Search results for: Overset grid

Authors: A.F.A. Abidin, N.S.M. Usop

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A computer cluster is a group of tightly coupled computers that work together closely so that in many respects they can be viewed as though they are a single computer. The components of a cluster are commonly, but not always, connected to each other through fast local area networks. Clusters are usually deployed to improve performance and/or availability over that provided by a single computer, while typically being much more cost-effective than single computers of comparable speed or availability. This paper proposed the way to implement the Beowulf Cluster in order to achieve high performance as well as high availability.

Keywords: Beowulf Cluster, grid computing, GridMPI, MPICH.

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Authors: Amy LeBar, Kim L. Trenbath, Bennett Doherty, William Livingood

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Plug and process loads (PPLs) account for a large portion of U.S. commercial building energy use. There is a huge potential to reduce whole building consumption by targeting PPLs for energy savings measures or implementing some form of plug load management (PLM). Despite this potential, there has yet to be a widely adopted commercial PLM technology. This paper describes the Automatic Type and Location Identification System (ATLIS), a PLM system framework with automatic and dynamic load detection (ADLD). ADLD gives PLM systems the ability to automatically identify devices as they are plugged into the outlets of a building. The ATLIS framework takes advantage of smart, connected devices to identify device locations in a building, meter and control their power, and communicate this information to a central database. ATLIS includes five primary capabilities: location identification, communication, control, energy metering, and data storage. A laboratory proof of concept (PoC) demonstrated all but the energy metering capability, and these capabilities were validated using a series of system tests. The PoC was able to identify when a device was plugged into an outlet and the location of the device in the building. When a device was moved, the PoC’s dashboard and database were automatically updated with the new location. The PoC implemented controls to devices from the system dashboard so that devices maintained correct schedules regardless of where they were plugged in within the building. ATLIS’s primary technology application is improved PLM, but other applications include asset management, energy audits, and interoperability for grid-interactive efficient buildings. An ATLIS-based system could also be used to direct power to critical devices, such as ventilators, during a brownout or blackout. Such a framework is an opportunity to make PLM more widespread and reduce the amount of energy consumed by PPLs in current and future commercial buildings.

Keywords: commercial buildings, grid-interactive efficient buildings, miscellaneous electric loads, plug loads, plug load management

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Authors: Adel Hamad Rafa

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This paper, proposes a control system for use with microgrid consiste of  multiple small scale embedded generation networks (SSEG networks) connected to the 33kV distribution network. The proposed controller controls power flow in the grid-connected mode of operation, enables voltage and frequency control when the SSEG networks are islanded, and resynchronises the SSEG networks with the utility before reconnecting them. The performance of the proposed controller has been tested in simulations using PSCAD.

Keywords: Microgrid, Small scale embedded generation, island mode, resynchronisation.

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Authors: M. Tsebia, H. Bentarzi

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In the inter-connected power systems, a phenomenon called inter-area oscillation may be caused by several defects. In this paper, a study of the Maghreb countries inter-area power networks oscillation has been investigated. The inter-area oscillation monitoring can be enhanced by integrating Phasor Measurement Unit (PMU) technology installed in different places. The data provided by PMU and recorded by PDC will be used for the monitoring, analysis, and control purposes. The proposed approach has been validated by simulation using MATLAB/Simulink.

Keywords: Inter-area oscillation, Maghrebian power system, Simulink, PMU.

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Authors: A. Junaid, M. A. Z. Raja, I. M. Qureshi

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An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .

Keywords: Neural networks, Unsupervised learning, Evolutionary computing, Numerical methods, Fitness evaluation function.

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Authors: Fouzia Brihmat

Abstract:

Economic planning models, which are used to build microgrids and Distributed Energy Resources (DER), are the current norm for expressing such confidence. These models often decide both short-term DER dispatch and long-term DER investments. This research investigates the most cost-effective hybrid (photovoltaic-diesel) renewable energy system (HRES) based on Total Net Present Cost (TNPC) in an Algerian Saharan area, which has a high potential for solar irradiation and has a production capacity of 1 GW/h. Lead-acid batteries have been around much longer and are easier to understand, but have limited storage capacity. Lithium-ion batteries last longer, are lighter, but generally more expensive. By combining the advantages of each chemistry, we produce cost-effective high-capacity battery banks that operate solely on AC coupling. The financial implications of this research describe the corrosion process that occurs at the interface between the active material and grid material of the positive plate of a lead-acid battery. The best cost study for the HRES is completed with the assistance of the HOMER Pro MATLAB Link. Additionally, during the course of the project's 20 years, the system is simulated for each time step. In this model, which takes into consideration decline in solar efficiency, changes in battery storage levels over time, and rises in fuel prices above the rate of inflation, the trade-off is that the model is more accurate, but the computation takes longer. We initially utilized the optimizer to run the model without multi-year in order to discover the best system architecture. The optimal system for the single-year scenario is the Danvest generator, which has 760 kW, 200 kWh of the necessary quantity of lead-acid storage, and a somewhat lower Cost Of Energy (COE) of $0.309/kWh. Different scenarios that account for fluctuations in the gasified biomass generator's production of electricity have been simulated, and various strategies to guarantee the balance between generation and consumption have been investigated.

