Noniterative Implementation of Pressure-Dependent Demands Using the Hydraulic Analysis Engine of EPANET 2

To analyze water distribution networks under pressure-deficient conditions, most of the available hydraulic simulators, including EPANET 2, must be either modified by embedding pressure-dependent demands in the governing network equations or run repeatedly with successive adjustments made to specific parameters until a sufficient hydraulic consistency is obtained. This paper presents and discusses a simple technique that implements the square root relationship between the nodal demand and the nodal pressure using EPANET 2 tools and allows a water distribution network with pressure-dependent demands to be solved in a single run of the unmodified snapshot hydraulic analysis engine of EPANET 2. In this technique, artificial strings made up of a flow control valve, a pipe with a check valve, and a reservoir are connected to the demand nodes before running the engine, and the pressure-dependent demands are determined as the flows in the strings. The resistance of the artificial pipes is chosen such that the demands are satisfied in full at a desired nodal pressure. The proposed technique shows reasonable convergence as evidenced by its testing on example networks.     

Modelling Water Distribution Systems with Deficient Pressure: An Improved Iterative Methodology

In the last three decades, many researchers have proposed different models for water distribution network (WDN) hydraulic analysis by head-driven analysis (HDA). By considering a pressure-discharge relationship (PDR), head-driven analysis (HDA) can avoid deviation caused by traditional demand-driven analysis (DDA) under abnormal conditions. Generally, there are three types of HDA models: 1) models achieved by embedding a PDR into DDA, 2) models using EPANET structures such as emitter or tank to take place of PDR, 3) models aiming at modifying nodal outflows to satisfy PDR based on EPANET. Among these models, modifying nodal outflows is flexible to simulate network with different PDRs and specify parameters related to PDR. Most of the models use iterative algorithms to solve HDA problems; however, present ways to ensure convergence of models are still inadequate. The purpose of this paper is to present a new way to meet the iterative convergence when modifying nodal outflows based on PDR and leakage. This new methodology has been incorporated into the hydraulic network solver EPANET and is formalized algorithmically as EPANET-IMNO. Then two typical networks are used to test EPANET-IMNO, and the results demonstrate that EPANET-IMNO can converge well and applied successfully both in static simulation and extended period simulation. Different pressure deficiency conditions are tested to further confirm the flexibility and the convergence of EPANET-IMNO. Furthermore, quality analysis results back that pressure reduction can be a practical way in contamination accident response.     

A New Method for Simultaneous Calibration of Demand Pattern and Hazen-Williams Coefficients in Water Distribution Systems

Water distribution systems, where flow in some pipes is not measured or storage tanks are connected together, calculation of demand pattern coefficients of the network is difficult. Since, Hazen-Williams coefficients of the network are also unknown; the problem is becoming unintelligible further. The present study proposes a new method for simultaneous calibration of demand pattern and Hazen-Williams coefficients that uses the Ant Colony Optimization (ACO) algorithms coupled with the hydraulic simulator (EPANET2) in a MATLAB code. In this paper demand pattern and Hazen-Williams coefficients are the calibration parameters and measured data consist of nodal pressure heads and pipe flows. The defined objective function minimizes the difference between the measured and simulated values. The new proposed method was tested on a two-loop test example and a real water distribution network. The results show that the new calibration model is able to calibrate demand pattern and Hazen-Williams coefficients simultaneously with high precision and accuracy.     

Pressure-Dependent EPANET Extension

In water distribution systems (WDSs), the available flow at a demand node is dependent on the pressure at that node. When a network is lacking in pressure, not all consumer demands will be met in full. In this context, the assumption that all demands are fully satisfied regardless of the pressure in the system becomes unreasonable and represents the main limitation of the conventional demand driven analysis (DDA) approach to WDS modelling. A realistic depiction of the network performance can only be attained by considering demands to be pressure dependent. This paper presents an extension of the renowned DDA based hydraulic simulator EPANET 2 to incorporate pressure-dependent demands. This extension is termed “EPANET-PDX” (pressure-dependent extension) herein. The utilization of a continuous nodal pressure-flow function coupled with a line search and backtracking procedure greatly enhance the algorithm’s convergence rate and robustness. Simulations of real life networks consisting of multiple sources, pipes, valves and pumps were successfully executed and results are presented herein. Excellent modelling performance was achieved for analysing both normal and pressure deficient conditions of the WDSs. Detailed computational efficiency results of EPANET-PDX with reference to EPANET 2 are included as well.     

