Search results for: Turbine trip without bypass

Authors: Zdeňka Rendlová

Abstract:

This paper presents the mathematical description of the high-speed rotating system taking into account the influence of internal and external damping. The mathematical model is obtained by using the finite element method. The analyzed system is an automotive turbocharger understood as a rotor-bearing system. The circular cross-section shaft is equipped with one compressor wheel, one turbine wheel and is supported by two floating ring bearings. Based on the model, the dynamical analysis of a turbocharger is performed and stability conditions are evaluated.

Keywords: External damping, internal damping, journal bearing, stability, turbocharger.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

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A preliminary evaluation of the feasibility of installing small wind turbines on offshore oil and gas extraction platforms is presented. Some aerodynamic considerations are developed in order to determine the best rotor architecture to exploit the wind potential on such installations, assuming that wind conditions over the platforms are similar to those registered on the roofs of urban buildings. Economical considerations about both advantages and disadvantages of the exploitation of wind energy on offshore extraction platforms with respect to conventional offshore wind plants, is also presented. Finally, wind charts of European offshore winds are presented together with a map of the major offshore installations.

Keywords: Extraction platform, offshore wind energy, verticalaxis wind turbine (VAWT).

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Authors: Rassoli Aisa, Abrishami Movahhed Arezu, Faturaee Nasser, Seddighi Amir Saeed, Shafigh Mohammad

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Cardiovascular diseases are one of the most common causes of mortality in developed countries. Coronary artery abnormalities and carotid artery stenosis, also known as silent death, are among these diseases. One of the treatment methods for these diseases is to create a deviatory pathway to conduct blood into the heart through a bypass surgery. The saphenous vein is usually used in this surgery to create the deviatory pathway. Unfortunately, a re-surgery will be necessary after some years due to ignoring the disagreement of mechanical properties of graft tissue and/or applied prostheses with those of host tissue. The objective of the present study is to clarify the viscoelastic behavior of human saphenous tissue. The stress relaxation tests in circumferential and longitudinal direction were done in this vein by exerting 20% and 50% strains. Considering the stress relaxation curves obtained from stress relaxation tests and the coefficients of the standard solid model, it was demonstrated that the saphenous vein has a non-linear viscoelastic behavior. Thereafter, the fitting with Fung’s quasilinear viscoelastic (QLV) model was performed based on stress relaxation time curves. Finally, the coefficients of Fung’s QLV model, which models the behavior of saphenous tissue very well, were presented.

Keywords: Fung’s quasilinear viscoelastic (QLV) model, strain rate, stress relaxation test, uniaxial tensile test, viscoelastic behavior.

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Authors: M. H. Alhajeri, Jasem Alrajhi, Mohsen Alardhi, Saleh Alhajeri

Abstract:

A numerical prediction of flow in a tube bank is reported. The flow regimes considered cover a wide range of Reynolds numbers, which range from 380 to 99000 and which are equivalent to a range of inlet velocities from very low (0.072 m/s) to very high (60 m/s). In this study, calculations were made using the standard k-e model with standard wall function. The drag coefficient, skin friction drag, pressure drag, and pressure distribution around a tube were investigated. As the velocity increased, the drag coefficient decreased until the velocity exceeded 45 m/s, after which it increased. Furthermore, the pressure drag and skin friction drag depend on the velocity.

Keywords: Numerical, Fluid, Flow, Turbine, Cooling, Blade.

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Authors: Joon-Young Park, Beom-Joo Kim, Jae-Kyung Lee

Abstract:

As an effort to promote wind power industry in Korea, Korea South-East Power Corporation has been developing 22MW YeungHeung wind farm consisting of nine 2 to 3MW wind turbines supplied by three manufacturers. To maximize its availability and reliability and to solve the difficulty of operating three kinds of SCADA systems, Korea Electric Power Corporation has been developing a condition monitoring system integrated with control functions. This paper presents the developed condition monitoring system and its application to YeungHeung wind test bed, and the design of its control functions.

