Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

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

A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities

[EN] The allocation of water resources between different users is a traditional problem in many river basins. The objective is to obtain the optimal resource distribution and the associated circulating flows through the system. Network flow programming is a common technique for solving this problem. This optimisation procedure has been used many times for developing applications for concrete water systems, as well as for developing complete decision support systems. As long as many aspects of a river basin are not purely linear, the study of non-linearities will also be of great importance in water resources systems optimisation. This paper presents a generalised model for solving the optimal allocation of water resources in schemes where the objectives are minimising the demand deficits, complying with the required flows in the river and storing water in reservoirs. Evaporation from reservoirs and returns from demands are considered, and an iterative methodology is followed to solve these two non-network constraints. The model was applied to the Duero River basin (Spain). Three different network flow algorithms (Out-of-Kilter, RELAX-IVand NETFLO) were used to solve the allocation problem. Certain convergence issues were detected during the iterative process. There is a need to relate the data from the studied systems with the convergence criterion to be able to find the convergence criterion which yields the best results possible without requiring a long calculation time.We thank the Spanish Ministry of Economy and Competitivity (Comision Interministerial de Ciencia y Tecnologia, CICYT) for funding the projects INTEGRAME (contract CGL2009-11798) and SCARCE (program Consolider-Ingenio 2010, project CSD2009-00065). We also thank the European Commission (Directorate-General for Research & Innovation) for funding the project DROUGHT-R&SPI (program FP7-ENV-2011, project 282769). And last, but not least, to the Fundacion Instituto Euromediterraneo del Agua with the project "Estudio de Adaptaciones varias del modelo de optimizacion de gestiones de recursos hidricos Optiges".Haro Monteagudo, D.; Paredes Arquiola, J.; Solera Solera, A.; Andreu Álvarez, J. (2012). A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities. Water Resources Management. 26(14):4059-4071. https://doi.org/10.1007/s11269-012-0129-7S405940712614Ahuja R, Magnanti T, Orlin J (1993) Network flows: theory, algorithms and applications. Prentice Hall, New YorkAndreu J, Capilla J, Sanchís E (1996) AQUATOOL, a generalized decision-support system for water resources planning and operational management. 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Water Resour Res 25:169–176Kuczera G (1993) Network linear programming codes for water-supply headworks modeling. J Water Resour Plan Manag 119:412–417Labadie J (2004) Optimal operation of multireservoir systems: state-of-the-art review. J Water Resour Plan Manag 130:93–111Labadie J (2006) MODSIM: river basin management decision support system. In: Singh W, Frevert D (eds) Watershed models. CRC, Boca Raton, pp 569–592Labadie J, Baldo M, Larson R (2000) MODSIM: decision support system for river basin management. Documentation and user manual. Dept. Of Civil Engineering, CSU, Fort CollinsManca A, Sechi G, Zuddas P (2010) Water supply network optimisation using equal flow algorithms. Water Resour Manag 24:3665–3678MMA (2000) Libro blanco del agua en España. Ministerio de Medio Ambiente, Secretaría general Técnica, Centro de PublicacionesMMA (2008) Confederación Hidrográfica del Duero. Memoria 2008. http://www.chduero.es/Inicio/Publicaciones/tabid/159/Default.aspx . 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Multi-criteria analysis applied to multi-objective optimal pump scheduling in water systems

This work presents a multi-criteria-based approach to automatically select specific non-dominated solutions from a Pareto front previously obtained using multi-objective optimization to find optimal solutions for pump control in a water supply system. Optimal operation of pumps in these utilities is paramount to enable water companies to achieve energy efficiency in their systems. The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) is used to rank the Pareto solutions found by the Non-Dominated Sorting Genetic Algorithm (NSGA-II) employed to solve the multi-objective problem. Various scenarios are evaluated under leakage uncertainty conditions, resulting in fuzzy solutions for the Pareto front. This paper shows the suitability of the approach for quasi real-world problems. In our case-study, the obtained solutions for scenarios including leakage represent the best trade-off among the optimal solutions, under some considered criteria, namely, operational cost, operational lack of service, pressure uniformity and network resilience. Potential future developments could include the use of clustering alternatives to evaluate the goodness of each solution under the considered evaluation criteria

