Search results for: Gumbel distribution

Authors: R. A. Deshpande, P. Chandhra Sekhar, V. Sankar

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In this paper, we discussed the basic reliability evaluation techniques needed to evaluate the reliability of distribution systems which are applied in distribution system planning and operation. Basically, the reliability study can also help to predict the reliability performance of the system after quantifying the impact of adding new components to the system. The number and locations of new components needed to improve the reliability indices to certain limits are identified and studied.

Keywords: distribution system, reliability indices, urban feeder, rural feeder

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Authors: Alexandru George Vaduva, Adriana Vlad, Bogdan Badea

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In this research, we conduct a Monte Carlo analysis on a two-dimensional χ2 test, which is used to determine the minimum distance required for independent sampling in the context of chaotic signals. We investigate the impact of transforming initial data sets from any probability distribution to new signals with a uniform distribution using the Spearman rank correlation on the χ2 test. This transformation removes the randomness of the data pairs, and as a result, the observed distribution of χ2 test values differs from the expected distribution. We propose a solution to this problem and evaluate it using another chaotic signal.

Keywords: chaotic signals, logistic map, Pearson’s test, Chi Square test, bivariate distribution, statistical independence

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Authors: Zahira Belkacemi

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One of the most important tools in conservation biology is information on the geographic distribution of species and the variables determining those patterns. In this study, we used maximum-entropy niche modeling (Maxent) to predict the current and future distribution of Anthus pratensis using climatic variables. The results showed that the species would not be highly affected by the climate change in shifting its distribution; however, the results of this study should be improved by taking into account other predictors, and that the NATURA 2000 protected sites will be efficient at 42% in protecting the species.

Keywords: anthus pratensis, climate change, Europe, species distribution model

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

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A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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Authors: A. Amar

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A new model, namely the crystal model, has been modified to calculate the radius and density distribution of light nuclei up to ⁸Be. The crystal model has been modified according to solid-state physics, which uses the analogy between nucleon distribution and atoms distribution in the crystal. The model has analytical analysis to calculate the radius where the density distribution of light nuclei has obtained from analogy of crystal lattice. The distribution of nucleons over crystal has been discussed in a general form. The equation that has been used to calculate binding energy was taken from the solid-state model of repulsive and attractive force. The numbers of the protons were taken to control repulsive force, where the atomic number was responsible for the attractive force. The parameter has been calculated from the crystal model was found to be proportional to the radius of the nucleus. The density distribution of light nuclei was taken as a summation of two clusters distribution as in ⁶Li=alpha+deuteron configuration. A test has been done on the data obtained for radius and density distribution using double folding for d+⁶,⁷Li with M3Y nucleon-nucleon interaction. Good agreement has been obtained for both the radius and density distribution of light nuclei. The model failed to calculate the radius of ⁹Be, so modifications should be done to overcome discrepancy.

Keywords: nuclear physics, nuclear lattice, study nucleus as crystal, light nuclei till to ⁸Be

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Authors: Phutthiwat Waiyawuththanapoom, Wannapong Waiyawuththanapoom, Pimploi Tirastittam

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Nowadays, it is a globalization era which social media plays an important role to the lifestyle as an information source, tools to connect people together and etc. This research is object to find out about the significant level of the social media as a distribution channel to the agriculture product of Thailand. In this research, the agriculture product is the Rice Berry which is the cross-bred unmilled rice producing dark violet grain, is a combination of Hom Nin Rice and Thai Jasmine/ Fragrant Rice 105. Rice Berry has a very high nutrition and nice aroma so the product is in the growth stage of the product cycle. The problem for the Rice Berry product in Thailand is the production and the distribution channel. This study is to confirm that the social media is another option as the distribution channel for the product which is not a mass production product. This will be the role model for the other niche market product to select the distribution channel.