Keywords: Battery, Corrosion, Diesel, Economic planning optimization, Hybrid energy system, HES, Lead-acid battery, Li-ion battery, multi-year planning, microgrid, price forecast, total net present cost, wind.

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Authors: Marios N. Moschakis

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This paper deals with the assessment of faulted area around an industrial customer connected to a particular electric grid that will cause a certain sag magnitude on this customer. The faulted (critical or exposed) area’s length is calculated by adding all line lengths in the neighborhood of the critical node (customer). The applied method is the so-called Method of Critical Distances. By using advanced short-circuit analysis, the Critical Area can be accurately calculated for radial and meshed power networks due to all symmetrical and asymmetrical faults. For the demonstration of the effectiveness of the proposed methodology, a study case is used.

Keywords: Critical area, fault-induced voltage sags, industrial customers, power quality.

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Authors: N. J. Imu, N. Rabbani, Md E. Hossain

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Achieving national climate goals requires transforming the energy system and increasing the use of renewable energy in Bangladesh as renewable energy offers an environmentally friendly energy supply. In view of this, Bangladesh has set a goal of 100% renewable power generation by 2050. Among all the renewable energy, solar is the most effective and popular source of renewable energy in Bangladesh. In order to build up on-grid and off-grid solar systems to increase energy transformation, monocrystalline type (highly efficient) solar module, and the polycrystalline type (low-efficient) solar module are commonly used. Due to their low price and availability, polycrystalline-type solar modules dominated the local market in the past years. However, in recent times the use of monocrystalline types modules has increased considerably owing to the significant decrease in price difference that existed between these two modules. Despite the deployment of both mono- and poly-crystalline modules in the market, the proliferation of low-quality solar panels are dominating the market resulting in reduced generation of solar electricity than expected. This situation is further aggravated by insufficient information regarding the effect of solar irradiation on solar module performance in relation to the quality of the materials used for the production of the module. This research aims to evaluate the efficiency of monocrystalline and polycrystalline solar modules that are available in Bangladesh by considering seasonal variations. Both types of solar modules have been tested for three different capacities 45W, 60W, and 100W in Dhaka regions to evaluate their power generation capability under Standard Test Conditions (STC). Module testing data were recorded twelve months in a full year from January to December. Data for solar irradiation were collected using HT304N while HT I-V400 multifunction instrument was used for testing voltage and current of photovoltaic (PV) systems and complete power quality analyzer. Results obtained in this study indicated differences between the efficiencies of polycrystalline and monocrystalline solar modules under the country’s solar irradiation. The average efficiencies of 45W, 60W, and 100W monocrystalline solar panels were recorded as 11.73%, 13.41%, and 15.37% respectively while for polycrystalline panels were 8.66%, 9.37%, and 12.34%. Monocrystalline solar panels, which offer greater working output than polycrystalline ones, are also represented by the Pearson Correlation value. The output of polycrystalline solar panels fluctuated highly with the changes in irradiation and temperature whereas monocrystalline panels were much stable.

Keywords: Solar energy, solar irradiation, efficiency, polycrystalline solar module, monocrystalline solar module, SPSS analysis.

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

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The optimal grid spacing and turbulence model for the 2D numerical analysis of a vertical-axis water turbine (VAWaterT) operating in a 2 m/s freestream current has been investigated. The results of five different spatial domain discretizations and two turbulence models (k-ω SST and k-ε RNG) have been compared, in order to gain the optimal y+ parameter distribution along the blade walls during a full rotor revolution. The resulting optimal mesh has appeared to be quite similar to that obtained for the numerical analysis of a vertical-axis wind turbine.