Keywords: condition monitoring, control function, reliability, wind turbine

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Authors: R. Chakib, A. Essadki, M. Cherkaoui

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This paper proposes the study of a robust control of the doubly fed induction generator (DFIG) used in a wind energy production. The proposed control is based on the linear active disturbance rejection control (ADRC) and it is applied to the control currents rotor of the DFIG, the DC bus voltage and active and reactive power exchanged between the DFIG and the network. The system under study and the proposed control are simulated using MATLAB/SIMULINK.

Keywords: Doubly fed induction generator DFIG, Active disturbance rejection control ADRC, Vector control, MPPT, Extended state observer, back to back converter, Wind turbine.

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Authors: Y. Duvarci, S. Mizokami

Abstract:

Traffic enforcement units (the Police) are partly responsible for the severity and frequency of the traffic accidents via the effectiveness of their safety measures. The Police claims that the reductions in accidents and their severities occur largely by their timely interventions at the black spots, through traffic management or temporary changes in the road design (guiding, reducing speeds and eliminating sight obstructions, etc.). Yet, some other external factors than the Police measures may intervene into which such claims require a statistical confirmation. In order to test the net impact of the Police contribution in the reduction of the number of crashes, Chi square test was applied for 25 spots (streets and intersections) and an average evaluation was achieved for general conclusion in the case study of Izmir city. Separately, the net impact of economic crisis in the reduction of crashes is assessed by the trend analysis for the case of the economic crisis with the probable reduction effects on the trip generation or modal choice. Finally, it was proven that the Police measures were effective to some degree as they claimed, though the economic crisis might have only negligible contribution to the reductions in the same period observed.

Keywords: Road Safety, Police, Enforcement units, Chi Squaretest, Economic Impact.

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Authors: Morteza Raki, Abolghasem Zabihollah, Omid Askari

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Cantilever beam is a simplified sample of a lot of mechanical components used in a wide range of applications, including many industries such as gas turbine blade. Due to the nature of the operating conditions, beams are subject to variety of damages especially crack propagates. Crack propagation may lead to catastrophic failure during operation. Therefore, online detection of crack presence and its propagation is very important and may reduce possible significant cost of the whole system failure. This paper aims to investigate the effect of cracks presence and crack propagation on one end fixed beam`s vibration. A finite element model will be developed for the blade in which the modal response of the structure with and without crack will be studied. 

Keywords: Blade, crack propagation, health monitoring, modal analysis.

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Authors: Boukelkoul Lahcen

Abstract:

The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: Cost, finite state, Markov model, operation, maintenance.

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Authors: Pimploi Tirastittam, Phutthiwat Waiyawuththanapoom

Abstract:

Nowadays the promotion of the public transportation system in the Bangkok Metropolitan Area is increased such as the “Free Bus for Thai Citizen” Campaign and the prospect of the several MRT       routes to increase the convenient and comfortable to the Bangkok Metropolitan area citizens. But citizens do not make full use of them it because the citizens are lack of the data and information and also the confident to the public transportation system of Thailand especially in the time and safety aspects. This research is the Public Transport Planning System by Dijkstra Algorithm: Case Study Bangkok Metropolitan Area by focusing on buses, BTS and MRT schedules/routes to give the most information to passengers. They can choose the way and the routes easily by using Dijkstra STAR Algorithm of Graph Theory which also shows the fare of the trip. This Application was evaluated by 30 normal users to find the mean and standard deviation of the developed system. Results of the evaluation showed that system is at a good level of satisfaction (4.20 and 0.40). From these results we can conclude that the system can be used properly and effectively according to the objective.

Keywords: Dijkstra Algorithm, Graph Theory, Shortest Route, Public Transport, Bangkok Metropolitan Area.