Approximation of System Components for Pump Scheduling Optimisation

© 2015 The Authors. Published by Elsevier Ltd.The operation of pump systems in water distribution systems (WDS) is commonly the most expensive task for utilities with up to 70% of the operating cost of a pump system attributed to electricity consumption. Optimisation of pump scheduling could save 10-20% by improving efficiency or shifting consumption to periods with low tariffs. Due to the complexity of the optimal control problem, heuristic methods which cannot guarantee optimality are often applied. To facilitate the use of mathematical optimisation this paper investigates formulations of WDS components. We show that linear approximations outperform non-linear approximations, while maintaining comparable levels of accuracy

Reliability-based economic model predictive control for generalized flow-based networks including actuators' health-aware capabilities

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalized flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamically allocate safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the considered case study.Peer ReviewedPostprint (author's final draft

Demonstrating demand response from water distribution system through pump scheduling

Significant changes in the power generation mix are posing new challenges for the balancing systems of the grid. Many of these challenges are in the secondary electricity grid regulation services and could be met through demand response (DR) services. We explore the opportunities for a water distribution system (WDS) to provide balancing services with demand response through pump scheduling and evaluate the associated benefits. Using a benchmark network and demand response mechanisms available in the UK, these benefits are assessed in terms of reduced green house gas (GHG) emissions from the grid due to the displacement of more polluting power sources and additional revenues for water utilities. The optimal pump scheduling problem is formulated as a mixed-integer optimisation problem and solved using a branch and bound algorithm. This new formulation finds the optimal level of power capacity to commit to the provision of demand response for a range of reserve energy provision and frequency response schemes offered in the UK. For the first time we show that DR from WDS can offer financial benefits to WDS operators while providing response energy to the grid with less greenhouse gas emissions than competing reserve energy technologies. Using a Monte Carlo simulation based on data from 2014, we demonstrate that the cost of providing the storage energy is less than the financial compensation available for the equivalent energy supply. The GHG emissions from the demand response provision from a WDS are also shown to be smaller than those of contemporary competing technologies such as open cycle gas turbines. The demand response services considered vary in their response time and duration as well as commitment requirements. The financial viability of a demand response service committed continuously is shown to be strongly dependent on the utilisation of the pumps and the electricity tariffs used by water utilities. Through the analysis of range of water demand scenarios and financial incentives using real market data, we demonstrate how a WDS can participate in a demand response scheme and generate financial gains and environmental benefits

Single-layer economic model predictive control for periodic operation

In this paper we consider periodic optimal operation of constrained periodic linear systems. We propose an economic model predictive controller based on a single layer that unites dynamic real time optimization and control. The proposed controller guarantees closed-loop convergence to the optimal periodic trajectory that minimizes the average operation cost for a given economic criterion. A priori calculation of the optimal trajectory is not required and if the economic cost function is changed, recursive feasibility and convergence to the new periodic optimal trajectory is guaranteed. The results are demonstrated with two simulation examples, a four tank system, and a simplified model of a section of Barcelona's water distribution network.Peer ReviewedPostprint (author’s final draft

Design and operation methods for better performing heat recovery loops

Inter-plant integration via a heat recovery loop (HRL) is an economic method for increasing total site process energy efficiency of semi-continuous processes. Results show that both the constant storage temperature approach and variable storage temperature approach have merit. Depending on the mix of source and sink streams attached, it may be advantageous to change the operation of an existing HRL from a constant temperature storage to a variable temperature storage. To realise the full benefits of this change in operation, a redistribution of the existing heat exchanger area may be needed