Keywords: CFD, vertical axis water turbine, NACA 0025, blade y+.

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Authors: Chokri Baccouch, Chayma Bahhar, Hedi Sakli, Nizar Sakli, Taoufik Aguili

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This paper presents a hybrid system solar cell antenna for 5G mobile communications networks. We propose here a solar cell antenna with either a front face collection grid or mesh patch. The solar cell antenna of our contribution combines both optical and radiofrequency signals. Thus, we propose two solar cell antenna structures in the frequency bands of future 5G standard respectively in both 2.6 and 3.5 GHz bands. Simulation using the Advanced Design System (ADS) software allows us to analyze and determine the antenna parameters proposed in this work such as the reflection coefficient (S11), gain, directivity and radiated power.

Keywords: Patch antenna, solar cell, DC, RF, 5G.

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Authors: Kasun Karunanayaka, Sanath Siriwardana, Chamari Edirisinghe, Ryohei Nakatsu, PonnampalamGopalakrishnakone

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In this paper, we are presenting a new type of pointing interface for computers which provides mouse functionalities with near surface haptic feedback. Further, it can be configured as a haptic display where users may feel the basic geometrical shapes in the GUI by moving the finger on top of the device surface. These functionalities are achieved by tracking three dimensional positions of the neodymium magnet using Hall Effect sensors grid and generating like polarity haptic feedback using an electromagnet array. This interface brings the haptic sensations to the 3D space where previously it is felt only on top of the buttons of the haptic mouse implementations.

Keywords: Pointing interface, near surface haptic feedback, tactile display, tangible user interface.

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Authors: Esra İpekci, Murad Aydın Sanda

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The flora of Bozdağ (Konya) and its surroundings were investigated between 2003 and 2005 years; 700 herbarium specimens belonging to 482 taxa, 257 genera and 57 families were collected and identified from the area. The families which have the most taxa in research area are Asteraceae 67 (14.0%), Fabaceae 60 (12.6%), Lamiaceae 57 (11.9%), Brassicaceae 34 (7.1%), Poaceae 30 (6.3%), Rosaceae 24 (5.0%), Caryophyllaceae 23 (4.8%), Liliaceae 19 (4.0%), Boraginaceae 17 (3.6%), and Apiaceae 13 (2.7%). The research area is in the district of Konya and is in the B4 square according to the Grid System. The phytogeographic elements are represented in the study area as follows; Irano-Turanian 91 (18.9%), Mediterranean 72 (14.9%), Euro-Siberian 21 (4.3%). The phytogeographic regions of 273 (56.6%) taxa are either multi-regional or unknown. The number of endemic taxa is 79 (16.3%).

Keywords: Bozdağ, Flora, Konya, Sızma, Turkey.

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Authors: M. Raciti Castelli, P. Cioppa, E. Benini

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This paper presents a CFD analysis of the flow around a 30° inclined flat plate of infinite span. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a flat plate invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested and flow field characteristics in the neighborhood of the flat plate have been numerically investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a twodimensional inclined plate.

Keywords: CFD, lift, drag, flat plate

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Authors: Chokri Baccouch, Chayma Bahhar, Hedi Sakli, Nizar Sakli

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In this article, we present the combination of an antenna patch structure with a photovoltaic cell in one device for telecommunication applications in isolated environments. The radiating patch element of a patch antenna was replaced by a solar cell. DC current generation is the original feature of the solar cell, but now it was additionally able to receive and transmit electromagnetic waves. A mathematical model which serves in the minimization of power losses of the cell and therefore the improvement in conversion performance was studied. Simulation results of this antenna show a resonance at a frequency of 16.55 GHz in Ku-band with a gain of 4.24 dBi.

Keywords: Electric power collected, optical and electrical losses, optimization of the grid of collection, patch antenna, photovoltaic cell.

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

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A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: Eigenvalue analysis, microgrid, modal analysis, voltage stability.

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Authors: Jiang Fan

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With growth of PV market in tropical region, it is necessary to investigate the performance of different types of PV technology under the tropical weather conditions. Singapore Polytechnic was funded by Economic Development Board (EDB) to set up a solar PV test-bed for the research on performance of different types of PV modules in the country. The PV test-bed installed the nine different types of PV systems that are integrated to power utility grid for monitoring and analyzing their operating performances. This paper presents the 12 months operational data of nine different PV systems and analyses on performances of installed PV systems using energy yield and performance ratio. The nine types of PV systems under test have shown their energy yields ranging from 2.67 to 3.36 kWh/kW_p and their performance ratios (PRs) ranging from 70% to 88%.

