Search results for: wind power uncertainty.

Authors: WooYoung Jung, Buntheng Chhorn, Min-Gi Kim

Abstract:

Recently, damage to domestic facilities by strong winds and typhoons are growing. Therefore, this study focused on sign structure among various vulnerable facilities. The evaluation of the wind fragility was carried out considering the destruction of the anchor, which is one of the various failure modes of the sign structure. The performance evaluation of the anchor was carried out to derive the wind fragility. Two parameters were set and four anchor types were selected to perform the pull-out and shear tests. The resistance capacity was estimated based on the experimental results. Wind loads were estimated using Monte Carlo simulation method. Based on these results, we derived the wind fragility according to anchor type and wind exposure category. Finally, the evaluation of the wind fragility was performed according to the experimental parameters such as anchor length and anchor diameter. This study shows that the depth of anchor was more significant for the safety of structure compare to diameter of anchor.

Keywords: Sign structure, wind fragility, set anchor, pull-out test, shear test, Monte Carlo simulation.

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Authors: Hicham Gourgue, Ahmed Aharoune, Ahmed Ihlal

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We present in this work our model of road traffic emissions (line sources) and dispersion of these emissions, named DISPOLSPEM (Dispersion of Poly Sources and Pollutants Emission Model). In its emission part, this model was designed to keep the consistent bottom-up and top-down approaches. It also allows to generate emission inventories from reduced input parameters being adapted to existing conditions in Morocco and in the other developing countries. While several simplifications are made, all the performance of the model results are kept. A further important advantage of the model is that it allows the uncertainty calculation and emission rate uncertainty according to each of the input parameters. In the dispersion part of the model, an improved line source model has been developed, implemented and tested against a reference solution. It provides improvement in accuracy over previous formulas of line source Gaussian plume model, without being too demanding in terms of computational resources. In the case study presented here, the biggest errors were associated with the ends of line source sections; these errors will be canceled by adjacent sections of line sources during the simulation of a road network. In cases where the wind is parallel to the source line, the use of the combination discretized source and analytical line source formulas minimizes remarkably the error. Because this combination is applied only for a small number of wind directions, it should not excessively increase the calculation time.

Keywords: Air pollution, dispersion, emissions, line sources, road traffic, urban transport.

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Authors: C. Shih, J. R. Wang, H. C. Chang, S. W. Chen, S. C. Chiang, T. Y. Yu

Abstract:

After the measurement uncertainty recapture (MUR) power uprates, Kuosheng nuclear power plant (NPP) was uprated the power from 2894 MWt to 2943 MWt. For power upgrade, several codes (e.g., TRACE, RELAP5, etc.) were applied to assess the safety of Kuosheng NPP. Hence, the main work of this research is to establish a RELAP5/MOD3.3 model of Kuosheng NPP with SNAP interface. The establishment of RELAP5/SNAP model was referred to the FSAR, training documents, and TRACE model which has been developed and verified before. After completing the model establishment, the startup test scenarios would be applied to the RELAP5/SNAP model. With comparing the startup test data and TRACE analysis results, the applicability of RELAP5/SNAP model would be assessed.

Keywords: RELAP5, TRACE, SNAP, BWR.

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Authors: Tomislav Stambolic, Anton Causevski

Abstract:

The deficit of power for electricity demand reaches almost 30% for consumers in the last few years. This reflects with continually increasing the price of electricity, and today the price for small industry is almost 110Euro/MWh. The high price is additional problem for the owners in the economy crisis which is reflected with higher price of the goods. The paper gives analyses of the energy needs for real agro complex in Macedonia, private vinery with capacity of over 2 million liters in a year and with self grapes and fruits fields. The existing power supply is from grid with 10/04 kV transformer. The geographical and meteorological condition of the vinery location gives opportunity for including renewable as a power supply option for the vinery complex. After observation of the monthly energy needs for the vinery, the base scenario is the existing power supply from the distribution grid. The electricity bill in small industry has three factors: electricity in high and low tariffs in kWh and the power engaged for the technological process of production in kW. These three factors make the total electricity bill and it is over 110 Euro/MWh which is the price near competitive for renewable option. On the other side investments in renewable (especially photovoltaic (PV)) has tendency of decreasing with price of near 1,5 Euro/W. This means that renewable with PV can be real option for power supply for small industry capacities (under 500kW installed power). Therefore, the other scenarios give the option with PV and the last one includes wind option. The paper presents some scenarios for power supply of the vinery as the followings: • Base scenario of existing conventional power supply from the grid • Scenario with implementation of renewable of Photovoltaic • Scenario with implementation of renewable of Photovoltaic and Wind power The total power installed in a vinery is near 570 kW, but the maximum needs are around 250kW. At the end of the full paper some of the results from scenarios will be presented. The paper also includes the environmental impacts of the renewable scenarios, as well as financial needs for investments and revenues from renewable.