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Authors: Amir Bak Khoshnevis, Mahdieh Khodadadi, Aghil Lotfi

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For a bluff body, roughness elements in simulating a turbulent boundary layer, leading to delayed flow separation, a smaller wake, and lower form drag. In the present work, flow past a circular cylinder with using tripping wires is studied experimentally. The wind tunnel used for modeling free stream is open blow circuit (maximum speed = 30m/s and maximum turbulence of free stream = 0.1%). The selected Reynolds number for all tests was constant (Re = 25000). The circular cylinder selected for this experiment is 20 and 400mm in diameter and length, respectively. The aim of this research is to find the optimal operation mode. In this study installed some tripping wires 1mm in diameter, with a different number of wires on the circular cylinder and the wake characteristics of the circular cylinder is studied. Results showed that by increasing number of tripping wires attached to the circular cylinder (6, 8, and 10, respectively), The optimal angle for the tripping wires with 1mm in diameter to be installed on the cylinder is 60̊ (or 6 wires required at angle difference of 60̊). Strouhal number for the cylinder with tripping wires 1mm in diameter at angular position 60̊ showed the maximum value.

Keywords: Wake of a circular cylinder, trip wire, velocity defect, Strouhal number.

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Authors: Nozomu Hashimoto, Hiroyuki Nishida, Yasushi Ozawa, Tetsushiro Iwatsubo, Jun Inumaru

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Palm methyl ester (PME) is one of the alternative biomass fuels to liquid fossil fuels. To investigate the combustion characteristics of PME as an alternative fuel for gas turbines, combustion experiments using two types of burners under atmospheric pressure were performed. One of the burners has a configuration making strong non-premixed flame, whereas the other has a configuration promoting prevaporization of fuel droplets. The results show that the NOx emissions can be reduced by employing the latter burner without accumulation of soot when PME is used as a fuel. A burner configuration promoting prevaporzation of fuel droplets is recommended for PME.

Keywords: Palm methyl ester (PME), biodiesel fuel, gas turbine, spray combustion, NOx emission.

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Authors: Dongheon Shin, Kyungnam Ko, Jongchul Huh

Abstract:

The investigation on wind turbine degradation was carried out using the nacelle wind data. The three Vestas V80-2MW wind turbines of Sungsan wind farm in Jeju Island, South Korea were selected for this work. The SCADA data of the wind farm for five years were analyzed to draw power curve of the turbines. It is assumed that the wind distribution is the Rayleigh distribution to calculate the normalized capacity factor based on the drawn power curve of the three wind turbines for each year. The result showed that the reduction of power output from the three wind turbines occurred every year and the normalized capacity factor decreased to 0.12%/year on average.

Keywords: Wind energy, Power curve, Capacity factor, Annual energy production.

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Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

Abstract:

Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: Boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control.

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Authors: Aurelian Octavian Ciucâ, Ioan Bitir-Istrate, Mircea Scripcariu

Abstract:

The rapidly increasing costs of power line extensions and fossil fuel, combined with the desire to reduce carbon dioxide emissions pushed the development of hybrid power system suited for remote locations, the purpose in mind being that of autonomous local power systems. The paper presents the suggested solution for a “high penetration" hybrid power system, it being determined by the location of the settlement and its “zero policy" on carbon dioxide emissions. The paper focuses on the technical solution and the power flow management algorithm of the system, taking into consideration local conditions of development.

Keywords: Renewable energy, hybrid power system, wind turbine, photovoltaic panels, bio-diesel cogeneration, bio-fuel.

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Authors: Mehmet Savsar

Abstract:

Reliability and availability of power stations are extremely important in order to achieve a required level of power generation. In particular, in the hot desert climate of Kuwait, reliable power generation is extremely important because of cooling requirements at temperatures exceeding 50-centigrade degrees. In this paper, a particular power plant, named Sabiya Power Plant, which has 8 steam turbines and 13 gas turbine stations, has been studied in detail; extensive data are collected; and availability of station units are determined. Furthermore, a simulation model is developed and used to analyze the effects of different maintenance policies on availability of these stations. The results show that significant improvements can be achieved in power plant availabilities if appropriate maintenance policies are implemented.