Keywords: Monocrystalline, Multicrystalline, Amorphous Silicon, Cadmium Telluride and thin film PV.

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Authors: Sven Borén, Lisiana Nurhadi, Henrik Ny

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From a theoretical perspective, electric buses can be more sustainable and can be cheaper than fossil fuelled buses in city traffic. The authors have not found other studies based on actual urban public transport in Swedish winter climate. Further on, noise measurements from buses for the European market were found old. The aims of this follow-up study was therefore to test and possibly verify in a real-life environment how energy efficient and silent electric buses are, and then conclude on if electric buses are preferable to use in public transport. The Ebusco 2.0 electric bus, fitted with a 311 kWh battery pack, was used and the tests were carried out during November 2014-April 2015 in eight municipalities in the south of Sweden. Six tests took place in urban traffic and two took place in more of a rural traffic setting. The energy use for propulsion was measured via logging of the internal system in the bus and via an external charging meter. The average energy use turned out to be 8% less (0,96 kWh/km) than assumed in the earlier theoretical study. This rate allows for a 320 km range in public urban traffic. The interior of the bus was kept warm by a diesel heater (biodiesel will probably be used in a future operational traffic situation), which used 0,67 kWh/km in January. This verified that electric buses can be up to 25% cheaper when used in public transport in cities for about eight years. The noise was found to be lower, primarily during acceleration, than for buses with combustion engines in urban bus traffic. According to our surveys, most passengers and drivers appreciated the silent and comfortable ride and preferred electric buses rather than combustion engine buses. Bus operators and passenger transport executives were also positive to start using electric buses for public transport. The operators did however point out that procurement processes need to account for eventual risks regarding this new technology, along with personnel education. The study revealed that it is possible to establish a charging infrastructure for almost all studied bus lines. However, design of a charging infrastructure for each municipality requires further investigations, including electric grid capacity analysis, smart location of charging points, and tailored schedules to allow fast charging. In conclusion, electric buses proved to be a preferable alternative for all stakeholders involved in public bus transport in the studied municipalities. However, in order to electric buses to be a prominent support for sustainable development, they need to be charged either by stand-alone units or via an expansion of the electric grid, and the electricity should be made from new renewable sources.

Keywords: Sustainability, Electric, Bus, Noise, GreenCharge.

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Authors: M. Nassereddine, A. Hellany, M. Nagrial, J. Rizk

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The demand on High voltage (HV) infrastructures is growing due to the corresponding growth in industries and population. Many areas are being developed and therefore require additional electrical power to comply with the demand. Substation upgrade is one of the rapid solutions to ensure the continuous supply of power to customers. This upgrade requires civil modifications to structures and fences. The civil work requires excavation and steel works that may create unsafe touch conditions. This paper presents a brief theoretical overview of the touch voltage inside and around substations and uses CDEGS software to simulate a case study.

Keywords: Earth safety, High Voltage, AC interference, Earthing Design.

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Authors: Samee Ullah Khan, C. Ardil

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The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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Authors: Ahmet Y. Arabul, Ibrahim Senol, Fatma Keskin Arabul, Mustafa G. Aydeniz, Yasemin Oner, Gokhan Kalkan

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In the standards of IEC 60076-2 and IEC 60076-7, three different hot-spot temperature estimation methods are suggested. In this study, the algorithms which used in hot-spot temperature calculations are analyzed by comparing the algorithms with the results of an experimental set-up made by a Transformer Monitoring System (TMS) in use. In tested system, TMS uses only top oil temperature and load ratio for hot-spot temperature calculation. And also, it uses some constants from standards which are on agreed statements tables. During the tests, it came out that hot-spot temperature calculation method is just making a simple calculation and not uses significant all other variables that could affect the hot-spot temperature.

Keywords: Hot-spot temperature, monitoring system, power transformer, smart grid.

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Authors: P Bumb, U Desideri, F Quattrocchi, L Arcioni

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This paper presents the feasibility study of CO2 sequestration from the sources to the sinks in the prospective of Italian Industries. CO2 produced at these sources captured, compressed to supercritical pressures, transported via pipelines and stored in underground geologic formations such as depleted oil and natural gas reservoirs, un-minable coal seams and deep saline aquifers. In this work, we present the optimized pipeline infrastructure for the CO2 with appropriate constraints to find lower cost system by the use of nonlinear optimization software LINGO 11.0. This study was conducted on CO2 transportation complex network of Italian Industries, to find minimum cost network for transporting the CO2 from sources to the sinks.

