Water loss has been changed into a global concern in recent decades [1]. Since water demand has been increased, it is necessary to manage its consumption patterns to overcome this problem. The most important part of managing water consumption, is to decrease the water loss. In this paper a new idea has been presented to detect the leakage location and its quantity in a water distribution network, using NODAL PRESSUREs analyzes in two cases of with and without leakage discharges. The results have shown that this method not only can determine the location of leaky node, but also the leakage quantity, by using NODAL PRESSURE data.

Given that, observational data have different uncertainties, the calibration of water distribution networks based on a definite value can affect the results of the calibrated model. In this research, the calibration of water distribution networks by considering the uncertainty of NODAL PRESSURE has been investigated. For this purpose, first, by generating a series of NODAL PRESSURE data using the Monte Carlo method, the Hazen-Williams coefficients of the network have been obtained. Then, by producing a series of Hazen-Williams coefficients, the NODAL PRESSURE values have been calculated and the results of the two PRESSUREs have been compared. The calibration model was performed using the particle swarm optimization algorithm by linking the EPANET simulator in MATLAB. The proposed method has been implemented on the two-loop sample network and real water distribution network of Sufian city. The results show that the application of node PRESSURE uncertainty in network nodes leads to multiple sets of solutions for Hazen-Williams coefficients of pipes with different variation ranges and standard deviations, which according to the average absolute error of 4 and 3.8 percent between the average NODAL PRESSURE in the sample and the real network in the non-deterministic mode with the deterministic mode, the proposed method, can be a more accurate method for calibrating networks. However, it should be noted that there are challenges in the modeling and execution time of calibration models.

Leak has always been one of the problems in water distribution networks, whose preventing not only results in the saving of water sources but also has profound effects on the maintenance cost of networks. In the present paper, a new method is applied for leak detection in water collection and transmission network. In this method, detection of leak location is performed by PRESSURE difference analysis at junctions and by the help of the relative index of the leak. The PRESSURE measurements should be performed at least at two nodes for two cases of with and without the presence of leak. The minimum number of PRESSURE measurements to form a relative leak index is two. However, in this case, two NODAL PRESSURE measurements are too few, and the number of PRESSURE measurement should be increased. Therefore the next option for the number of measurements is three. The investigated network in this research includes 7 wells with an approximate length of 7800 m located in the northwestern city of Mashhad. A real leak with a rate of 7. 57 l/s is created at one of the network nodes whose amount is measurable by a volume counter. The real leak is a hypothetical leak which is known in advance, and its magnitude is not necessarily a round number in term of a liter per second. Finally, this leak is identified by the proposed method via 3 NODAL PRESSURE measurements.

The leakage is one of the most important issues in Water Distribution Systems (WDS) which imposes huge costs to water industries. Current methods detecting leakages are costly, time consuming, and labor intensive. New methods have recently been considered based on calibrating NODAL PRESSUREs. Modeling and calibrating the NODAL PRESSURE using genetic algorithm is one of these methods which unfortunately is not yet accurate enough to be applied widely on real networks and more investigations is needed in this regard. In this paper, a new approach is developed which detects and eliminate the nodes with no leakage among unknown demand nodes step-by-step. In this method, an ordinary calibration was accomplished. Some nodes with no leakages are then eliminated from the set of leaky nodes and the network was calibrated again. Several iteration of this process have shown a good improvement in the leakage detection in WDS.

A Sturm-Liouville problem with n-potential functions in the second order differential equation and which contains spectral parameter depending on linearly in one boundary condition is considered. The asymptotic formulas for the eigenvalues, NODAL parameters (NODAL points and NODAL lengths) of this problem are calculated by the Prüfer's substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions are given. Finally, a numerical example is given.

Topological aspects of meshless element free Galerkian method (EFGM) as the NODAL connectivity of matrices are studied. Four different graphs are defined for meshless discretizations of EFGM and their connectivity is investigated. Graphs are used for NODAL ordering of meshless models in order to reduce the bandwidth, profile, maximum front width, and root-mean-square wave front of the corresponding matrices.      

Various reliability indices have been defined by researchers for the water distribution networks. Due to the complexity and heterogeneous nature of distribution networks, results of indicies can vary substantially and municipalities have hard time to select the most practical indicies for their networks. This study was undertaken to develop a new method for identifying the best reliability index by considering various factors including the appropriate sensitivity to changes in network parameters, the appropriate shift in extreme conditions, the capability in covering critical condition, hydraulic condition, and water quality reliability. To accomplish the objective of the study, several water distribution networks were evaluated under multiple scenarios and the optimum reliability indices were verified with an example real water distribution network in Ahar. Controlling parameters included in scenario analysis for network reliability indices include: minimum, maximum and optimal PRESSURE, residual chlorine in nodes, velocity in pipes, NODAL PRESSURE reliability, pipe velocity reliability, and NODAL residual chlorine reliability. To evaluate the performance of defined index, a two-loop test (critical) were compared with the conventional single-lop test (normal). The performance assessment of indices obtained from this study showed that the index values ranged between 0. 11 and 1. 0, which indicate the normality and the appropriate sensitivity of the indices. Also, by increasing the residual chlorine of the reservoir, the network reliability index changed from 0. 54 to 0. 75 and then as the residual chlorine decreases in the distributon network the reliability index decreased back to 0. 54. This appropriate shift in reliability index while changing residual chlorine in the network, cearly shows the the effectiveness of new method in determining the reliability indicies under extreme conditions. Also, the new method did not respond to the failure of some network components, as were evident with insignificant change in the indices values under critical conditions. From the results of this study generally can be concluded that the newly defined relability indices is an efficient way for evaluating the performance of water distribution networks.

Abstract: This paper proposes an index for NODAL market power detection in power market under Locational Marginal Pricing (LMP). This index is an ex-ante technique to detect the market power. More precisely, this criterion detects the potential of exercising market power regardless of detecting the actual market power. Also it is obvious that pricing and market clearing method affect the potential of exercising market power. Different potential of market power exists in different pricing methods. This index has been analyzed under LMP method which seems to be a desirable environment to exercise market power. In LMP method by load growth, in some determined load levels which is called Critical Load Levels (CLLs), locational marginal prices have step change. This step change in locational marginal prices causes step change in revenue and benefit of Gencos. So it is significant to detect the behavior of Gencos in the CLLs. The proposed criterion has been tested on constant system load and CLLs for two test system.