Nodal Analysis of Urban Water Distribution Networks

There are three methods for analysing the flow and pressure distribution in looped water supply networks (the loop method, the node method, the pipe method), accounting for the chosen unknown hydraulic parameters. For all of these methods, the nonlinear system of equations can be solved using iterative procedures (Hardy–Cross, Newton–Raphson, linear theory). In the cases of the extension or the rehabilitation of distribution networks, the unknown parameters are the hydraulic heads at nodes, and the nodal method for network analysis is preferred. In this paper, a generalised classic model is developed for the nodal analysis of complex looped systems with non-standard network components and the solvability of new problems, along with the determination of the pressure state in the system. In addition, this paper exhibits a different approach to this problem by using the variational formulation method for the development of a new analysis model based on unconditioned optimisation techniques. This model has the advantage of using a specialised optimisation algorithm, which directly minimises an objective multivariable function without constraints, implemented in a computer program. The two proposed models are compared with the classic Hardy–Cross method, and the results indicated a good performance of these models. Finally, a study is performed regarding the implications of the long-term operation of the pipe network on energy consumption using these models. The new models can serve as guidelines to supplement existing procedures of network analysis.     

Evolutionary Testing of Hydraulic Simulator Functionality

A method for automatic functional testing of hydraulic simulators is proposed. The method is based on using genetic algorithms to search for network parameter values at which the simulator under test computes solutions that do not satisfy the governing network equations. The search is made by maximizing the residual of the governing equations. The application of the method to the latest version of the EPANET hydraulic simulator demonstrates its efficiency in detecting incorrect results. The results of quantitative assessment of the functional adequacy of the EPANET solver by random testing are presented. The paper provides examples of hydraulic networks and of parameter value combinations for which incorrect results occur. An example of the use of automatic functional testing together with automatic convergence testing in a comprehensive study of the flow control valve model of the EPANET solver is given.     

基于精细积分法的城市配水系统动态建模

基于功率键合图理论,将所研究的城市配水系统的动态结构绘制成功率键合图,从功率键合图推导出系统的非线性状态空间方程.首先通过增维法将非齐次系统方程转化成齐次方程的形式,避免了系统矩阵求逆,节省计算时间,增强了计算稳定性.模型应用精细积分法迭代求解.实例计算表明,模型计算得到的稳态值同EPANET软件的稳态计算结果一致,验证了算法的正确性.     

Simulation of Water Distribution Network under Pressure-Deficient Condition

Pressure deficient condition occurs in the water distribution network (WDN) when the nodal demands are in excess of the design discharge as in the case of fire demand, pump failure, pipe breaks, valve failure etc. It causes either no-flow or partial-flow depending upon the available pressure head at the nodes. To evaluate the nodal flows in such condition, node flow analysis (NFA) gives reasonable results in comparison to demand-driven analysis (DDA) and head-dependent analysis (HDA). The NFA works on the predefined pressure-discharge relationship to evaluate the nodal flows. However, this approach requires human intervention and hence cannot be applied to large WDN. Recently, modified pressure-deficient network algorithm (M-PDNA) has been developed by Babu and Mohan (2012) for pressure-deficient analysis with EPANET toolkit. However, it requires modification of the source code of EPANET. In this study a relationship with the M-PDNA and node flow analysis (Gupta and Bhave 1996) has been investigated and it is found that M-PDNA is the simplified version of NFA. Further, the working principle of M-PDNA has been investigated with suitable examples of Babu and Mohan (2012). The theoretical basis of M-PDNA has not been investigated in terms of head-discharge relationship. Herein, a head-discharge relationship based on the working principal of M-PDNA is proposed. Some of the toolkits are also readily available to modify demand driven solver of EPANET 2 to suit for the pressure-driven analysis and then it can be used for analysing pressure deficient network. Also in this study, a modification in M-PDNA approach is proposed which does not require the use of EPANET toolkit which is found to be capable of simulating both pressure-sufficient and pressure-deficient conditions in a single hydraulic simulation. Using the proposed approach, pressure-deficient condition is analysed with constant and variable demand pattern.     