Keywords: CCS, CO2, ECBM, EU, NAP, LINGO, UNMIG.

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Authors: P. V. V. Rama Rao, M. V. Srikanth, S. Dileep Kumar Varma

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With advances in solid-state power electronic devices and microprocessors, various pulse-width-modulation (PWM) techniques have been developed for industrial applications. This paper presents the comparison of two different PWM techniques, the sinusoidal PWM (SPWM) technique and the space-vector PWM (SVPWM) technique applied to two level VSI for micro grid applications. These two methods are compared by discussing their ease of implementation and by analyzing the output harmonic spectra of various output voltages (line-to-neutral voltages, and line-to-line voltages) and their total harmonic distortion (THD). The SVPWM technique in the under-modulation region can increase the fundamental output voltage by 15.5% over the SPWM technique.

Keywords: SPWM, SVPWM, VSI, Modulation Index.

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Abdelhalim Kessal

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This paper treats a design of combined control of a single phase power factor correction (PFC). The strategy of the proposed control is based on two parts, the first, for the outer loop (DC output regulated voltage), and the second govern the input current of the converter in order to achieve a sinusoidal form in phase with the grid voltage. Two kinds of regulators are used, Fuzzy controller for the outer loop and predictive controller for the inner loop. The controllers are verified and discussed through simulation under MATLAB/Simulink platform. Also an experimental confirmation is applied. Results present a high dynamic performance under various parameters changes.

Keywords: Boost converter, harmonic distortion, Fuzzy, prediction, unity power factor.

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Authors: Maysam Saidi, Hassan Basirat Tabrizi, Reza Maddahian

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In this paper, numerical simulations are performed to investigate the effect of disturbance block on flow field of the classical square lid-driven cavity. Attentions are focused on vortex formation and studying the effect of block position on its structure. Corner vortices are different upon block position and new vortices are produced because of the block. Finite volume method is used to solve Navier-Stokes equations and PISO algorithm is employed for the linkage of velocity and pressure. Verification and grid independency of results are reported. Stream lines are sketched to visualize vortex structure in different block positions.

Keywords: Disturbance Block, Finite Volume Method, Lid-Driven Cavity

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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This paper presents a model predictive control (MPC) of a utility interactive three phase inverter (TPI) for a photovoltaic (PV) system at commercial level. The proposed model uses phase locked loop (PLL) to synchronize the TPI with the power electric grid (PEG) and performs MPC control in a dq reference frame. TPI model consists of a boost converter (BC), maximum power point tracking (MPPT) control, and a three-leg voltage source inverter (VSI). The operational model of VSI is used to synthesize the sinusoidal current and track the reference. The model is validated using a 35.7 kW PV system in Matlab/Simulink. Implementation results show simplicity and accuracy, as well as reliability of the model.

Keywords: Model predictive control, three phase voltage source inverter, PV system, Matlab/Simulink.

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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: Sajjad Hashemi, Khalil Monfaredi, Mohammad Masdari

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Cloud computing is a style of computing which is formed from the aggregation and development of technologies such as grid computing distributed computing, parallel computing and service-oriented architecture. And its aim is to provide computing, communication and storage resources in a safe environment based on service, as fast as possible, which is virtually provided via Internet platform. Considering that the provided Services in e-government are available via the Internet, thus cloud computing can be used in the implementation of e-government architecture and provide better service with the lowest economic cost using its benefits. In this paper, the Methods of using cloud computing in e-government has been studied and it's been attempted to identify the challenges and benefits of the cloud to get used in the e-government and proposals have been offered to overcome its shortcomings, encourage and partnership of governments and people to use this economical and new technology.

Keywords: Benefits, Cloud computing, Committee, Challenges, E-Government, Participation.

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Authors: Mahmoud Gilany, Wael Al-Hasawi

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Preliminary studies on Kuwait high voltage transmission system show significant increase in the short circuit level at some of the grid substations and some generating stations. This increase results from the growth in the power transmission systems in size and complexity. New generating stations are expected to be added to the system within the next few years. This paper describes the study analysis performed to evaluate the available and potential solutions to control SC levels in Kuwait power system. It also presents a modified planning of the transmission network in order to fulfill this task.

Keywords: Short circuit current, network splitting, fault current limiter, power transmission planning.

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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