Search results for: Electrical Resistivity

Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: Sezen Yildirim, Tahir Çetin Akinci, Serhat Seker, Nazmi Ekren

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Ferroresonance is an electrical phenomenon in nonlinear character, which frequently occurs in power system due to transmission line faults and single or more-phase switching on the lines as well as usage of the saturable transformers. In this study, the ferroresonance phenomena are investigated under the modeling of the West Anatolian Electric Power Network of 380 kV in Turkey. The ferroresonance event is observed as a result of removing the loads at the end of the lines. In this sense, two different cases are considered. At first, the switching is applied at 2nd second and the ferroresonance affects are observed between 2nd and 4th seconds in the voltage variations of the phase-R. Hence the ferroresonance and nonferroresonance parts of the overall data are compared with each others using the Fourier transform techniques to show the ferroresonance affects.

Keywords: Ferroresonance, West Anatolian Electric Power System, Power System Modeling, Switching, Spectral Analysis.

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Authors: F.Agalianos, S.Patelis , P. Kyratsis, E. Maravelakis, E.Vasarmidis, A.Antoniadis

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Laser engraving is a manufacturing method for those applications where previously Electrical Discharge Machining (EDM) was the only choice. Laser engraving technology removes material layer-by-layer and the thickness of layers is usually in the range of few microns. The aim of the present work is to investigate the influence of the process parameters on the surface quality when machined by laser engraving. The examined parameters were: the pulse frequency, the beam speed and the layer thickness. The surface quality was determined by the surface roughness for every set of parameters. Experimental results on Al7075 material showed that the surface roughness strictly depends on the process parameters used.

Keywords: Laser engraving, Al7075, Yb: YAG laser, laser process parameters, material roughness.

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Authors: A. Morsli, A.Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to a shunt Active Power Filter (sAPF) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: Fuzzy logic controller, P-Q method, Pulse Width Modulation (PWM), shunt Active Power Filter (sAPF), Total Harmonic Distortion (THD).

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Authors: Zhypargul Abdullaeva, Emil Omurzak, Tsutomu Mashimo

Abstract:

Copper sulfide nanoparticles (CuS) were successfully synthesized by the pulsed plasma in liquid method, using two copper rod electrodes submerged in molten sulfur. Low electrical energy and no high temperature were applied for synthesis. Obtained CuS nanoparticles were then analyzed by means of X-ray diffraction, Low and High Resolution Transmission Electron Microscopy, Electron Diffraction, X-ray Photoelectron, Raman Spectroscopies and Field Emission Scanning Electron Microscopy. XRD analysis revealed peaks for CuS with hexagonal phase composition. TEM and HRTEM studies showed that sizes of CuS nanoparticles ranged between 10-60 nm, with the average size of about 20 nm. Copper sulfide nanoparticles have short nanorod-like structure. Raman spectroscopy found peak for CuS at 474.2cm-1of Raman region.

Keywords: Copper sulfide, Nanoparticles, Pulsed plasma, Synthesis.

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Authors: Ilya Kavalchuk, Hayrettin Arisoy, Alex Stojcevski, Aman Maun Than Oo

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Electric vehicles are one of the most complicated electric devices to simulate due to the significant number of different processes involved in electrical structure of it. There are concurrent processes of energy consumption and generation with different onboard systems, which make simulation tasks more complicated to perform. More accurate simulation on energy consumption can provide a better understanding of all energy management for electric transport. As a result of all those processes, electric transport can allow for a more sustainable future and become more convenient in relation to the distance range and recharging time. This paper discusses the problems of energy consumption simulations for electric vehicles using different software packages to provide ideas on how to make this process more precise, which can help engineers create better energy management strategies for electric vehicles.

Keywords: Electric Vehicles, EV, Power Consumption, Power Management, Simulation.