Keywords: Energy, Power Supply, Renewable, Efficiency.

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Authors: C. Ardil

Abstract:

Uncertainty set theory is a generalization of fuzzy set theory and intuitionistic fuzzy set theory. It serves as an effective tool for dealing with inconsistent, imprecise, and vague information. The technique for order preference by similarity to ideal solution (TOPSIS) method is a multiple-attribute method used to identify solutions from a finite set of alternatives. It simultaneously minimizes the distance from an ideal point and maximizes the distance from a nadir point. In this paper, an extension of the TOPSIS method for multiple attribute group decision-making (MAGDM) based on uncertainty sets is presented. In uncertainty decision analysis, decision-makers express information about attribute values and weights using uncertainty numbers to select the best stealth combat aircraft.

Keywords: Uncertainty set, stealth combat aircraft selection multiple criteria decision-making analysis, MCDM, uncertainty decision analysis, TOPSIS

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Authors: Om Parkash, C.P.Gandhi

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Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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Authors: Tsuyoshi Yamazaki, Etsuo Morishita

Abstract:

Cyclists often run through a crosswind and sometimes we experience the adverse pressure. We came to an idea that Wells turbine can be used as power augmentation device in the crosswind something like sails of a yacht. Wells turbine always rotates in the same direction irrespective of the incoming flow direction, and we use it in the small-scale power generation in the ocean where waves create an oscillating flow. We incorporate the turbine to the wheel of a bike. A commercial device integrates strain gauges in the crank of a bike and transmitted force and torque applied to the pedal of the bike as an e-mail to the driver’s mobile phone. We can analyze the unsteady data in a spreadsheet sent from the crank sensor. We run the bike with the crank sensor on the rollers at the exit of a low-speed wind tunnel and analyze the effect of the crosswind to the wheel with a Wells turbine. We also test the aerodynamic characteristics of the turbine separately. Although power gain depends on the flow direction, several Watts increase might be possible by the Wells turbine incorporated to a bike wheel.

Keywords: Aerodynamics, wells turbine, bicycle, wind engineering.

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Authors: A. Aissani, H. Benaoudia

Abstract:

Stochastic comparison has been an important direction of research in various area. This can be done by the use of the notion of stochastic ordering which gives qualitatitive rather than purely quantitative estimation of the system under study. In this paper we present applications of comparison based uncertainty related to entropy in Reliability analysis, for example to design better systems. These results can be used as a priori information in simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

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Authors: F. Rasi Marzabadi

Abstract:

A series of experiments were carried out to study unsteady behavior of the flow field as well as the boundary layer of an airfoil oscillating in plunging motion in a subsonic wind tunnel. The measurements involved surface pressure distribution complimented with surface-mounted hot-films. The effect of leadingedge roughness that simulates surface irregularities on the wind turbine blades was also studied on variations of aerodynamic loads and boundary layer behavior.

Keywords: Boundary layer transition, plunging, reduced frequency, wind turbine.

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Authors: Rade M. Ciric, Nikola L. J. Rajakovic

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This paper presents a curriculum of the subject small power plants and renewable energy sources, dealing with the concept of distributed generation, renewable energy sources, hydropower, wind farms, geothermal power plants, cogeneration plants, biogas plants of agriculture and animal origin, solar power and fuel cells. The course is taught the manner of connecting small power plants to the grid, the impact of small generators on the distribution system, as well as economic, environmental and legal aspects of operation of distributed generators.

