrictions and uncertainties. Methods that rely on surrogate network measures do not take into account the complex interactions between topological and energy redundancy. To bridge this gap, the presented work introduces a hydraulically informed surrogate measure of pipe criticality for the resilience analysis of WDNs, called Water Flow Edge Betweenness Centrality (WFEBC). The WFEBC combines the random walk betweenness centrality with hydraulic (energy) loss principles in pipes. The proposed network resilience estimation method is applied to a case study network and an operational network. Furthermore, a network decomposition approach is proposed to complement the network estimation method and facilitate its scalability to large operational networks. The described resilience analysis method is benchmarked against a hydraulic model-based analysis of WDN reserve capacity. WFEBC is also applied to assess the improvement in resilience allowed by the implementation of a dynamically adaptive topology in an operational network. The benefits and limitations of the proposed method are discussed.
Armand H, Stoianov I, Graham N, 2018, Impact of network sectorisation on water quality management, Journal of Hydroinformatics, Vol: 20, Pages: 424-439, ISSN: 1464-7141
The sectorisation of water supply networks includes the permanent closure of valves in order to achieve a cost-effective leakage management and simplify pressure control. The impact of networks sectorisation, also known as District Metered Areas (DMAs), on water quality and discolouration has not been extensively studied and it remains unknown. In addition, hydraulic variables used in the literature for assessing the likelihood of potential discolouration are limited and inconclusive. This paper investigates a methodology to evaluate the impact of networks sectorisation (DMAs) on water quality and the likelihood of discolouration incidents. The methodology utilises a set of surrogate hydraulic variables and an analysis of the hydraulic condition in pipes with historic discolouration complaints. The proposed methodology has been applied to a large-scale water supply network, with and without sectors, in order to assess the potential impact of DMAs on water quality. The results demonstrate that the sectorisation of water supply networks (DMAs) could compromise the overall water quality and increase the likelihood of discolouration incidents. The results of this study and the proposed surrogate hydraulic variables facilitate the formulation of optimisation problems for the re-design and control of water supply networks with sectorised topologies.
Abraham E, Blokker M, Stoianov I, 2018, Decreasing the discoloration risk of drinking water distribution systems through optimized topological changes and optimal flow velocity control, Journal of Water Resources Planning and Management, Vol: 144, ISSN: 0733-9496
In this paper, a new mathematical framework is proposed for maximizing the self-cleaning capacity (SCC) of drinking water distribution systems by controlling the diurnal peak flow velocities in the pipes under normal operation. This is achieved through an optimal change of the network connectivity (topology). This paper proposes an efficient algorithm for the network analysis of valve closures, which allows enforcing favorable changes in the flow velocities for maximizing the SCC by determining an optimal set of links to isolate in the forming of a more branched network, while concurrently satisfying the hydraulic and regulatory pressure constraints at the demand nodes. Multiple stochastic demands from an end-use demand model are generated to test the robustness in the improved SCC for the modified network connectivity under changing demand. An operational network model is used to demonstrate the efficacy of the proposed approach.
Pecci F, Abraham E, Stoianov I, 2017, Outer approximation methods for the solution of co-design optimisation problems in water distribution networks, 20th IFAC World Congress, Publisher: Elsevier, Pages: 5373-5379, ISSN: 1474-6670
In the present manuscript, we investigate and demonstrate the use of outer approximation methods for simultaneously optimising the placement and operation of control valves in water distribution networks. The problem definition results in a mixed-integer nonlinear program with nonconvex constraints. We simplify the formulation, compared to previous literature, in order to reduce the degree of nonlinearity in the constraints and decrease the total problem size. We then formulate the application of outer approximation based methods for the generation of good quality local optimal solutions for the considered co-design problem. Finally, we present the results of applying the developed techniques to two case studies, and also comparing the performances of the outer approximation approaches with those of other local mixed integer nonlinear programming solution methods.
Menke R, Abraham E, Parpas P, et al., 2017, Extending the envelope of demand response provision though variable Speed pumps, 18th Water Distribution System Analysis Conference, WDSA2016, Publisher: Elsevier, Pages: 584-591, ISSN: 1877-7058
Changes in power generation and supply and changes in water distribution systems are creating new opportunities for water utilities to enhance operational efficiency and income through the use of advanced control and optimisation. First, the increase in renewables penetration into the grid is causing a growth in energy storage schemes. Second, variable speed pumps are now fitted to most new systems and many existing water distribution systems are being retrofitted with variable speed pumps to improve the efficiency of the operation. We study how these trends can be jointly exploited to provide energy storage from a water distribution system. We investigate how variable speed drive pumps can enhance the ability of a water distribution network to provide demand response energy to the grid. We show that demand response provision from water distribution systems can be improved through the use of variable speed pumps. We also demonstrate that a network equipped with variable speed pumps can provide demand response profitably across a wider range of operating scenarios compared to a network equipped with only fixed-speed pumps. The results highlight another potential benefit of variable speed pumps in water distribution systems.