Keywords: distribution, social media, rice berry, distribution channel

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Authors: Chao-Yang Huang, Rwey-Hua Cherng, Chung-Lin Fu, Yuan-Lung Lo

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Solar energy is one of the replaceable choices to reduce the CO2 emission produced by conventional power plants in the modern society. As an island which is frequently visited by strong typhoons and earthquakes, it is an urgent issue for Taiwan to make an effort in revising the local regulations to strengthen the safety design of photovoltaic systems. Currently, the Taiwanese code for wind resistant design of structures does not have a clear explanation on photovoltaic systems, especially when the systems are arranged in arrayed format. Furthermore, when the arrayed photovoltaic system is mounted on the rooftop, the approaching flow is significantly altered by the building and led to different pressure pattern in the different area of the photovoltaic system. In this study, L-shape arrayed photovoltaic system is mounted on the ground of the wind tunnel and then mounted on the building rooftop. The system is consisted of 60 PV models. Each panel model is equivalent to a full size of 3.0 m in depth and 10.0 m in length. Six pressure taps are installed on the upper surface of the panel model and the other six are on the bottom surface to measure the net pressures. Wind attack angle is varied from 0° to 360° in a 10° interval for the worst concern due to wind direction. The sampling rate of the pressure scanning system is set as high enough to precisely estimate the peak pressure and at least 20 samples are recorded for good ensemble average stability. Each sample is equivalent to 10-minute time length in full scale. All the scale factors, including timescale, length scale, and velocity scale, are properly verified by similarity rules in low wind speed wind tunnel environment. The purpose of L-shape arrayed system is for the understanding the pressure characteristics at the corner area. Extreme value analysis is applied to obtain the design pressure coefficient for each net pressure. The commonly utilized Cook-and-Mayne coefficient, 78%, is set to the target non-exceedance probability for design pressure coefficients under Gumbel distribution. Best linear unbiased estimator method is utilized for the Gumbel parameter identification. Careful time moving averaging method is also concerned in data processing. Results show that when the arrayed photovoltaic system is mounted on the ground, the first row of the panels reveals stronger positive pressure than that mounted on the rooftop. Due to the flow separation occurring at the building edge, the first row of the panels on the rooftop is most in negative pressures; the last row, on the other hand, shows positive pressures because of the flow reattachment. Different areas also have different pressure patterns, which corresponds well to the regulations in ASCE7-16 describing the area division for design values. Several minor observations are found according to parametric studies, such as rooftop edge effect, parapet effect, building aspect effect, row interval effect, and so on. General comments are then made for the proposal of regulation revision in Taiwanese code.

Keywords: aerodynamic force coefficient, ground-mounted, roof-mounted, wind tunnel test, photovoltaic

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Authors: Priti Kumari, Tricha Anjali

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Body Area Networks (BANs) have emerged as the most promising technology for pervasive health care applications. Since they facilitate communication of very sensitive health data, information leakage in such networks can put human life at risk, and hence security inside BANs is a critical issue. Safe distribution and periodic refreshment of cryptographic keys are needed to ensure the highest level of security. In this paper, we focus on the key distribution techniques and how they are categorized for BAN. The state-of-art pre-shared key distribution algorithms are surveyed. Possible attacks on algorithms are demonstrated with examples.

Keywords: attacks, body area network, key distribution, key refreshment, pre-shared keys

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.

Keywords: Karkheh River, Log Pearson Type III, probability distribution, residual sum of squares

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Authors: Abdullah M. Alodhaiani, Yasir A. Alturki, Mohamed A. Elkady

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Complex power flow distribution factors, which relate line complex power flows to the bus injected complex powers, have been widely used in various power system planning and analysis studies. In particular, AC distribution factors have been used extensively in the recent power and energy pricing studies in free electricity market field. As was demonstrated in the existing literature, many of the electricity market related costing studies rely on the use of the distribution factors. These known distribution factors, whether the injection shift factors (ISF’s) or power transfer distribution factors (PTDF’s), are linear approximations of the first order sensitivities of the active power flows with respect to various variables. This paper presents a novel model for evaluating the universal distribution factors (UDF’s), which are appropriate for an extensive range of power systems analysis and free electricity market studies. These distribution factors are used for the calculations of lines complex power flows and its independent of bus power injections, they are compact matrix-form expressions with total flexibility in determining the position on the line at which line flows are measured. The proposed approach was tested on IEEE 9-Bus system. Numerical results demonstrate that the proposed approach is very accurate compared with exact method.

Keywords: distribution factors, power system, sensitivity factors, electricity market

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Authors: Ayman Baklizi

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This paper discusses the problem of testing hypotheses about the lifetime distributions of a matched pair based on censored data. A distribution free test based on a runs statistic is proposed. Its null distribution and power function are found in a simple convenient form. Some properties of the test statistic and its power function are studied.