Technical and Environmental Sustainability Assessment of Water Distribution Systems

An environmental and technical sustainability assessment methodology is developed for both centralized and dual water distribution systems (WDSs) with and without fire flow scenarios. Technical sustainability of potable and reclaimed water networks is measured by a sustainability index (SI) assessment using reliability, resiliency, and vulnerability performance criteria. The U.S. Environmental Protection Agency EPANET software is used to simulate hydraulic (i.e. nodal pressure) and water quality (i.e. water age) analysis in a WDS. Total fresh water use and total energy intensity are considered as environmental sustainability criteria. The procedure considers two separate alternatives for meeting fire flows: (1) adding pumping to a system or (2) adding a non-potable WDS. The reclaimed system is designed using linear programming (LP) optimization. For each alternative, multi-criteria decision analysis (MCDA) is used to combine technical and environmental sustainability criteria for an urban WDS.     

用盘式负压入渗仪数据计算土壤导水参数

本研究提出了用盘式负压入渗仪(Disc infiltrometer)测定的入渗数据计算土壤导水参数的一种新方法。该方法可以用大于10min入渗时间的任何入渗率数据计算土壤导水参数。一种迅速准确的数值迭代法被用于解所得的高度非线形的方程组。新方法所计算的土壤导水参数与实验室测定数据比较吻合，与其他计算方法相比，新方法所得到的导水率与宏观毛管上升高度准确合理。     

Sustainability Assessment of Urban Water Distribution Systems

A methodology is presented for determining sustainability indices for pressure and water age in water distribution systems (WDSs). These sustainability indices are based upon performance criteria including reliability, resiliency, and vulnerability. Pressure and water age are determined for a WDS as a function of operation time using the U.S. Environmental Protection Agency EPANET model. The values of pressure and water age are used to determine reliability, resiliency, and vulnerability performance criteria, which are then combined into the nodal sustainability indices for water age and pressure. In addition, the sustainability index (SI) computations are performed for zones to define the SI for water age and SI for pressure. A combined SI calculation is performed to produce an overall sustainability score for the entire zone in the water distribution network. The proposed methodology can be used to monitor the sustainability of existing WDSs and to help define alternative solutions including changes in pump operation and modifications to WDS to increase the sustainability.     

Extending EPANET hydraulic solver capacity with rigid water column global gradient algorithm

EPANET is one of the most commonly used open-source programs in hydraulic modelling water distribution networks (WDNs), based on steady-state and extended period simulation approaches. These approaches effectively estimate flow capacity and average pressures in networks; however, EPANET is not yet fully effective in modelling incompressible unsteady flows in WDNs. In this study, the hydraulic solver capacity of EPANET 3 is extended with the Rigid Water Column Global Gradient Algorithm (RWC-GGA) to model incompressible unsteady flow hydraulics in WDNs. Moreover, we incorporated dynamically more accurate valve expressions than the existing ones in the default EPANET code and introduced a new global convergence algorithm, Convergence Tracking Control Method (CTCM), in the solver code. The RWC-GGA, CTCM, and valve expressions are tested and validated in three different WDNs varying from simple to sophisticated set-ups. The results show that incompressible unsteady flows can be modelled with RWC-CGA and dynamic valve representations. Finally, the convergence problem due to the valve motion and the pressure-dependent algorithm (PDA) is solved by the implemented global convergence algorithm, i.e. CTCM.     

基于非线性映射理论的城市供水管网压力监测点布置方法研究

通过对非线性映射理论及技术的研究和应用,提出了一种新的城市供水管网压力监测点布置方法。以某开发区供水管网为例,首先利用EPANET水力模拟软件对供水管网不同运行工况进行水力模拟,得到各节点压力模拟数值矩阵。然后,采用非线性映射分析方法对该压力模拟数值矩阵进行非线性映射变换,得到一系列独立的二维点群,实现压力变化特征相似节点的聚类和分组。最后,根据各节点压力变化的近似程度和特征,提出供水管网压力监测点的布置方案。应用表明,该方法实用性强,提高了节点压力分析的直观程度和可视化水平。     

Uncertainty Analysis of Transient Flow in Water Distribution Networks

For transient analysis of a pipe network, the unsteady flow governing equations should be solved to obtain the extreme pressure heads in the system, which may be faced with several uncertainties. To evaluate that to what extent the input uncertainties can affect the system responses, a simulation model based on the fuzzy sets theory is introduced. For this purpose, triangular fuzzy numbers are used to represent the input uncertainties. Then, to obtain the extreme pressure heads in each location of the network and at each level of uncertainty, four independent optimization problems are solved. In these problems, the nodal maximum and minimum pressure heads are the objective functions and the simulation parameters are the decision variables. Accordingly, for fuzzy analysis of a pipe network, a complicated many-objective optimization problem arises. To solve the problem efficiently a many-objective genetic algorithm is coupled to the transient simulation model. To speed up the analysis, a transient simulation model in the frequency domain is used. The proposed model is applied to a pipe network and the results are discussed. The model is found computationally fast and promising for real applications.     