Keywords: Power plants, steam turbines, gas turbines, maintenance, availability, simulation.

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Authors: Sourabh Jain, Sukhvir Singh Jain, Gaurav V. Jain

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Intelligent Transportation System is an integrated application of communication, control and monitoring and display process technologies for developing a user–friendly transportation system for urban areas in developing countries. In fact, the development of a country and the progress of its transportation system are complementary to each other. Urban traffic has been growing vigorously due to population growth as well as escalation of vehicle ownership causing congestion, delays, pollution, accidents, high-energy consumption and low productivity of resources. The development and management of urban transport in developing countries like India however, is at tryout stage with very few accumulations. Under the umbrella of ITS, urban corridor management strategy have proven to be one of the most successful system in accomplishing these objectives. The present study interprets and figures out the performance of the 27.4 km long Urban Bus route having six intersections, five flyovers and 29 bus stops that covers significant area of the city by causality analysis. Performance interpretations incorporate Passenger Boarding and Alighting, Dwell time, Distance between Bus Stops and Total trip time taken by bus on selected urban route.

Keywords: Congestion, Dwell time, delay, passengers boarding alighting, travel time.

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Authors: Stefano Degrassi, Marco Raciti Castelli, Ernesto Benini

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Since the European renewable energy directives set the target for 22.1% of electricity generation to be supplied by 2010 [1], there has been increased interest in using green technologies also within the urban enviroment. The most commonly considered installations are solar thermal and solar photovoltaics. Nevertheless, as observed by Bahaj et al. [2], small scale turbines can reduce the built enviroment related CO2 emissions. Thus, in the last few years, an increasing number of manufacturers have developed small wind turbines specifically designed for the built enviroment. The present work focuses on the integration into architectural systems of such installations and presents a survey of successful case studies.

Keywords: Wind turbines, architectural integration, wind resources, urban areas, built enviroment, renewable technologies.

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Authors: Zaw Tun, Aung Htein Maw

Abstract:

The nature of wireless ad hoc and sensor networks make them very attractive to attackers. One of the most popular and serious attacks in wireless ad hoc networks is wormhole attack and most proposed protocols to defend against this attack used positioning devices, synchronized clocks, or directional antennas. This paper analyzes the nature of wormhole attack and existing methods of defending mechanism and then proposes round trip time (RTT) and neighbor numbers based wormhole detection mechanism. The consideration of proposed mechanism is the RTT between two successive nodes and those nodes- neighbor number which is needed to compare those values of other successive nodes. The identification of wormhole attacks is based on the two faces. The first consideration is that the transmission time between two wormhole attack affected nodes is considerable higher than that between two normal neighbor nodes. The second detection mechanism is based on the fact that by introducing new links into the network, the adversary increases the number of neighbors of the nodes within its radius. This system does not require any specific hardware, has good performance and little overhead and also does not consume extra energy. The proposed system is designed in ad hoc on-demand distance vector (AODV) routing protocol and analysis and simulations of the proposed system are performed in network simulator (ns-2).

Keywords: AODV, Wormhole attacks, Wireless ad hoc andsensor networks

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Authors: Rumena D. Stancheva, Ilona I. Iatcheva

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In working mode some unexpected changes could be arise in inner structure of electromagnetic device. They influence modification in electromagnetic field propagation map. The field values at an observed boundary are also changed. The development of the process has to be watched because the arising structural changes would provoke the device to be gone out later. The probabilistic assessment of the state is possible to be made. The numerical assessment points if the resulting changes have only accidental character or they are due to the essential inner structural disturbances. The presented application example is referring to the 200MW turbine-generator. A part of the stator core end teeth zone is simulated broken. Quasi three-dimensional electromagnetic and temperature field are solved applying FEM. The stator core state diagnosis is proposed to be solved as an identification problem on the basis of a statistical criterion.

Keywords: Identification, structural disturbance, statistical criterion.