Keywords: censored data, distribution free, matched pair, runs statistics

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Authors: Olawale J. Olaluyi, Ayodele S. Oluwole, O. Akinsanmi, Johnson O. Adeogo

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Communication using visible light VLC is considered a cutting-edge technology used for data transmission and illumination since it uses less energy than radio frequency (RF) technology and has a large bandwidth, extended lifespan, and high security. The room's irregular distribution of small base stations, or LED array distribution, is the cause of the obscured area, minimum signal-to-noise ratio (SNR), and received power. In order to maximize the received power distribution and SNR at the center of the room for an indoor VLC system, the researchers offer an innovative model for the placement of eight LED array distributions in this work. We have investigated the arrangement of the LED array distribution with regard to receiving power to fill the open space in the center of the room. The suggested LED array distribution saved 36.2% of the transmitted power, according to the simulation findings. Aside from that, the entire room was equally covered. This leads to an increase in both received power and SNR.

Keywords: visible light communication (VLC), light emitted diodes (LED), optical power distribution, signal-to-noise ratio (SNR).

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Authors: M. R. Ebrahimi, B. Mahdaviani

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Conventional electric distribution systems are radial in nature, supplied at one end through a main source. These networks generally have a simple protection system usually implemented using fuses, re-closers, and over-current relays. Recently, great attention has been paid to applying Distributed energy resources (DERs) throughout electric distribution systems. Presence of such generation in a network leads to losing coordination of protection devices. Therefore, it is desired to develop an algorithm which is capable of protecting distribution systems that include DER. On the other hand smart grid brings opportunities to the power system. Fast advancement in communication and measurement techniques accelerates the development of multi agent system (MAS). So in this paper, a new approach for the protection of distribution networks in the presence of DERs is presented base on MAS. The proposed scheme has been implemented on a sample 27-bus distribution network.

Keywords: distributed energy resource, distribution network, protection, smart grid, multi agent system

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Authors: A. B. Arani, R. Shojaee

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Electrical power distribution system is one of the vital infrastructures of an oil refinery, which requires wide area of study and planning before construction. In this paper, power distribution reliability of Tehran Refinery’s KHDS/GHDS unit has been taken into consideration to investigate the importance of these kinds of studies and evaluate the designed system. In this regard, the authors chose and evaluated different configurations of electrical power distribution along with the existing configuration with the aim of finding the most suited configuration which satisfies the conditions of minimum cost of electrical system construction, minimum cost imposed by loss of load, and maximum power system reliability.

Keywords: power distribution system, oil refinery, reliability, investment cost, interruption cost

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: O. Arikan, C. Kocatepe, G. Ucar, Y. Hacialiefendioglu

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In this paper, influence of harmonics on medium voltage distribution system of Bogazici Electricity Distribution Inc. (BEDAS) which takes place at Istanbul/Turkey is investigated. A ring network consisting of residential loads is taken into account for this study. Real system parameters and measurement results are used for simulations. Also, probable working conditions of the system are analyzed for %50, %75 and %100 loading of transformers with similar harmonic contents. Results of the study are exhibited the influence of nonlinear loads on %THDV, P.F. and technical losses of the medium voltage distribution system.

Keywords: distribution system, harmonic, technical losses, power factor, total harmonic distortion, residential load, medium voltage

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Authors: Ahmed Mateen, Zhu Qingsheng, Ahmad Bilal

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In the current age of technology, information is the most precious asset of a company. Today, companies have a large amount of data. As the data become larger, access to data for some particular information is becoming slower day by day. Faster data processing to shape it in the form of information is the biggest issue. The major problems in distributed databases are the efficiency of data distribution and response time of data distribution. The security of data distribution is also a big issue. For these problems, we proposed a strategy that can maximize the efficiency of data distribution and also increase its response time. This technique gives better results for secure data distribution from multiple heterogeneous sources. The newly proposed technique facilitates the companies for secure data sharing efficiently and quickly.