Pecci F, Abraham E, Stoianov II, 2017, Quadratic head loss approximations for optimisation problems in water supply networks, Journal of Hydroinformatics, Vol: 19, Pages: 493-506, ISSN: 1464-7141
This paper presents a novel analysis on the accuracy of quadratic approximations for Hazen--Williams head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the absolute and relative errors, respectively, from the original non-smooth Hazen--Williams head loss function over a range of flows.Since the quadratic approximations are used to formulate head loss constraints for different optimisation problems, we are interested in quantifying and controlling their absolute errors, which affect the degree of constraint violations of candidate feasible solutions. We derive new exact analytical formulae for the absolute errors as a function of the approximation domain, pipe roughness and relative error tolerance. We assess the efficacy of the quadratic approximations in mathematical optimisation for optimal pressure regulation in an operational water supply network. We propose a strategy on how to choose the approximation domain for each pipe such that the optimisation results are sufficiently close to the exact hydraulic feasibility region. By using simulations with multiple parameters, the approximation errors are shown to be consistent with our analytical predictions.
Menke R, Kadehjian K, Abraham E, et al., 2017, Investigating trade-offs between the operating cost and green house gas emissions from water distribution systems, Sustainable Energy Technologies and Assessments, Vol: 21, Pages: 13-22, ISSN: 2213-1388
For electricity grids with an increasing share of intermittent renewables, the power generation mix can have significant daily variations. This leads to time-dependent emission intensities and volatile electricity prices in the day-ahead and spot market tariffs that can be better utilised by energy intensive industries such as water supply utilities. A multi-objective optimisation method for scheduling the operation of pumps is investigated in this paper for the reduction of both electricity costs and greenhouse gas emissions for a benchmark water distribution system. A set of energy supply scenarios has been formulated based on future projections from National Grid plc (UK) in order to investigate the range of cost savings and emission reductions that could be possibly achieved. Pump scheduling options with fixed time-of-use and day ahead market tariffs are analysed in order to compare potential reduction tradeoffs for both electricity costs and greenhouse gas emissions using Pareto optimality. The presented analysis concludes that the explicit inclusion of greenhouse gas emission reductions in optimising the scheduling of pumps operation in water distribution systems could provide considerable benefits; however, more compelling fiscal and regulatory incentives are needed.
Pecci F, Abraham E, Stoianov I, 2016, Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks, Computational Optimization and Applications, Vol: 67, Pages: 201-223, ISSN: 1573-2894
In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.
Menke RM, Abraham EA, Stoianov IS, et al., 2016, Exploring optimal pump scheduling in water distribution networks with branch and bound methods, Water Resources Management, Vol: 30, Pages: 5333-5349, ISSN: 0920-4741
Water utilities can achieve signi cant savings in operating costs by optimising pump scheduling to improve efficiency and shift electricity consumption to low-tari periods. Due to the complexityof the optimal scheduling problem, heuristic methods that cannot guarantee global optimality are often applied. This paper investigates formulations of the pump scheduling problem solved using a branch and bound method. Piecewise linear component approximations outperform non-linear approximationswithin application driven accuracy bounds and demand uncertainties. It is shown that the reduction of symmetry through the grouping of pumps signi cantly reduces the computational e ort, whereas loopsin the network have the opposite e ect. The computational e ort of including convex, non-linear pump operating, and maintenance cost functions is investigated. Using case studies, it is shown that linear and xed-cost functions can be used to nd schedules which, when simulated in a full hydraulic simulation, have performances that are within the solver optimality gap and the uncertainty of demand forecasts.
Wilson RE, Stoianov I, O'Hare D, 2016, Biofouling and in situ electrochemical cleaning of a boron-doped diamond free chlorine sensor, Electrochemistry Communications, Vol: 71, Pages: 79-83, ISSN: 1873-1902
Biofouling presents a significant obstacle to the long-term use of electrochemical sensors in complex media. Drinking water biofilms reduce performance of sensors by insulating electrode surfaces by inter alia inhibiting mass transport. Boron-doped diamond (BDD) electrodes are relatively resistant to biofouling and inert at high potentials. These qualities can be exploited to create a drinking water quality sensor that resists biofouling to meet performance criteria for longer, and to enable electrochemical cleaning of the sensor surface in situ using high potentials without disconnecting or disassembling the sensor.A purpose-built BDD wall-jet sensor was compared with a glassy carbon (GC) sensor in ability to determine free chlorine, detect biofilm and remove biofilm in situ. It was found that the BDD produced accurate and reliable readings with a 4.86% standard error and a LOD of 0.18 ppm. The BDD could be electrochemically cleaned in situ whereas this was less successful with the GC electrode. The BDD electrode could also detect electroactive pyocyanin, secreted in the biofilm of the drinking water biofilm indicator organism Pseudomonas aeruginosa, potentially enabling biofouling and non-biological fouling such as scaling to be distinguished. Observed changes in flow sensitivity and current-voltage curves that correspond to fouling provide multiple fouling detection methods, resulting in an accurate, sensitive, water quality sensor that can be cleaned without disassembly or replacement of parts and can identify when cleaning is required.