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Authors: Hoda Molavi, Alireza Zahiri, Katayoon Anvarizadeh

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Dissolved gas analysis has been accepted as a sensitive, informative and reliable technique for incipient faults detection in power transformers and is widely used. In the last few years this method, which has been recommended by IEEE Power & Energy society, has been applied for fault detection in load tap changers. Regarding the critical role of load tap changers in electrical network and essential of catastrophic failures prevention, it is necessary to choose "condition based preventative maintenance strategy" which leads to reduction in costs, the number of unnecessary visits as well as the probability of interruptions and also increment in equipment reliability. In current work, considering the condition based preventative maintenance strategy, condition assessment of an Elin tap changer was carried out using dissolved gas analysis.

Keywords: Condition Assessment, Dissolved Gas Analysis, Load Tap Changer

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Authors: Onder Yakut, Oguzhan Timus, Emine Dogru Bolat

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Health diseases have a vital significance affecting human being's life and life quality. Sudden death events can be prevented owing to early diagnosis and treatment methods. Electrical signals, taken from the human being's body using non-invasive methods and showing the heart activity is called Electrocardiogram (ECG). The ECG signal is used for following daily activity of the heart by clinicians. Heart Rate Variability (HRV) is a physiological parameter giving the variation between the heart beats. ECG data taken from MITBIH Arrhythmia Database is used in the model employed in this study. The detection of arrhythmic heart beats is aimed utilizing the features extracted from the HRV time domain parameters. The developed model provides a satisfactory performance with ~89% accuracy, 91.7 % sensitivity and 85% specificity rates for the detection of arrhythmic beats.

Keywords: Arrhythmic beat detection, ECG, HRV, kNN classifier.

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Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

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Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: State of charge estimation, battery modeling, one-state hysteresis, filtering and estimation.

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Authors: Seong-Ho Song, Ki-Seob Kim, Seop-Hyeong Park, Seon-Woo Lee

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In this paper, the data correction algorithm is suggested when the environmental air temperature varies. To correct the infrared data in this paper, the initial temperature or the initial infrared image data is used so that a target source system may not be necessary. The temperature data obtained from infrared detector show nonlinear property depending on the surface temperature. In order to handle this nonlinear property, Taylor series approach is adopted. It is shown that the proposed algorithm can reduce the influence of environmental temperature on the components in the board. The main advantage of this algorithm is to use only the initial temperature of the components on the board rather than using other reference device such as black body sources in order to get reference temperatures.

Keywords: Infrared camera, Temperature Data compensation, Environmental Ambient Temperature, Electric Component

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Authors: M. Salehi, A. A. Motie Birjandi, F. Namdari

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Weak damping of low frequency oscillations is a frequent phenomenon in electrical power systems. These frequencies can be damped by power system stabilizers. Unified power flow controller (UPFC), as one of the most important FACTS devices, can be applied to increase the damping of power system oscillations and the more effect of this controller on increasing the damping of oscillations depends on its proper placement in power systems. In this paper, a technique based on controllability is proposed to select proper location of UPFC and the best input control signal in order to enhance damping of power oscillations. The effectiveness of the proposed technique is demonstrated in IEEE 9 bus power system.

Keywords: Unified power flow controller (UPFC), controllability, small signal analysis, eigenvalues.

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Authors: Görkem Ülkü, Esin A. Güvel, Nesrin Köken, Nilgün Kızılcan

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This study presents synthesis of novel block copolymers of thienyl end capped ethoxylated nonyl phenol and pyrrole via chemical oxidative polymerization. Ethoxylated nonyl phenol (ENP) was reacted with 2-thiophenecarbonyl chloride in order to synthesize a macromonomer containing thienyl end-group (ENPThC). Then copolymers of ENP-ThC and pyrrole were synthesized by chemical oxidative polymerization using iron (III) chloride as an oxidant. ENP-ThC served both as a macromonomer and an emulsifier for pyrrole with poor solubility in water. The synthesized block copolymers (ENP-ThC-b-PPy) were characterized by spectroscopic analysis and the electrical conductivities were investigated with 4-point probe technique.

Keywords: End capped polymer, ethoxylated nonyl phenol, heterophase polymerization, polypyrrole.

