This note proposes models for efficiency and mechanical input power of a group of parallel identical pumps which can be fixed or variable speed. Two approaches are considered. In the first approach, the power characteristic is evaluated from hydraulic and efficiency curves. In the second approach, the mechanical power is approximated directly by a cubic polynomial and scaled by pump speed and number of pumps. In both cases, the obtained power curves are well suited for use in simulation and optimization software; however, if the power data points are available, the second approach can lead to a more accurate representation. The effects of the electric motor efficiency characteristic on the performance of the entire pump plant are also discussed. The developed theory is illustrated by a practical case study. For completeness, the studies are performed using two types of fitted pump hydraulic curves, one quadratic and one described by a power law.

The behavior of transients in water pipe networks is well understood but the influence of modulating control valves on this behavior is less well known. Experimental work on networks supplied through pressure reducing valves (PRVs) has demonstrated that, in certain conditions, undesirable phenomena such as sustained or slowly decaying oscillation and large pressure overshoot can occur. This paper presents results from modeling studies to investigate interaction between PRVs and water network transients. Transient pipe network models incorporating random demand are combined with a behavioral PRV model to demonstrate how the response of the system to changes in demand can produce large or persistent pressure variations, similar to those seen in practical experiments. A proportional-integral-derivative (PID) control mechanism, to replace the existing PRV hydraulic controller, is proposed and this alternative controller is shown to significantly improve the network response. PID controllers are commonly used ...

Models are currently available for representing the dynamical behavior of most water network components. Such models are relatively simple, accurate and can be easily solved. However, there is no generally accepted dynamic model of a pressure reducing valve (PRV). The key contributions of this paper are the development of several dynamic models—two phenomenological, one behavioral, and one linear—to represent the behavior of PRVs. The models vary in complexity but perform similarly. Experimental data is used to assess the accuracy of the models. The phenomenological models are derived from physical laws and provide an excellent but complex representation of a PRV. The behavioral model is simpler and sufficient for most practical purposes. The linear model does not take the needle valve setting (which controls the valve’s speed) into account and therefore has limited use.

In this paper a parallel computing based software demonstrator for the simulation and leakage minimization of water networks is presented. This demonstrator, based on the EPANET package, tackles three different types of problems making use of parallel computing. First, the solution of the hydraulic problem is treated by means of the gradient method. The key point in the parallelization of the method is the solution of the underlying linear systems, which is carried out by means of a multifrontal Choleski method. Second, the water quality simulation problem is approached by using the discrete volume element method. The application of parallel computing is based on dividing the water network in several parts using the multilevel recursive bisection graph partitioning algorithm. Finally, the problem of leakage minimization using pressure reducing valves is approached. This results in the formulation of an optimization problem for each time step, which is solved by means of sequential quadratic programming. B...