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This paper presents a new valve positioning algorithm (VPA) for water network pressure reduction. The proposed algorithm is a graph theory-based algorithm combined with EPANET2.2 to position pressure-reducing valves (PRVs) at the most effective locations, having the most effect on downstream pressure reduction, and then calculates the setpoint for locally controlled valves. Each algorithm solution positions one valve on the edge with the highest-pressure reduction indicator calculated using the depth-first search algorithm. The setpoint is then calculated according to downstream pressure differences to the minimum service pressure to be supplied. The PRV location and setpoint found by the algorithm may be used to install and set locally controlled PRVs or serve as a guide for positioning remote-controlled PRVs. The algorithm is demonstrated on a simple example network using demand-driven analysis (DDA), pressure-driven analysis (PDA), and genetic algorithms (GA) and on a medium and a large example application (DDA). Any number of PRVs may be installed using the algorithm, which returns stable results and very short solution times while maintaining minimum service pressure requirements to the critical consumers. [ABSTRACT FROM AUTHOR]

Finding the optimal pump operation in water distribution systems, taking into account hydraulic and water quality constraints, is a complex problem due to the nonlinear relationship between dynamic head loss and flow rate and between chlorine decay and water age, and due to the size of the problem. The proposed algorithm, for minimum cost pump scheduling, utilizes the operational graph algorithm applied to hydraulic and quality constraints. The proposed algorithm utilizes a graph algorithm that considers hydraulic and water quality constraints to find the pump scheduling that minimizes pump operational costs. The algorithm has short solution times and therefore is suitable for real-time water system control or, if used offline, for giving a recommendation on the pump operation taking into account hydraulic and water quality constraints. The algorithm results were compared with the best results found by enumeration to show that the operational graph algorithm returns a global minimal solution and, when combined with quality constraints, returns near-optimal results. The proposed algorithm was successfully demonstrated on a 24-h example application with a single pumping unit and, on the C-Town example application, with 11 pumping units and 168 time steps. [ABSTRACT FROM AUTHOR]

A graph theory-based algorithm is demonstrated for optimal pump scheduling of two example application water networks. The hydraulic part of the problem is solved using a dedicated and efficient hydraulic solver. The pump scheduling part of the problem is solved using a skeletonized operational graph, representing only the basic logic operational relations existing in the network required for pump selection: the pumping units (with nominal operating costs), water tanks and clustered demand nodes. The hydraulic solver advances one time step at a time. After each time step advance, the nodes of the model are checked to see if satisfy minimum service pressure and minimum water tank level. For nodes not satisfying the service constraints, the Dijkstra's shortest path algorithm is applied to the skeletonized graph to determine the optimal pumping unit to be activated and then updating the pumps operation pattern in the model. The hydraulic solver is then reinitialized to resolve and recheck the time steps one by one. The algorithm ends when the solver reaches the last time step with all nodes meeting service constraints. The algorithm returns an optimal minimal cost pump-scheduling pattern under greater-than constraints over the examined time period, such as (1) minimal consumer service pressure, and (2) water balance closure at the water tanks. The algorithm returns discrete pump operation scheduling with minimal pump switching and minimal water age in the tanks, demonstrating short solution times (28 s to schedule 11 pumps over a 168-hour period). The algorithm may be applicable for real-time pump scheduling. Future research may include water quality constraints and variable frequency drive pump scheduling. Pump selection is based on the assumption that the optimal pump operation order is not affected by changes in the network's hydraulic conditions, such as water tank levels and location along the pump efficiency curve (assuming constant efficiency). If hydraulic conditions change the optimal activation order, then the pumps' working points must by updated after each time step solution, which is not addressed in the current work. [ABSTRACT FROM AUTHOR]

• A pragmatic solution to regulating water pressures and leakage by introducing PRVs. • Optimal selection of positions and setpoints of PRVs in a distribution network. • Graph theory-based algorithm employing the depth-first search method. • Pipes leading to the most extended downstream networks are ideal locations for PRVs. • The algorithm maintains the minimum pressure at the minimum required service level. Optimal pressure management is a standard strategy for water loss minimization in water distribution systems (WDS). A pragmatic solution to regulating water pressures and leakage is introducing pressure-reducing valves (PRVs). This paper presents a valve positioning algorithm for optimally deciding the positions and setpoints of PRVs in a WDS. The algorithm derives the hydraulic solution of a WDS as a directed graph, established on the flow directions, using EPANET 2.2 and develops the downstream network supplied by water flowing out of every pipe in the network by applying the depth-first search method. The algorithm later recognizes the pipes leading to the most extended downstream networks, with pressures above the minimum required service pressure, and prioritizes them as the ideal locations for PRV placement. In this way, the proposed algorithm overcomes the limitations of the state-of-the-art in realistically conceptualizing the leakage reduction for optimally positioning the PRVs in WDS. Four studies with varying complexities were selected to demonstrate the algorithm's applicability for deriving pressure management solutions. The solution time for PRV positioning was in seconds for the first three networks and several minutes for the extensive fourth case study. The results corroborate the algorithm's ability to pinpoint the critical nodes with the most increased potential for downstream pressure control and for maintaining the pressure at the least required service pressure level through optimally allocating the PRVs, with acceptable setpoint values, within the pipe network. [Display omitted]. [ABSTRACT FROM AUTHOR]