Keywords: ER-schema, electronic record, P2P framework, API, query formulation

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Authors: M. A. Hasan, M. R. Islam, R. A. Tarefder

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This study investigates how the site specific traffic data differs from the Mechanistic Empirical Pavement Design Software default values. Two Weigh-in-Motion (WIM) stations were installed in Interstate-40 (I-40) and Interstate-25 (I-25) to developed site specific data. A computer program named WIM Data Analysis Software (WIMDAS) was developed using Microsoft C-Sharp (.Net) for quality checking and processing of raw WIM data. A complete year data from November 2013 to October 2014 was analyzed using the developed WIM Data Analysis Program. After that, the vehicle class distribution, directional distribution, lane distribution, monthly adjustment factor, hourly distribution, axle load spectra, average number of axle per vehicle, axle spacing, lateral wander distribution, and wheelbase distribution were calculated. Then a comparative study was done between measured data and AASHTOWare default values. It was found that the measured general traffic inputs for I-40 and I-25 significantly differ from the default values.

Keywords: AASHTOWare, traffic, weigh-in-motion, axle load distribution

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Authors: Bashara Want

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One of the key factors limiting the performance of magnetic memory is that the coercivity has a distribution with finite width, and the reversal starts at the weakest link in the distribution. So one must first know the distribution of coercivities in order to learn how to reduce the width of distribution and increase the coercivity field to obtain a system with narrow width. First Order Reversal Curve (FORC) method characterizes a system with hysteresis via the distribution of local coercivities and, in addition, the local interaction field. The method is more versatile than usual conventional major hysteresis loops that give only the statistical behaviour of the magnetic system. The FORC method will be presented and discussed at the conference.

Keywords: magnetic materials, hysteresis, first-order reversal curve method, nanostructures

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Authors: Zakir Husain, Neem Sagar, Neeraj Gupta

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Due to the increased penetration of renewable energy resources in the distribution system, the system is no longer passive in nature. In this paper, a steady state analysis of the distribution system has been done with the inclusion of wind generation. The modeling of wind turbine generator system and wind generator has been made to obtain the average active and the reactive power injection into the system. The study has been conducted on a IEEE-33 bus system with two wind generators. The present research work is useful not only to utilities but also to customers.

Keywords: distributed generation, distribution network, radial network, wind turbine generating system

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Authors: Fatma Zehra Doğru, Olcay Arslan

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In this paper, we propose alternative robust estimators for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators.

Keywords: burr xii distribution, robust estimator, m-estimator, least squares

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Authors: Chengming Li, Yong Yin, Peipei Guo, Xiaoli Liu

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Without taking account of the attribute richness of POI (point of interest) data and spatial distribution limited by roads, a POI generalization method considering both attribute information and spatial distribution has been proposed against the existing point generalization algorithm merely focusing on overall information of point groups. Hierarchical characteristic of urban POI information expression has been firstly analyzed to point out the measurement feature of the corresponding hierarchy. On this basis, an urban POI generalizing strategy has been put forward: POIs urban road network have been divided into three distribution pattern; corresponding generalization methods have been proposed according to the characteristic of POI data in different distribution patterns. Experimental results showed that the method taking into account both attribute information and spatial distribution characteristics of POI can better implement urban POI generalization in the mapping presentation.

Keywords: POI, road network, selection method, spatial information expression, distribution pattern

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, nonlinearity distribution, particle filter, system identification

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Authors: S. Sudhharani

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Energy distribution networks are the main link between the energy industry and consumers and are subject to the most scrutiny and testing of any category. As a result, it is important to monitor energy levels during the distribution phase. Power distribution networks, on the other hand, remain subject to common problems, including voltage breakdown, power outages, harmonics, and capacitor switching, all of which disrupt sinusoidal waveforms and reduce the quality and power of the network. Using power appliances in the form of custom power appliances is one way to deal with energy quality issues. Dynamic Voltage Restorer (DVR), integrated with network and distribution networks, is one of these devices. At the same time, by injecting voltage into the system, it can adjust the voltage amplitude and phase in the network. In the form of injections and three-phase syncing, it is used to compensate for the difficulty of energy quality. This article examines the recent use of DVR for power compensation and provides data on the control of each DVR in distribution networks.