Keywords: Distributed generation, renewable energy sources, techno-economic analysis, energy policy, curriculum.

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Authors: M. Mahboubkhah, H. Fayazfar

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In this research, Forming Limit Diagrams for supertension sheet metals which are using in automobile industry have been obtained. The exerted strains to sheet metals have been measured with four different methods and the errors of each method have also been represented. These methods have been compared with together and the most efficient and economic way of extracting of the exerted strains to sheet metals has been introduced. In this paper total error and uncertainty of FLD extraction procedures have been derived. Determination of the measurement uncertainty in extracting of FLD has a great importance in design and analysis of the sheet metal forming process.

Keywords: Forming Limit Diagram, Major and Minor Strain, Measurement Uncertainty.

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Authors: Atul K. Desai, Jigar K. Sevalia, Sandip A. Vasanwala

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When a building is located in an urban area, it is exposed to a wind of different characteristics then wind over an open terrain. This is development of turbulent wake region behind an upstream building. The interaction with upstream building can produce significant changes in the response of the tall building. Here, in this paper, an attempt has been made to study wind induced interference effects on tall building. In order to study wind induced interference effect (IF) on Tall Building, initially a tall building (which is termed as Principal Building now on wards) with square plan shape has been considered with different Height to Width Ratio and total drag force is obtained considering different terrain conditions as well as different incident wind direction. Then total drag force on Principal Building is obtained by considering adjacent building which is termed as Interfering Building now on wards with different terrain conditions and incident wind angle. To execute study, Computational Fluid Dynamics (CFD) Code namely Fluent and Gambit have been used.

Keywords: Computational Fluid Dynamics, Tall Building, Turbulent, Wake Region, Wind.

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Authors: Elena M. Capitanul, Carlos A. Nunes Cosenza, Walid El Moudani, Felix Mora Camino

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The construction of a new airport or the extension of an existing one requires massive investments and many times public private partnerships were considered in order to make feasible such projects. One characteristic of these projects is uncertainty with respect to financial and environmental impacts on the medium to long term. Another one is the multistage nature of these types of projects. While many airport development projects have been a success, some others have turned into a nightmare for their promoters. This communication puts forward a new approach for airport investment risk assessment. The approach takes explicitly into account the degree of uncertainty in activity levels prediction and proposes milestones for the different stages of the project for minimizing risk. Uncertainty is represented through fuzzy dual theory and risk management is performed using dynamic programming. An illustration of the proposed approach is provided.

Keywords: Airports, fuzzy logic, risk, uncertainty.

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Authors: F. Ahwide, Y. Bouker, K. Hatem

Abstract:

This paper presents long term wind data analysis in terms of annual and diurnal variations at different areas of Libya. The data of the wind speed and direction are taken each ten minutes for a period, at least two years, are used in the analysis. ‘WindPRO’ software and Excel workbook were used for the wind statistics and energy calculations. As for Darnah, average speeds are 10m, 20m and 40m and 6.57 m/s, 7.18 m/s, and 8.09 m/s, respectively. Highest wind speeds are observed at SSW, followed by S, WNW and NW sectors. Lowest wind speeds are observed between N and E sectors. Most frequent wind directions are NW and NNW. Hence, wind turbines can be installed against these directions. The most powerful sector is NW (31.3% of total expected wind energy), followed by 17.9% SSW, 11.5% NNW and 8.2% WNW

In Excel workbook, an estimation of annual energy yield at position of Derna, Al-Maqrun, Tarhuna and Al-Asaaba meteorological mast has been done, considering a generic wind turbine of 1.65 MW. (mtORRES, TWT 82-1.65MW) in position of meteorological mast. Three other turbines have been tested and a reduction of 18% over the net AEP. At 80m, the estimation of energy yield for Derna, Al- Maqrun, Tarhuna and Asaaba is 6.78 GWh or 3390 equivalent hours, 5.80 GWh or 2900 equivalent hours, 4.91 GWh or 2454 equivalent hours and 5.08 GWh or 2541 equivalent hours respectively. It seems a fair value in the context of a possible development of a wind energy project in the areas, considering a value of 2400 equivalent hours as an approximate limit to consider a wind warm economically profitable. Furthermore, an estimation of annual energy yield at positions of Misalatha, Azizyah and Goterria meteorological mast has been done, considering a generic wind turbine of 2 MW. We found that, at 80 m the estimation of energy yield is 3.12 GWh or 1557 equivalent hours, 4.47 GWh or 2235 equivalent hours and 4.07GWh or 2033 respectively.