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Authors: S. B. Alavi, G. Cerri, L. Chennaoui, A. Giovannelli, S. Mazzoni

Abstract:

Power Regeneration in Refrigeration Plant concept has been analyzed and has been shown to be capable of saving about 25% power in Cryogenic Plants with the Power Regeneration System (PRS) running under nominal conditions. The innovative component Compressor Expander Group (CEG) based on turbomachinery has been designed and built modifying CETT compressor and expander, both selected for optimum plant performance. Experiments have shown the good response of the turbomachines to run with R404a as working fluid. Power saving up to 12% under PRS derated conditions (50% loading) has been demonstrated. Such experiments allowed predicting a power saving up to 25% under CEG full load.

Keywords: Compressor, Expander, Power Saving, Refrigeration Plant, Turbine, Turbomachinery Selection, Vapor Pressure Booster.

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Authors: Kevin Wongleedee

Abstract:

Culinary culture differences can cause health problems for international tourists in Thailand. This paper drew upon data collected from an international tourist survey conducted in Bangkok, Thailand during summer of 2012. Summer is the period that a variety food safety issues and incidents are often publicized in Thailand. The survey targeted European Union tourists- concerns toward a variety of food safety issues that they encountered during their trip in Thailand. A total of 400 respondents were elicited as data input for t-test, and one way ANOVA test. The findings revealed an astonishing result that up to 46.5 percent of respondents were sick at least one time or more in Thailand. However, the majority of respondents trusted that the Thai hotel and Thai restaurants would ensure food safety, but they did not trust street vendors to ensure food safety. The level of food safety concern can be ranked from most concern to least concern by using the value of mean scores as follows: 1) artificial coloring, 2) use of preservatives, 3) antibiotics, 4) growth hormones, 5) chemical residues, and 6) bacterial contamination. The overall mean score for level of concerns was 3.493 with standard deviation of 1.677 which did not indicate a very high level of concern. In addition, the result for t-test and one way ANOVA test revealed that there was not much effect from the demographic differences to level of food safety concerns.

Keywords: Concerns, European Union Tourists, Food Safety Management.

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Authors: M. Sedighizadeh, A. Rezazadeh

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In this paper a PID control strategy using neural network adaptive RASP1 wavelet for WECS-s control is proposed. It is based on single layer feedforward neural networks with hidden nodes of adaptive RASP1 wavelet functions controller and an infinite impulse response (IIR) recurrent structure. The IIR is combined by cascading to the network to provide double local structure resulting in improving speed of learning. This particular neuro PID controller assumes a certain model structure to approximately identify the system dynamics of the unknown plant (WECS-s) and generate the control signal. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution.

Keywords: Adaptive PID Control, RASP1 Wavelets, WindEnergy Conversion Systems.

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Authors: M. Raciti Castelli, S. Mogno, S. Giacometti, E. Benini

Abstract:

A boundary layer wind tunnel facility has been adopted in order to conduct experimental measurements of the flow field around a model of the Panorama Giustinelli Building, Trieste (Italy). Information on the main flow structures has been obtained by means of flow visualization techniques and has been compared to the numerical predictions of the vortical structures spread on top of the roof, in order to investigate the optimal positioning for a vertical-axis wind energy conversion system, registering a good agreement between experimental measurements and numerical predictions.

Keywords: Boundary layer wind tunnel, flow around buildings, atmospheric flow field, vertical-axis wind turbine (VAWT).

