Search results for: flow line

Authors: Ali Hamad, Ibrahim Al-Drous, Saleh Al-Jufout

Abstract:

This paper presents a case study of using STATCOM to enhance the performance of Al-Qatraneh 33-kV transmission line. The location of the STATCOM was identified by maintaining minimum voltage drops at the 110 load nodes. The transmission line and the 110 load nodes have been modeled by MATLAB/Simulink. The suggested STATCOM and its location will increase the transmission capability of this transmission line and overcome the overload expected in the year 2020. The annual percentage loading rise has been considered as 14.35%. A graphical representation of the line-to-line voltages and the voltage drops at different load nodes is illustrated.

Keywords: FACTS, MATLAB, STATCOM, transmission line, voltage drop.

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Authors: Aniruddha Bhattacharya, Pranab Kumar Chattopadhyay

Abstract:

Optimal reactive power flow is an optimization problem with one or more objective of minimizing the active power losses for fixed generation schedule. The control variables are generator bus voltages, transformer tap settings and reactive power output of the compensating devices placed on different bus bars. Biogeography- Based Optimization (BBO) technique has been applied to solve different kinds of optimal reactive power flow problems subject to operational constraints like power balance constraint, line flow and bus voltages limits etc. BBO searches for the global optimum mainly through two steps: Migration and Mutation. In the present work, BBO has been applied to solve the optimal reactive power flow problems on IEEE 30-bus and standard IEEE 57-bus power systems for minimization of active power loss. The superiority of the proposed method has been demonstrated. Considering the quality of the solution obtained, the proposed method seems to be a promising one for solving these problems.

Keywords: Active Power Loss, Biogeography-Based Optimization, Migration, Mutation, Optimal Reactive Power Flow.

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

Abstract:

This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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Authors: A.V.Naresh Babu, S.Sivanagaraju

Abstract:

A considerable progress has been achieved in transient stability analysis (TSA) with various FACTS controllers. But, all these controllers are associated with single transmission line. This paper is intended to discuss a new approach i.e. a multi-line FACTS controller which is interline power flow controller (IPFC) for TSA of a multi-machine power system network. A mathematical model of IPFC, termed as power injection model (PIM) presented and this model is incorporated in Newton-Raphson (NR) power flow algorithm. Then, the reduced admittance matrix of a multi-machine power system network for a three phase fault without and with IPFC is obtained which is required to draw the machine swing curves. A general approach based on L-index has also been discussed to find the best location of IPFC to reduce the proximity to instability of a power system. Numerical results are carried out on two test systems namely, 6-bus and 11-bus systems. A program in MATLAB has been written to plot the variation of generator rotor angle and speed difference curves without and with IPFC for TSA and also a simple approach has been presented to evaluate critical clearing time for test systems. The results obtained without and with IPFC are compared and discussed.

Keywords: Flexible alternating current transmission system (FACTS), first swing stability, interline power flow controller (IPFC), power injection model (PIM).

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Authors: M. Elkhoury

Abstract:

A recently developed one-equation turbulence model has been successfully applied to simulate turbulent flows with various complexities. The model, which is based on the transformation of the k-ε closure, is wall-distance free and equipped with lagging destruction/dissipation terms. Test cases included shockboundary- layer interaction flows over the NACA 0012 airfoil, an axisymmetric bump, and the ONERA M6 wing. The capability of the model to operate in a Scale Resolved Simulation (SRS) mode is demonstrated through the simulation of a massive flow separation over a circular cylinder at Re= 1.2 x106. An assessment of the results against available experiments Menter (k-ε)1Eq and the Spalart- Allmaras model that belongs to the single equation closure family is made.

Keywords: Turbulence modeling, complex flow simulation, scale adaptive simulation, one-equation turbulence model.