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Authors: Sara Mensou, Ahmed Essadki, Issam Minka, Tamou Nasser, Badr Bououlid Idrissi

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In this paper we present a contribution for the modeling and control of wind energy conversion system based on a Doubly Fed Induction Generator (DFIG). Since the wind speed is random the system has to produce an optimal electrical power to the Network and ensures important strength and stability. In this work, the Backstepping controller is used to control the generator via two converter witch placed a DC bus capacitor and connected to the grid by a Filter R-L, in order to optimize capture wind energy. All is simulated and presented under MATLAB/Simulink Software to show performance and robustness of the proposed controller.

Keywords: Wind turbine, doubly fed induction generator, MPPT control, backstepping controller, power converter.

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Authors: S. S. Ngu, L. C. Kho, T. P. Tan, M. S. Osman

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This work deals with the design of the robotic assembly system for the roller clamps. The task is characterized by high speed, high yield and safety engagement. This paper describes the design of different parts of an automated high speed machine to assemble the parts of roller clamps. The roller clamp robotic assembly system performs various processes in the assembly line which include clamp body and roller feeding, inserting the roller into the clamp body, and dividing the rejected clamp and successfully assembled clamp into their own tray. The electrical/electronics design of the machine is discussed. The target is to design a cost effective, minimum maintenance and high speed machine for the industry applications.

Keywords: Machine design, assembly machine, roller clamp, industry applications.

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Authors: J. H. Choi, S. J. Kim, M. S. Jung, S. J. Kim, S. J. Joo, S. C. Kim

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There are a many of needs for the development of SiC-based hydrogen sensor for harsh environment applications. We fabricated and investigated Pd/Ta2O5/SiC-based hydrogen sensors with MOS capacitor structure for high temperature process monitoring and leak detection applications in such automotive, chemical and petroleum industries as well as direct monitoring of combustion processes. In this work, we used silicon carbide (SiC) as a substrate to replace silicon which operating temperatures are limited to below 200°C. Tantalum oxide was investigated as dielectric layer which has high permeability for hydrogen gas and high dielectric permittivity, compared with silicon dioxide or silicon nitride. Then, electrical response properties, such as I-V curve and dependence of capacitance on hydrogen concentrations were analyzed in the temperature ranges of room temperature to 500°C for performance evaluation of the sensor.

Keywords: High temperature, hydrogen sensor, SiC, Ta2O5 dielectric layer.

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Authors: A. Tashakori, M. Ektesabi

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Electric vehicle (EV) is one of the effective solutions to control emission of greenhouses gases in the world. It is of interest for future transportation due to its sustainability and efficiency by automotive manufacturers. Various electrical motors have been used for propulsion system of electric vehicles in last decades. In this paper brushed DC motor, Induction motor (IM), switched reluctance motor (SRM) and brushless DC motor (BLDC) are simulated and compared. BLDC motor is recommended for high performance electric vehicles. PWM switching technique is implemented for speed control of BLDC motor. Behavior of different modes of PWM speed controller of BLDC motor are simulated in MATLAB/SIMULINK. BLDC motor characteristics are compared and discussed for various PWM switching modes under normal and inverter fault conditions. Comparisons and discussions are verified through simulation results.

Keywords: BLDC motor, PWM switching technique, in-wheel technology, electric vehicle.

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Authors: Djalal Eddine Khodja, Aissa Kheldoun

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In this work we present the modelling of the induction machine, taking into consideration the stator defects of the induction machine. It is based on the theory of electromagnetic coupling of electrical circuits. In fact, for the modelling of stationary defects such as short circuit between turns in the same phase, we introduce only in the matrix the coefficients of resistance and inductance of stator and in the mutual inductance stator-rotor. These coefficients take account the number of turns in short-circuit deducted from the total number of turns in the same phase; in this way we obtain the number of useful turns. In addition, all these faults involved, will be used for the creation of the database that will be used to develop an automated system failures of the induction machine.

Keywords: Asynchronous machine, Indicatory Values Statorfaults, Multi-turns Model, Three-phases Model.