It seems a very poor value in the context of possible development of a wind energy project in the areas, considering a value of 2400 equivalent hours as an approximate limit to consider a wind warm economically profitable. Anyway, more data and a detailed wind farm study would be necessary to draw conclusions.

Keywords: Wind turbines, wind data, energy yield, micrositting.

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Authors: Imane El Karaoui, Mohammed Maaroufi, Hamid Chaikhy

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Doubly Fed Induction Generator (DFIG) is one of the most reliable wind generator. Major problem in wind power generation is to generate Sinusoidal signal with very low THD on variable speed caused by inverter two levels used. This paper presents a multi-level inverter whose objective is to reduce the THD and the dimensions of the output filter. This work proposes a three-level NPC-type inverter, the results simulation are presented demonstrating the efficiency of the proposed inverter.

Keywords: DFIG, multilevel inverter, NPC inverter , THD, Induction machine.

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Authors: Gábor Szűcs, Gyula Sallai

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The goal of this paper is to find Wardrop equilibrium in transport networks at case of uncertainty situations, where the uncertainty comes from lack of information. We use simulation tool to find the equilibrium, which gives only approximate solution, but this is sufficient for large networks as well. In order to take the uncertainty into account we have developed an interval-based procedure for finding the paths with minimal cost using the Dempster-Shafer theory. Furthermore we have investigated the users- behaviors using game theory approach, because their path choices influence the costs of the other users- paths.

Keywords: Dempster-Shafer theory, S-O and U-Otransportation network, uncertainty of information, Wardropequilibrium.

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Authors: Jennifer Penton, Charitha Pattiaratchi

Abstract:

Surface currents play a major role in the distribution of contaminants, the connectivity of marine populations, and can influence the vertical and horizontal distribution of nutrients within the water column. This paper aims to determine the effects of sea breeze-wind patterns on the climatology of the surface currents on the continental shelf surrounding Rottnest Island, WA Australia. The alternating wind patterns allow for full cyclic rotations of wind direction, permitting the interpretation of the effect of the wind on the surface currents. It was found that the surface currents only clearly follow the northbound Capes Current in times when the Fremantle Doctor sets in. Surface currents react within an hour to a change of direction of the wind, allowing southerly currents to dominate during strong northerly sea breezes, often followed by mixed currents dominated by eddies in the inter-lying times.

Keywords: HF radar, surface currents, sea breeze.

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Authors: George Yungchih Wang

Abstract:

This paper argues that increased uncertainty, in certain situations, may actually encourage investment. Since earlier studies mostly base their arguments on the assumption of geometric Brownian motion, the study extends the assumption to alternative stochastic processes, such as mixed diffusion-jump, mean-reverting process, and jump amplitude process. A general approach of Monte Carlo simulation is developed to derive optimal investment trigger for the situation that the closed-form solution could not be readily obtained under the assumption of alternative process. The main finding is that the overall effect of uncertainty on investment is interpreted by the probability of investing, and the relationship appears to be an invested U-shaped curve between uncertainty and investment. The implication is that uncertainty does not always discourage investment even under several sources of uncertainty. Furthermore, high-risk projects are not always dominated by low-risk projects because the high-risk projects may have a positive realization effect on encouraging investment.

Keywords: real options, geometric Brownian motion, mixeddiffusion-jump process, mean- reverting process, jump amplitudeprocess

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Authors: Zhen Wu, David Lupien St-Pierre, Georges Abdul-Nour

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In decision making under strict uncertainty, decision makers have to choose a decision without any information about the states of nature. The classic criteria of Laplace, Wald, Savage, Hurwicz and Starr are introduced and compared in a case study of sewer network planning. Furthermore, results from different criteria are discussed and analyzed. Moreover, this paper discusses the idea that decision making under strict uncertainty (DMUSU) can be viewed as a two-player game and thus be solved by a solution concept in game theory: Nash equilibrium.