供水管网中压力真实值的批次平差算法

分析了测压点优化布置的意义及原则,并根据供水周期性,依靠数量有限的测压点压力数据,结合管网的水力计算,利用传统的平差原理,将测压点以外的其它节点压力进行真实性校正,推算出了管网各节点的真实压力值,实现了通过有限测压点数据对管网所有节点压力的全面了解。     

喀腊塑克碾压混凝土重力坝坝体渗控方案研究

结合求解有自由面问题的等效结点虚流量法和模拟坝体排水孔的改进排水子结构技术，对喀腊塑克碾压混凝土重力坝坝体渗流场进行了多个工况的求解，在分析了坝体等水头线分布规律之后，认为拟设计坝体渗控方案可以适当改进，并提出了优选渗控方案。     

Pressure Control for Leakage Minimisation in Water Distribution Systems Management

A model to support decision systems regarding the quantification, location and opening adjustment of control valves in a network system, with the main objective to minimise pressures and consequently leakage levels is developed. This research work aims at a solution that allows simultaneously optimising the number of valves and its location, as well as valves opening adjustments for simulation in an extended period, dependently of the system characteristics. EPANET model is used for hydraulic network analysis and two operational models are developed based on the Genetic Algorithm optimisation method for pressure control, and consequently leakage reduction, since a leak is a pressure dependent function. In these two modules, this method has guaranteed an adequate technique performance, which demands a global evaluation of the system for different scenarios. A case study is presented to show the efficiency of the system by pressure control through valves management.     

明渠—结合池—暗管输水系统水力瞬变过程计算

分析了用Priessmann方法计算明渠—结合池—暗管结构的过渡过程的特点，给出了用明渠特征线方法算有压流的基本方程和建模过程。详细地分析了明渠—结合池—暗管结构在过渡过程计算中的边界条件。在编制程序对某具体的工程进行计算之后，指出了Priessmann法应用于明渠—结合池—暗管结构水力瞬变计算所应注意的问题，并对这些问题提出了相应的处理方法。     

Convergence of a Hydraulic Solver with Pressure-Dependent Demands

This paper analyzes the convergence of a pressure-driven analysis (PDA) model of a water distribution network solver based on Todini’s global gradient algorithm. The PDA model is constructed by embedding a pressure?demand relationship in the EPANET simulator code. To avoid spurious convergence, a residual-based convergence error was used. The introduction of pressure-dependent demands is shown to result in a far poorer convergence. The study of solver convergence as a function of the smoothness of the pressure?demand curve has demonstrated that, statistically, a smooth pressure?demand relationship gives a somewhat better convergence. To improve convergence, use was made of a quadratic approximation of the Hazen–Williams head loss?flow relationship in the vicinity of zero and the correct implementation of the Darcy?Weisbach formula in the solver. To further improve convergence, an iteration step control technique called the line search was used. The analysis of solver convergence for different line search variants has shown that the line search in its usual form is not efficient enough and may result in poorer convergence. A necessary error decrease algorithm, whose use in the line search improves solver convergence, is proposed. It is shown that due to the convergence improvement methods the convergence of the PDA solver is somewhat better than that of the demand-driven analysis solver and sufficient for direct problems such as design, for example.     

Water Distribution System Reliability Based on Minimum Cut – Set Approach and the Hydraulic Availability

Reliability analysis of water distribution systems is a complex task, as it requires both definition and calculation of several reliability measures. In this paper, a methodology for evaluating water distribution system reliability is developed and demonstrated on a simple water distribution network based on the minimum cut-set approach. In general, the definition of the minimum cut-set can arise either from the mechanical reliability or from the concept of hydraulic reliability. In the case of mechanical reliability, a new method based on graph theory is developed, in order to determine the minimum cut-set. This method is based on the counting of paths between nodes. Furthermore, the general concept of reliability is proposed, to include apart from the mechanical reliability, more generally, the pressure availability at nodes as a main hydraulic property. Based on the pressure availability, the sense of hydraulic availability can be expressed as a fuzzy set, while the combination of the water unavailability of the nodes can be achieved by using fuzzy averaging aggregator. Finally, an overall reliability index is proposed based on both the hydraulic and the mechanical reliability. An illustrative example is developed to indicate the methodology.