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Authors: Wendong Yang, Changhai Wang, Valeria Arrighi

Abstract:

Low ink sintering temperature is desired for flexible electronics, as it would widen the application of the ink on temperature-sensitive substrates where the selection of silver precursor is very critical. In this paper, four types of organic silver precursors, silver carbonate, silver oxalate, silver tartrate and silver itaconate, were synthesized using an ion exchange method, firstly. Various characterization methods were employed to investigate their physical phase, chemical composition, morphologies and thermal decomposition behavior. It was found that silver oxalate had the ideal thermal property and showed the lowest decomposition temperature. An ink was then formulated by complexing the as-prepared silver oxalate with ethylenediamine in organic solvents. Results show that a favorable conductive film with a uniform surface structure consisting of silver nanoparticles and few voids could be produced from the ink at a sintering temperature of 150 °C.

Keywords: Conductive ink, electrical property, film, organic silver.

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Authors: Marco Raciti Castelli, Ernesto Benini

Abstract:

This work presents a comparison between the Annual Energy Output (AEO) of two commercial vertical-axis wind turbines (VAWTs) for a low-wind urban site: both a drag-driven and a liftdriven concepts are examined in order to be installed on top of the new Via dei Giustinelli building, Trieste (Italy). The power-curves, taken from the product specification sheets, have been matched to the wind characteristics of the selected installation site. The influence of rotor swept area and rated power on the performance of the two proposed wind turbines have been examined in detail, achieving a correlation between rotor swept area, electrical generator size and wind distribution, to be used as a guideline for the calculation of the AEO.

Keywords: Annual Energy Output, micro-generationtechnology, urban environment, Vertical-Axis Wind Turbine

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Authors: Sh. Foroughi, V. Karamzadeh, M. Packirisamy

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This paper presents design and analysis of an electrothermally symmetrical actuated microgripper applicable for performing micro assembly or biological cell manipulation. Integration of micro-optics with microdevice leads to achieve extremely precise control over the operation of the device. Geometry, material, actuation, control, accuracy in measurement and temperature distribution are important factors which have to be taken into account for designing the efficient microgripper device. In this work, analyses of four different geometries are performed by means of COMSOL Multiphysics 5.2 with implementing Finite Element Methods. Then, temperature distribution along the fingertip, displacement of gripper site as well as optical efficiency vs. displacement and electrical potential are illustrated. Results show in addition to the industrial application of this device, the usage of that as a cell manipulator is possible.

Keywords: Electro thermal actuator, MEMS, Microgripper, MOEMS.

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Authors: R. Kazemzadeh, J. M. Kauffmann

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This research deals with investigations on the “Active Generator" under rotor speed variations and output frequency control. It runs at turbine speed and it is connected to a three phase electrical power grid which has its own frequency different from turbine frequency. In this regard the set composed of a four phase synchronous generator and a natural commutated matrix converter (NCMC) made with thyristors, is called active generator. It replaces a classical mechanical gearbox which introduces many drawbacks. The main idea in this article is the presentation of frequency control at grid side when turbine runs at variable speed. Frequency control has been done by linear and step variations of the turbine speed. Relation between turbine speed (frequency) and main grid zero sequence voltage frequency is presented.

Keywords: Power Generation, Energy Conversion, FrequencyControl, Matrix Converter.

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Authors: F. Fissou Amigue, S. Ndjakomo Essiane, S. Pérabi Ngoffé, G. Abessolo Ondoa, G. Mengata Mengounou, T. P. Nna Nna

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This document proposes a method for determining the optimal point of integration of distributed generation (DG) in distribution grid. Slime mould optimization is applied to determine best node in case of one and two injection point. Problem has been modeled as an optimization problem where the objective is to minimize joule loses and main constraint is to regulate voltage in each point. The proposed method has been implemented in MATLAB and applied in IEEE network 33 and 69 nodes. Comparing results obtained with other algorithms showed that slime mould optimization algorithms (SMOA) have the best reduction of power losses and good amelioration of voltage profile.