Keywords: Decision criteria, decision making, sewer network planning, strict uncertainty.

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Authors: Prateek Kishore, T. M. Muruganandam

Abstract:

Supersonic wind tunnel nozzles are generally capable of producing a constant Mach number flow in the test section of the wind tunnel. As a result, most of the supersonic vehicles are widely designed using steady state flow characteristics which may have errors while facing unsteady situations. This study aims to explore the possibility of varying the Mach number of the flow during wind tunnel operation. The nozzle walls are restricted to be inflexible for cooling near the throat due to high stagnation temperature requirement of the flow to simulate the conditions as experienced by the vehicle. Two simple independent mechanisms, rotation and translation of nozzle walls have been analyzed and the nozzle ranges have been optimized to vary the Mach number from Mach 2 to Mach 5 using minimum number of nozzles in the wind tunnel.

Keywords: Method of characteristics, Nozzle, supersonic wind tunnel, variable Mach number.

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Authors: B.J.C. Horsten, L.L.M. Veldhuis

Abstract:

Renewed interest in propeller propulsion on aircraft configurations combined with higher propeller loads lead to the question how the effects of the propulsion on model support disturbances should be accounted for. In this paper, the determination of engine power effects on support interference of sting-mounted models is demonstrated by a measurement on a four-engine turboprop aircraft. CFD results on a more generic model are presented in order to clarify the possible mechanism behind engine power effects on support interference. The engine slipstream induces a local change in angle of sideslip at the model sting thereby influencing the sting near-field and far-field effects. Whether or not the net result of these changes in the disturbance pattern leads to a significant engine power effect depends on the configuration of the wind tunnel model and the test setup.

Keywords: CFD, engine power effects, measurements, support interference.

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Authors: Ying Shang, Chencheng Wang

Abstract:

The wind field is the main driving factor for the spread of forest fires. For the simulation results of forest fire spread to be more accurate, it is necessary to obtain more detailed wind field data. Therefore, this paper studied the mountainous fine wind field simulation method coupled with WRF (Weather Research and Forecasting Model) and CFD (Computational Fluid Dynamics) to realize the numerical simulation of the wind field in a mountainous area with a scale of 30 m and a small measurement error. Local topographical changes have an important impact on the wind field. Based on the Rothermel fire spread model, a forest fire in Idaho in the western United States was simulated. The historical data proved that the simulation results had a good accuracy. They showed that the fire spread rate will decrease rapidly with time and then reach a steady state. After reaching a steady state, the fire spread growth area will not only be affected by the slope, but will also show a significant quadratic linear positive correlation with the wind speed change.

Keywords: Wind field, numerical simulation, forest fire spread, fire behavior model, complex terrain.

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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Authors: Jerome T. Tolentino, Ma. Victoria Rejuso, Jara Kaye Villanueva, Loureal Camille Inocencio, Ma. Rosario Concepcion O. Ang

Abstract:

Wind energy is rapidly emerging as the primary source of electricity in the Philippines, although developing an accurate wind resource model is difficult. In this study, Weather Research and Forecasting (WRF) Model, an open source mesoscale Numerical Weather Prediction (NWP) model, was used to produce a 1-year atmospheric simulation with 4 km resolution on the Ilocos Region of the Philippines. The WRF output (netCDF) extracts the annual mean wind speed data using a Python-based Graphical User Interface. Lastly, wind resource assessment was produced using a GIS software. Results of the study showed that it is more flexible to use Python scripts than using other post-processing tools in dealing with netCDF files. Using WRF Model, Python, and Geographic Information Systems, a reliable wind resource map is produced.

Keywords: Wind resource assessment, Weather Research and Forecasting (WRF) Model, python, GIS software.

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Authors: H. Sediki, Dj. Ould Abdeslam, T. Otmane-cherif, A. Bechouche, K. Mesbah

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This paper explores steady-state characteristics of grid-connected doubly fed induction motor (DFIM) in case of unity power factor operation. Based on the synchronized mathematical model, analytic determination of the control laws is presented and illustrated by various figures to understand the effect of the applied rotor voltage on the speed and the active power. On other hand, unlike previous works where the stator resistance was neglected, in this work, stator resistance is included such that the equations can be applied to small wind turbine generators which are becoming more popular. Finally the work is crowned by integration of the studied induction generator in a wind system where an open loop control is proposed confers a remarkable simplicity of implementation compared to the known methods.