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Authors: Zahra Lashgari, Naghmeh Sadat MaghamiTekiyeh

Abstract:

Recent evidences on liquidity and valuation of securities in the capital markets clearly show the importance of stock market liquidity and valuation of firms. In this paper, relationship between transparency, liquidity, and valuation is studied by using data obtained from 70 companies listed in Tehran Stock Exchange during2003-2012. In this study, discriminatory earnings management, as a sign of lack of transparency and Tobin's Q, was used as the criteria of valuation. The results indicate that there is a significant and reversed relationship between earnings management and liquidity. On the other hand, there is a relationship between liquidity and transparency.The results also indicate a significant relationship between transparency and valuation. Transparency has an indirect effect on firm valuation alone or through the liquidity channel. Although the effect of transparency on the value of a firm was reduced by adding the variable of liquidity, the cumulative effect of transparency and liquidity increased.

Keywords: Firm valuation, Earnings management, Liquidity, Tobin's Q, Transparency.

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Authors: K. Nagaraju, S. Sivanagaraju, T. Ramana, V. Ganesh

Abstract:

This paper presents a simple method for estimation of additional load as a factor of the existing load that may be drawn before reaching the point of line maximum loadability of radial distribution system (RDS) with different realistic load models at different substation voltages. The proposed method involves a simple line loadability index (LLI) that gives a measure of the proximity of the present state of a line in the distribution system. The LLI can use to assess voltage instability and the line loading margin. The proposed method also compares with the existing method of maximum loadability index [10]. The simulation results show that the LLI can identify not only the weakest line/branch causing system instability but also the system voltage collapse point when it is near one. This feature enables us to set an index threshold to monitor and predict system stability on-line so that a proper action can be taken to prevent the system from collapse. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on two bus and 69 bus RDS.

Keywords: line loadability index, line loading margin, maximum line loadability, system stability, radial distribution system

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

Abstract:

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

Keywords: Distribution Factors, Power System, Sensitivity Factors, Electricity Market.

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Authors: W. Koranuntachai, T. Chantrasmi, U. Nontakaew

Abstract:

Medical latex gloves are made from the latex compound in production lines. Latex dipping is considered one of the most important processes that directly affect the final product quality. In a continuous production line, a chain conveyor carries the formers through the process and partially submerges them into an open channel flow in a latex dipping tank. In general, the conveyor speed is determined by the desired production capacity, and the latex-dipping tank can then be designed accordingly. It is important to understand the flow behavior in the dipping tank in order to achieve high quality in the process. In this work, Computational Fluid Dynamics (CFD) was used to simulate the flow past an array of formers in a simplified latex dipping process. The computational results showed both the flow structure and the vortex generation between two formers. The maximum shear stress over the surface of the formers was used as the quality metric of the latex-dipping process when adjusting operation parameters.

Keywords: medical latex gloves, latex dipping, dipping tank, computational fluid dynamics

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Authors: Inaki Maulida Hakim, T. Yuri M. Zagloel, Astari Wulandari

Abstract:

Six sigma is a framework that is used to identify inefficiency so that the cause of inefficiency will be known and right improvement to overcome cause of inefficiency can be conducted. This paper presents result of implementing six sigma to improve piston assembly line in Manufacturing Laboratory, Universitas Indonesia. Six sigma framework will be used to analyze the significant factor of inefficiency that needs to be improved which causes bottleneck in assembly line. After analysis based on six sigma framework conducted, line balancing method was chosen for improvement to overcome causative factor of inefficiency which is differences time between workstation that causes bottleneck in assembly line. Then after line balancing conducted in piston assembly line, the result is increase in efficiency. Efficiency is shown in the decreasing of Defects per Million Opportunities (DPMO) from 900,000 to 700,000, the increasing of level of labor productivity from 0.0041 to 0.00742, the decreasing of idle time from 121.3 seconds to 12.1 seconds, and the increasing of output, which is from 1 piston in 5 minutes become 3 pistons in 5 minutes.

Keywords: Assembly line, efficiency, improvement, line balancing, productivity, six sigma, workstation.