Pecci F, Abraham E, Stoianov I, 2016, Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach, Structural and Multidisciplinary Optimization, Vol: 55, Pages: 857-869, ISSN: 1615-1488
In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.
Menke RMM, Abraham EA, Stoianov IS, 2016, Modeling variable speed pumps for optimal pumpscheduling, World Environment and Water resource congress
Increasingly more variable speed drive pumps are installed in water distributionsystems worldwide. However, the modeling of variable speed drives in such networksremains difficult, especially in the context of mathematical optimization for pumpscheduling. For the problem of energy usage minimization, formulated as a mixedinteger program, we propose a new simplified convex relaxation of the hydrauliccharacteristics of a variable speed pump. By using different model approximations forthe power curve, as a function of pump speed and volumetric flow rate, we study thetrade-off in the computational complexity and quality of solutions obtained. We usetwo small benchmark networks and real pump data from three different pumps tocalculate operating schedules. We show that these schedules, are computed in a timesuitable for operational usage, enable operation with lower operating cost compared tofixed speed pumps, and their sub-optimality can be computed.
Abraham E, stoianov I, 2016, Constraint preconditioned inexact Newton method for hydraulic simulation of large-scale water distribution networks, IEEE Transactions on Control of Network Systems, Vol: 4, Pages: 610-619, ISSN: 2325-5870
Many sequential mathematical optimization methodsand simulation-based heuristics for optimal control anddesign of water distribution networks rely on a large numberof hydraulic simulations. In this paper, we propose an efficientinexact subspace Newton method for hydraulic analysis of waterdistribution networks. By using sparse and well-conditionedfundamental null space bases, we solve the nonlinear systemof hydraulic equations in a lower-dimensional kernel space ofthe network incidence matrix. In the inexact framework, theNewton steps are determined by solving the Newton equationsonly approximately using an iterative linear solver. Since largewater network models are inherently badly scaled, a Jacobianregularization is employed to improve the condition number ofthese linear systems and guarantee positive definiteness. Afterpresenting a convergence analysis of the regularised inexactNewton method, we use the conjugate gradient (CG) methodto solve the sparse reduced Newton linear systems. Since CGis not effective without good preconditioners, we propose tailoredconstraint preconditioners that are computationally cheapbecause they are based only on invariant properties of the nullspace linear systems and do not change with flows and pressures.The preconditioners are shown to improve the distribution ofeigenvalues of the linear systems and so enable a more efficientuse of the CG solver. Since contiguous Newton iterates can havesimilar solutions, each CG call is warm-started with the solutionfor a previous Newton iterate to accelerate its convergence rate.Operational network models are used to show the efficacy ofthe proposed preconditioners and the warm-starting strategy inreducing computational effort.