Keywords: Optimization, distributed generation, integration, slime mould algorithm.

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Authors: Kyongsoo Lee, , Seong-Il Kim, Byeong-Kwon Ju

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An aqueous methanol sensor for use in direct methanol fuel cells (DMFCs) applications is demonstrated; the methanol sensor is built using dispersed single-walled carbon nanotubes (SWCNTs) with Nafion117 solution to detect the methanol concentration in water. The study is aimed at the potential use of the carbon nanotubes array as a methanol sensor for direct methanol fuel cells (DMFCs). The concentration of methanol in the fuel circulation loop of a DMFC system is an important operating parameter, because it determines the electrical performance and efficiency of the fuel cell system. The sensor is also operative even at ambient temperatures and responds quickly to changes in the concentration levels of the methanol. Such a sensor can be easily incorporated into the methanol fuel solution flow loop in the DMFC system.

Keywords: methanol concentration, SWCNT, nafion composites

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Authors: Khin Fai Chen, Jee-Hou Ho, Eng Hwa Yap

Abstract:

An Acoustic Micro-Energy Harvester (AMEH) is developed to convert wasted acoustical energy into useful electrical energy. AMEH is mathematically modeled using Lumped Element Modelling (LEM) and Euler-Bernoulli beam (EBB) modelling. An experiment is designed to validate the mathematical model and assess the feasibility of AMEH. Comparison of theoretical and experimental data on critical parameter value such as Mm, Cms, dm and Ceb showed the variances are within 1% to 6%, which is reasonably acceptable. Then, AMEH undergoes bandwidth tuning for performance optimization. The AMEH successfully produces 0.9V/(m/s^2) and 1.79μW/(m^2/s^4) at 60Hz and 400kΩ resistive load which only show variances about 7% compared to theoretical data. At 1g and 60Hz resonance frequency, the averaged power output is about 2.2mW which fulfilled a range of wireless sensors and communication peripherals power requirements. Finally, the design for AMEH is assessed, validated and deemed as a feasible design.

Keywords: Piezoelectric, acoustic, energy harvester, thermoacoustic.

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Authors: S. S. Deswal, Ratna Dahiya, D. K. Jain

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Process control and energy conservation are the two primary reasons for using an adjustable speed drive. However, voltage sags are the most important power quality problems facing many commercial and industrial customers. The development of boost converters has raised much excitement and speculation throughout the electric industry. Now utilities are looking to these devices for performance improvement and reliability in a variety of areas. Examples of these include sags, spikes, or transients in supply voltage as well as unbalanced voltages, poor electrical system grounding, and harmonics. In this paper, simulations results are presented for the verification of the proposed boost converter topology. Boost converter provides ride through capability during sag and swell. Further, input currents are near sinusoidal. This eliminates the need of braking resistor also.

Keywords: Adjustable speed drive, power quality, boost converter, ride through capabilities.

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Authors: Marios Poulos, Eirini Maliagani, Minas Paschopoulos, George Bokos

Abstract:

The purpose of my research proposal is to demonstrate that there is a relationship between EEG and endometrial cancer. The above relationship is based on an Aristotelian Syllogism; since it is known that the 14-3-3 protein is related to the electrical activity of the brain via control of the flow of Na+ and K+ ions and since it is also known that many types of cancer are associated with 14-3-3 protein, it is possible that there is a relationship between EEG and cancer. This research will be carried out by well-defined diagnostic indicators, obtained via the EEG, using signal processing procedures and pattern recognition tools such as neural networks in order to recognize the endometrial cancer type. The current research shall compare the findings from EEG and hysteroscopy performed on women of a wide age range. Moreover, this practice could be expanded to other types of cancer. The implementation of this methodology will be completed with the creation of an ontology. This ontology shall define the concepts existing in this research-s domain and the relationships between them. It will represent the types of relationships between hysteroscopy and EEG findings.

Keywords: Bioinformatics, Protein 14-3-3, EEG, Endometrial cancer, Ontology.