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Authors: Il Dong Kim, Jin Rak Lee, Young Jun Ko, Young Taek Jin

Abstract:

An on-line condition monitoring method for transmission line is proposed using electrical circuit theory and IT technology in this paper. It is reasonable that the circuit parameters such as resistance (R), inductance (L), conductance (g) and capacitance (C) of a transmission line expose the electrical conditions and physical state of the line. Those parameters can be calculated from the linear equation composed of voltages and currents measured by synchro-phasor measurement technique at both end of the line. A set of linear voltage drop equations containing four terminal constants (A, B ,C ,D ) are mathematical models of the transmission line circuits. At least two sets of those linear equations are established from different operation condition of the line, they may mathematically yield those circuit parameters of the line. The conditions of line connectivity including state of connecting parts or contacting parts of the switching device may be monitored by resistance variations during operation. The insulation conditions of the line can be monitored by conductance (g) and capacitance(C) measurements. Together with other condition monitoring devices such as partial discharge, sensors and visual sensing device etc.,they may give useful information to monitor out any incipient symptoms of faults. The prototype of hardware system has been developed and tested through laboratory level simulated transmission lines. The test has shown enough evident to put the proposed method to practical uses.

Keywords: Transmission Line, Condition Monitoring, Circuit Parameters, Synchro- phasor Measurement.

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Authors: M. Oloomi-Buygi, M. Reza Salehizadeh

Abstract:

In this paper a new approach for transmission pricing is presented. The main idea is voltage angle allocation, i.e. determining the contribution of each contract on the voltage angle of each bus. DC power flow is used to compute a primary solution for angle decomposition. To consider the impacts of system non-linearity on angle decomposition, the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow. Then, the contribution of each contract on power flow of each transmission line is computed based on angle decomposition. Contract-related flows are used as a measure for “extent of use" of transmission network capacity and consequently transmission pricing. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system.

Keywords: Deregulation, Power electric markets, Transmission pricing methodologies, decoupled Newton-Raphson power flow.

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Authors: Said Rabah Azzam, Laura Carolina Arias, Shikun Zhou

Abstract:

A product goes through various processes in a production flow which is also known as assembly line in manufacturing process management. Toyota created a new concept which is known as lean concept in manufacturing industry. Today it is the leading model in manufacturing plants through the globe. The linear walking worker assembly line is a flexible assembly system where each worker travels down the line carrying out each assembly task at each station; and each worker accomplishes the assembly of a unit from start to finish. This paper attempts to combine the flexibility of the walking worker and lean in order to quantify the benefits from applying the shop floor principles of lean management.

Keywords: Toyota Production System, TPS, LeanManufacturing, Walking Worker, Lean Management, Management, Linear Assembly Lines, U-shaped Assembly Lines, Shop FloorManagement

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Authors: Minho Bang, Seok Min Choi, Jun Su Park, Hokyu Moon, Hyung Hee Cho

Abstract:

Present study investigates the effect of unsteady wakes on heat transfer in blade tip. Heat/mass transfer was measured in blade tip region depending on a variety of strouhal number by naphthalene sublimation technique. Naphthalene sublimation technique measures heat transfer using a heat/mass transfer analogy. Experiments are performed in linear cascade which is composed of five turbine blades and rotating rods. Strouhal number of inlet flow are changed ranging from 0 to 0.22. Reynolds number is 100,000 based on 11.4 m/s of outlet flow and axial chord length. Three different squealer tip geometries such as base squealer tip, vertical rib squealer tip, and camber line squealer tip are used to study how unsteady wakes affect heat transfer on a blade tip. Depending on squealer tip geometry, different flow patterns occur on a blade tip. Also, unsteady wakes cause reduced tip leakage flow and turbulent flow. As a result, as strouhal number increases, heat/mass transfer coefficients decrease due to the reduced leakage flow. As strouhal number increases, heat/ mass transfer coefficients on a blade tip increase in vertical rib squealer tip.

Keywords: Gas turbine, blade tip, heat transfer, unsteady wakes.

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Authors: Mohd Hazwan bin Yusof, Hiroshi Katanoda

Abstract:

In order to clarify the structure of the cold flow discharged from the vortex tube (VT), the pressure of the cold flow was measured, and a simple flow visualization technique using a 0.75mm-diameter needle and an oily paint is made to study the reverse flow at the cold exit. It is clear that a negative pressure and positive pressure region exist at a certain pressure and cold fraction area, and that a reverse flow is observed in the negative pressure region.