Menke R, Abraham E, Parpas P, et al., 2016, Demonstrating demand response from water distribution system through pump scheduling, Applied Energy, Vol: 170, Pages: 377-387, ISSN: 1872-9118
Significant changes in the power generation mix are posing new challenges for the balancing systems of the grid. Many of thesechallenges are in the secondary electricity grid regulation services and could be met through demand response (DR) services. Weexplore the opportunities for a water distribution system (WDS) to provide balancing services with demand response through pumpscheduling and evaluate the associated benefits. Using a benchmark network and demand response mechanisms available in theUK, these benefits are assessed in terms of reduced green house gas (GHG) emissions from the grid due to the displacement ofmore polluting power sources and additional revenues for water utilities. The optimal pump scheduling problem is formulated as amixed-integer optimization problem and solved using a branch and bound algorithm. This new formulation finds the optimal levelof power capacity to commit to the provision of demand response for a range of reserve energy provision and frequency responseschemes offered in the UK. For the first time we show that DR from WDS can offer financial benefits to WDS operators whileproviding response energy to the grid with less greenhouse gas emissions than competing reserve energy technologies. Using aMonte Carlo simulation based on data from 2014, we demonstrate that the cost of providing the storage energy is less than thefinancial compensation available for the equivalent energy supply. The GHG emissions from the demand response provision froma WDS are also shown to be smaller than those of contemporary competing technologies such as open cycle gas turbines. Thedemand response services considered vary in their response time and duration as well as commitment requirements. The financialviability of a demand response service committed continuously is shown to be strongly dependent on the utilisation of the pumpsand the electricity tariffs used by water utilities. Through the analysis of range of water demand scenarios and financial in
Herrera Fernandez A, Abraham E, Stoianov I, 2016, A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks, Water Resources Management, Vol: 30, Pages: 1685-1699, ISSN: 1573-1650
Water utilities face a challenge in maintaining a good quality ofservice under a wide range of operational management and failure conditions.Tools for assessing the resilience of water distribution networks are thereforeessential for both operational and maintenance optimization. In this paper, anovel graph-theoretic approach for the assessment of resilience for large scalewater distribution networks is presented. This is of great importance for themanagement of large scale water distribution systems, most models containingup to hundreds of thousands of pipes and nodes. The proposed frameworkis mainly based on quantifying the redundancy and capacity of all possibleroutes from demand nodes to their supply sources. This approach works wellwith large network sizes since it does not rely on precise hydraulic simulations,which require complex calibration processes and computation, while remainingmeaningful from a physical and a topological point of view. The proposal isalso tailored for the analysis of sectorised networks through a novel multiscalemethod for analysing connectivity, which is successfully tested in operationalutility network models made of more than 100,000 nodes and 110,000 pipes.
Abraham E, Stoianov I, An efficient null space inexact Newton method for hydraulic simulation of water distribution networks, ArXiv e-prints
Wright R, Abraham E, Parpas P, et al., 2015, Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming, Water Resources Research, Vol: 51, Pages: 9925-9941, ISSN: 1944-7973
The operation of water distribution networks (WDN) with a dynamic topology is a recently pioneered approach for the advanced management of district metered areas (DMA) that integrates novel developments in hydraulic modelling, monitoring, optimization and control. A common practice for leakage management is the sectorization of WDNs into small zones, called DMAs, by permanently closing isolation valves. This facilitates water companies to identify bursts and estimate leakage levels by measuring the inlet flow for each DMA. However, by permanently closing valves, a number of problems have been created including reduced resilience to failure and suboptimal pressure management. By introducing a dynamic topology to these zones, these disadvantages can be eliminated whilst still retaining the DMA structure for leakage monitoring. In this paper, a novel optimization method based on sequential convex programming (SCP) is outlined for the control of a dynamic topology with the objective of reducing average zone pressure (AZP). A key attribute for control optimization is reliable convergence. To achieve this, the SCP method we propose guarantees that each optimization step is strictly feasible, resulting in improved convergence properties. By using a null space algorithm for hydraulic analyses, the computations required are also significantly reduced. The optimized control is actuated on a real WDN operated with a dynamic topology. This unique experimental programme incorporates a number of technologies set up with the objective of investigating pioneering developments in WDN management. Preliminary results indicate AZP reductions for a dynamic topology of up to 6.5% over optimally controlled fixed topology DMAs.
Armand H, Stoianov II, Graham NJD, 2015, A holistic assessment of discolouration processes in water distribution networks, URBAN WATER JOURNAL, Vol: 14, Pages: 263-277, ISSN: 1573-062X
Abraham E, Stoianov IVAN, 2015, Sparse Null Space Algorithms for Hydraulic Analysis of Large Scale Water Supply Networks, Journal of Hydraulic Engineering, Vol: 142, ISSN: 1943-7900
In this article, a comprehensive review of existing methods is presented and computationally efficient sparse null space algorithms are proposed for the hydraulic analysis of water distribution networks. The linear systems at each iteration of the Newton method for nonlinear equations are solved using a null space algorithm. The sparsity structure of these linear equations, which arises from the sparse network connectivity, is exploited to reduce computations. A significant fraction of the total flops in the Newton method are spent in computing pipe head losses and matrix-matrix multiplications involving flows. Because most flows converge after a few iterations, a novel partial update of head losses and matrix products is used to further reduce computational complexity. Convergence analyses are also presented for the partial-update formulas. A new heuristic for reducing the number of pressure head computations of a null space method is proposed. These savings enable fast near-real-time control of large-scale water networks. It is often observed that the linear equations that arise in solving the hydraulic equations become ill-conditioned due to hydraulic solutions with very small and zero flows. The condition numbers of the Newton equations are bounded using a regularization technique with insignificant computational overheads. The convergence properties of all proposed algorithms are analyzed by posing them as an inexact-Newton method. Small-scale to large-scale models of operational water networks are used to evaluate the proposed algorithms.
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