Keywords: DFIM, equivalent circuit, induction machine, steady state

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Authors: S. Dehghan, B. Kiani, A. Kazemi, A. Parizad

Abstract:

The utilization of renewable energy sources in electric power systems is increasing quickly because of public apprehensions for unpleasant environmental impacts and increase in the energy costs involved with the use of conventional energy sources. Despite the application of these energy sources can considerably diminish the system fuel costs, they can also have significant influence on the system reliability. Therefore an appropriate combination of the system reliability indices level and capital investment costs of system is vital. This paper presents a hybrid wind/photovoltaic plant, with the aim of supplying IEEE reliability test system load pattern while the plant capital investment costs is minimized by applying a hybrid particle swarm optimization (PSO) / harmony search (HS) approach, and the system fulfills the appropriate level of reliability.

Keywords: Distributed Generation, Fuel Cell, HS, Hybrid Power Plant, PSO, Photovoltaic, Reliability.

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Authors: Three-Dimensional Modeling of a Twisted-Blade Darrieus Vertical-Axis Wind Turbine

Abstract:

A complete CAD procedure to model a twisted-bladed vertical-axis wind turbine (VAWT) is presented with the aim of determining some practical guidelines to be used for the generation of an easily-meshable CAD geometry to be adopted as the basis of both CFD and FEM numerical simulations.

Keywords: Vertical-axis wind turbine (VAWT), twisted blade, CAD, 3D modeling.

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Authors: M. Safaei, M. Seifert, K. D. Thoben

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Supply network management adopts a systematic and integrative approach to managing the operations and relationships of various parties in a supply network. The objective of the manufactures in their supply network is to reduce inventory costs and increase customer satisfaction levels. One way of doing that is to synchronize delivery performance. A supply network can be described by nodes representing the companies and the links (relationships) between these nodes. Uncertainty in delivery time depends on type of network relationship between suppliers. The problem is to understand how the individual uncertainties influence the total uncertainty of the network and identify those parts of the network, which has the highest potential for improving the total delivery time uncertainty.

Keywords: Delivery time uncertainty, Distribution function, Statistical method, Supply Network.

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Authors: T. Brahimi, F. Saeed, I. Paraschivoiu

Abstract:

This paper details the progress made in the development of the different state-of-the-art aerodynamic tools for the analysis of vertical axis wind turbines including the flow simulation around the blade, viscous flow, stochastic wind, and dynamic stall effects. The paper highlights the capabilities of the developed wind turbine aerodynamic codes over the last thirty years which are currently being used in North America and Europe by Sandia Laboratories, FloWind, IMST Marseilles, and Hydro-Quebec among others. The aerodynamic codes developed at Ecole Polytechnique de Montreal, Canada, represent valuable tools for simulating the flow around wind turbines including secondary effects. Comparison of theoretical results with experimental data have shown good agreement. The strength of the aerodynamic codes based on Double-Multiple Stream tube model (DMS) lies in its simplicity, accuracy, and ability to analyze secondary effects that interfere with wind turbine aerodynamic calculations.

Keywords: Aerodynamics, wind turbines, VAWT, CARDAAV, Darrieus, dynamic stall.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Due to the increasing penetration of wind energy, it is necessary to possess design tools that are able to simulate the impact of these installations in utility grids. In order to provide a net contribution to this issue a detailed wind park model has been developed and is briefly presented. However, the computational costs associated with the performance of such a detailed model in describing the behavior of a wind park composed by a considerable number of units may render its practical application very difficult. To overcome this problem integral manifolds theory has been applied to reduce the order of the detailed wind park model, and therefore create the conditions for the development of a dynamic equivalent which is able to retain the relevant dynamics with respect to the existing a.c. system. In this paper integral manifold method has been introduced for order reduction. Simulation results of the proposed method represents that integral manifold method results fit the detailed model results with a higher precision than singular perturbation method.

Keywords: Wind, Reduced Order, Integral Manifold.

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