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Authors: Meng-Lung Lin, Chien-Min Chu, Chung-Hung Tsai, Chih-Cheng Chen, Chen-Yuan Chen

Abstract:

The study of tourist activities and the mapping of their routes in space and time has become an important issue in tourism management. Here we represent space-time paths for the tourism industry by visualizing individual tourist activities and the paths followed using a 3D Geographic Information System (GIS). Considerable attention has been devoted to the measurement of accessibility to shopping, eating, walking and other services at the tourist destination. I turns out that GIS is a useful tool for studying the spatial behaviors of tourists in the area. The value of GIS is especially advantageous for space-time potential path area measures, especially for the accurate visualization of possible paths through existing city road networks. This study seeks to apply space-time concepts with a detailed street network map obtained from Google Maps to measure tourist paths both spatially and temporally. These paths are further determined based on data obtained from map questionnaires regarding the trip activities of 40 individuals. The analysis of the data makes it possible to determining the locations of the more popular paths. The results can be visualized using 3D GIS to show the areas and potential activity opportunities accessible to tourists during their travel time.

Keywords: Tourist activity analysis, space-time path, GIS, geovisualization, activity-travel pattern.

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Authors: Hussain H. Al-Kayiem, Goh Jin Ming

Abstract:

The common practice of operating S-rotor is in an open environment; however there are times when the rotor is installed in a bounded environment and there might be changes in the performance of the rotor. This paper presents the changes in the performance of S-rotor when operated in bounded flows. The investigation was conducted experimentally to compare the performance of the rotors in bounded environment against open environment. Three different rotors models were designed, fabricated and subjected to experimental measurements. All of the three models were having 600 mm height and 300 mm Diameter. They were tested in three different flow environments; namely: partially bounded environment, fully bounded environment and open environment. Rotors were found to have better starting up capabilities when operated in bounded environment. Apart from that, all rotors manage to achieve higher Power and Torque Coefficients at a higher Tip Speed Ratio as compared to the open environment.

Keywords: Bounded Flows, Savonius Rotor, Wind Turbine, Wind energy, VAWT

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Authors: A. Boualouch, A. Essadki, T. Nasser, A. Boukhriss, A. Frigui

Abstract:

This paper presents a power control for a Doubly Fed Induction Generator (DFIG) using in Wind Energy Conversion System (WECS) connected to the grid. The proposed control strategy employs two nonlinear controllers, Backstipping (BSC) and slidingmode controller (SMC) scheme to directly calculate the required rotor control voltage so as to eliminate the instantaneous errors of active and reactive powers. In this paper the advantages of BSC and SMC are presented, the performance and robustness of this two controller’s strategy are compared between them. First, we present a model of wind turbine and DFIG machine, then a synthesis of the controllers and their application in the DFIG power control. Simulation results on a 1.5MW grid-connected DFIG system are provided by MATLAB/Simulink.

Keywords: Backstipping, DFIG, power control, sliding-mode, WESC.

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

Abstract:

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: N. M. Thao, I. Dolguntseva, M. Leijon

Abstract:

Flow blockages referring to the increase in flow are being considered as a vital equipment for marine current energy conversion. However, the shape of these devices will result in extracted energy under the operation. The present work investigates the effect of two configurations of a grating, convergent and divergent that located upstream, to the water flow velocity. The flow characteristics are studied by Computational Fluid Dynamic simulation by using the ANSYS Fluent solver for these specified arrangements of the grating. The results indicate that distinguished characteristics of flow velocity between “convergent” and “divergent” grating placements is up to 10% in confined conditions. Furthermore, the velocity in case of convergent grating is higher than that of divergent grating.

Keywords: Marine current energy, marine current energy converter, turbine grating, RANS simulation, water flow velocity.

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Authors: Hamed Jamshidi, Pooya Djamshidi

Abstract:

In this paper the complete rotor system including elastic shaft with distributed mass, allowing for the effects of oil film in bearings. Also, flexibility of foundation is modeled. As a whole this article is a relatively complete research in modeling and vibration analysis of rotor considering gyroscopic effect, damping, dependency of stiffness and damping coefficients on frequency and solving the vibration equations including these parameters. On the basis of finite element method and utilizing four element types including element of shaft, disk, bearing and foundation and using MATLAB, a computer program is written. So the responses in several cases and considering different effects are obtained. Then the results are compared with each other, with exact solutions and results of other papers.

Keywords: Damping coefficients , Finite element method, Modeling , Rotor vibration

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