Keywords: dynamic voltage restorer (DVR), power quality, distribution networks, control systems(PWM)

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

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Numerical study is performed to investigate the temperature distribution in an annular diffuser fitted with helical tape hub. Different pitches (Y = 20 mm, and Y = 30 mm) for the helical tape are studied with different heights (H = 20 mm, 22 mm, and 24 mm) to be compared. The geometry of the annular diffuser and the inlet condition for both hub arrangements are kept constant. The result obtains that using helical tape insert with different pitches and different heights will force the temperature to distribute in a helical direction; however the use of helical tape hub with height (H = 22 mm) for both pitches enhance the temperature distribution in a good manner.

Keywords: helical tape, divergent fluid flow, temperature distribution, swirl flow, CFD

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Authors: Atefeh Pourshafie, Homayoun Bakhtiari

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The main task of power distribution companies is to supply the power required by customers in an acceptable level of quality and reliability. Some key performance indicators for electric power distribution companies are those evaluating the continuity of supply within the network. More than other problems, power outages (due to lightning, flood, fire, earthquake, etc.) challenge economy and business. In addition, end users expect a reliable power supply. Reliability indices are evaluated on an annual basis by the specialized holding company of Tavanir (Power Produce, Transmission& distribution company of Iran) . Evaluation of reliability indices is essential for distribution companies, and with regard to the privatization of distribution companies, it will be of particular importance to evaluate these indices and to plan for their improvement in a not too distant future. According to IEEE-1366 standard, there are too many indices; however, the most common reliability indices include SAIFI, SAIDI and CAIDI. These indices describe the period and frequency of blackouts in the reporting period (annual or any desired timeframe). This paper calculates reliability indices for three sample feeders in Lorestan Electric Power Distribution Company and defines the threshold values in a ten-month period. At the end, strategies are introduced to reach the threshold values in order to increase customers' satisfaction.

Keywords: power, distribution network, reliability, outage

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Authors: Ezzat Mohamed El-Amin

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Mapping the earthquake-size distribution in various tectonic regimes on a local to regional scale reveals statistically significant variations in the range of at least 0.4 to 2.0 for the b-value in the frequency-magnitude distribution. We map the earthquake frequency–magnitude distribution (b value) as a function of depth in the Reservoir Triggered Seismicity (RTS) region in Kalabsha region, in south Egypt. About 1680 well-located events recorded during 1981–2014 in the Kalabsha region are selected for the analysis. The earthquake data sets are separated in 5 km zones from 0 to 25 km depth. The result shows a systematic decrease in b value up to 12 km followed by an increase. The increase in b value is interpreted to be caused by the presence of fluids. We also investigate the spatial distribution of b value with depth. Significant variations in the b value are detected, with b ranging from b 0.7 to 1.19. Low b value areas at 5 km depth indicate localized high stresses which are favorable for future rupture.

Keywords: seismicity, frequency-magnitude, b-value, earthquake

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Authors: Veerpaul Maan, Gaurav Mishra

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The evolution of omnichannel has revolutionized the supply chain of the organizations by enhancing customer shopping experience. For these organizations need to develop well-integrated multiple distribution channels to leverage the benefits of omnichannel. To adopt an omnichannel system in the supply chain has resulted in structuring and reconfiguring the practices of the traditional supply chain distribution network. In this paper a multiple distribution supply chain network (MDSCN) have been proposed which integrates online giants with a local retailers distribution network in uncertain environment followed by sustainability. To incorporate sustainability, an additional objective function is added to reduce the carbon content through minimizing the travel distance of the product. Through this proposed model, customers are free to access product and services as per their choice of channels which increases their convenience, reach and satisfaction. Further, a numerical illustration is being shown along with interpretation of results to validate the proposed model.

Keywords: sustainable supply chain network, omnichannel, multiple distribution supply chain network, integrate multiple distribution channels

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

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The influence of twist arrangement on the temperature distribution in an annular diffuser fitted with twisted rectangular hub is investigated. Different pitches (Y = 120 mm, 100 mm, 80 mm, and 60 mm) for the twist arrangements are simulated to be compared. The geometry of the annular diffuser and the inlet condition for the hub arrangements are kept constant. The result reveals that using twisted rectangular hub insert with different pitches will force the temperature to distribute in a circular direction. However, temperature distribution will be enhanced with the length pitch increases.

Keywords: numerical simulation, twist arrangement, annular diffuser, temperature distribution, swirl flow, pitches

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Authors: Autcha Araveeporn

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This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov chain Monte Carlo method, maximum likelihood method, normal distribution

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