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Authors: S. W. Hong, Y. S. Choi, T. H. Chung, J. H. Song, H. S. Kim

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Bio-electrical responses obtained from freshwater sediments by employing microbial fuel cell (MFC) technology were investigated in this experimental study. During the electricity generation, organic matter in the sediment was microbially oxidized under anaerobic conditions with an electrode serving as a terminal electron acceptor. It was found that the sediment organic matter (SOM) associated with electrochemically-active electrodes became more humified, aromatic, and polydispersed, and had a higher average molecular weight, together with the decrease in the quantity of SOM. The alteration of characteristics of the SOM was analogous to that commonly observed in the early stage of SOM diagenetic process (i.e., humification). These findings including an elevation of the sediment redox potential present a possibility of the MFC technology as a new soil/sediment remediation technique based on its potential benefits: non-destructive electricity generation and bioremediation.

Keywords: Anaerobic oxidation, microbial fuel cell, remediation, sediment.

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Authors: Murat Toren, Mehmet Çelebi

Abstract:

Reducing the weight of transformers while providing good performance, cost reduction and increased efficiency is important. Weight is one of the most significant factors in all electrical machines, and as such, many transformer design parameters are related to weight calculations. This study presents a comparison of the weight of oil type transformers and dry type transformer weight. Oil type transformers are mainly used in industry; however, dry type transformers are becoming more widespread in recent years. MATLAB is typically used for designing transformers and design parameters (rated voltages, core loss, etc.) along with design in ANSYS Maxwell. Similar to other studies, this study presented that the dry type transformer option is limited. Moreover, the commonly-used 50 kVA distribution transformers in the industry are oil type and dry type transformers are designed and considered in terms of weight. Currently, the preference for low-cost oil-type transformers would change if costs for dry-type transformer were more competitive. The aim of this study was to compare the weight of transformers, which is a substantial cost factor, and to provide an evaluation about increasing the use of dry type transformers.

Keywords: Weight, oil-type transformers, dry-type transformers.

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Authors: EL-Sayed M. M. EL-Refaie, Mohamed R. Salem, Wael A. Ahmed

Abstract:

Power systems and transformer are intrinsic apparatus, therefore its reliability and safe operation is important to determine their operation conditions, and the industry uses quality control tests in the insulation design of oil filled transformers. Hence the service period effect on AC dielectric strength is significant. The effect of aging on transformer oil physical, chemical and electrical properties was studied using the international testing methods for the evaluation of transformer oil quality. The study was carried out on six transformers operate in the field and for monitoring periods over twenty years. The properties which are strongly time dependent were specified and those which have a great impact on the transformer oil acidity, breakdown voltage and dissolved gas analysis were defined. Several tests on the transformers oil were studied to know the time of purifying or changing it, moreover prediction of the characteristics of it under different operation conditions.

Keywords: Dissolved Gas Analysis, Prediction, Purifying and Changing.

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Authors: Muhammad Tahir, Muhammad H. Sayyad, Dil N. Khan, Fazal Wahab

Abstract:

Herein, the organic semiconductor methyl orange (MO), is investigated for the first time for its electronic applications. For this purpose, Al/MO/n-Si heterojunction is fabricated through economical cheap and simple “drop casting” technique. The currentvoltage (I-V) measurements of the device are made at room temperature under dark conditions. The I-V characteristics of Al/MO/n-Si junction exhibits asymmetrical and rectifying behavior that confirms the formation of diode. The diode parameters such as rectification ratio (RR), turn on voltage (Vturn on), reverse saturation current (I0), ideality factor (n), barrier height ( b f ), series resistance (Rs) and shunt resistance (Rsh) are determined from I-V curves using Schottky equations. These values of these parameters are also extracted and verified by applying Cheung’s functions. The conduction mechanisms are explained from the forward bias I-V characteristics using the power law.

Keywords: Electrical properties, Organic/inorganic heterojunction diode, Methyl Orange, Cheungs Functions

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