Keywords: Flow visualization, Pressure measurement, Reverse flow, Vortex tube.

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Authors: A. Chaudhuri, C. Guha, T. K. Dutta

Abstract:

Pressure driven microscale gas flow-separation has been investigated by solving the compressible Navier-Stokes (NS) system of equations. A two dimensional explicit finite volume (FV) compressible flow solver has been developed using modified advection upwind splitting methods (AUSM+) with no-slip/first order Maxwell-s velocity slip conditions to predict the flowseparation behavior in microdimensions. The effects of scale-factor of the flow geometry and gas species on the microscale gas flowseparation have been studied in this work. The intensity of flowseparation gets reduced with the decrease in scale of the flow geometry. In reduced dimension, flow-separation may not at all be present under similar flow conditions compared to the larger flow geometry. The flow-separation patterns greatly depend on the properties of the medium under similar flow conditions.

Keywords: AUSM+, FVM, Flow-separation, Microflow.

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Authors: Asfar Ali Khan

Abstract:

Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.

Keywords: Power Transfer, PV Curve, Voltage Stability.

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Authors: Mehdi Fuladipanah, Mehdi Jorabloo

Abstract:

Water flow management is one of the most important parts of river engineering. Non-uniformity distribution of rainfall and various flow demand with unreasonable flow management will be caused destroyed of river ecosystem. Then, it is very serious to determine ecosystem flow requirement. In this paper, Flow duration curve indices method which has hydrological based was used to evaluate environmental flow in Gharasou River, Ardabil, Iran. Using flow duration curve, Q90 and Q95 for different return periods were calculated. Their magnitude were determined as 1-day, 3-day, 7-day and 30 day. According the second method, hydraulic alteration indices often had low and medium range. In order to maintain river at an acceptable ecological condition, minimum daily discharge of index Q95 is 0.7 m3.s-1.

Keywords: Ardabil, Environmental flow, Flow Duration Curve, Gharasou River.

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Authors: Syahanim Mohd Salleh, Zaihosnita Hood, Hairulliza Mohd Judi, Marini Abu Bakar

Abstract:

CFlow is a flow chart software, it contains facilities to draw and evaluate a flow chart. A flow chart evaluation applies a simulation method to enable presentation of work flow in a flow chart solution. Flow chart simulation of CFlow is executed by manipulating the CFlow data file which is saved in a graphical vector format. These text-based data are organised by using a data classification technic based on a Library classification-scheme. This paper describes the file format for flow chart simulation software of CFlow.

Keywords: CFlow, flow chart, file format.

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Authors: Mohammad Syuhaimi Ab-Rahman, Boonchuan Ng, Kasmiran Jumari

Abstract:

This paper presented a MATLAB-based system named Smart Access Network Testing, Analyzing and Database (SANTAD), purposely for in-service transmission surveillance and self restoration against fiber fault in fiber-to-the-home (FTTH) access network. The developed program will be installed with optical line terminal (OLT) at central office (CO) to monitor the status and detect any fiber fault that occurs in FTTH downwardly from CO towards residential customer locations. SANTAD is interfaced with optical time domain reflectometer (OTDR) to accumulate every network testing result to be displayed on a single computer screen for further analysis. This program will identify and present the parameters of each optical fiber line such as the line's status either in working or nonworking condition, magnitude of decreasing at each point, failure location, and other details as shown in the OTDR's screen. The failure status will be delivered to field engineers for promptly actions, meanwhile the failure line will be diverted to protection line to ensure the traffic flow continuously. This approach has a bright prospect to improve the survivability and reliability as well as increase the efficiency and monitoring capabilities in FTTH.

Keywords: MATLAB, SANTAD, in-service transmission surveillance, self restoration, fiber fault, FTTH

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Authors: M. O’Driscoll, M. Anwar, M. G. Rasul

Abstract:

The benefits of eco-roofs is quite well known, however there remains very little research conducted for the implementation of eco-roofs in subtropical climates such as Australia. There are many challenges facing Australia as it moves into the future, climate change is proving to be one of the leading challenges. In order to move forward with the mitigation of climate change, the impacts of rapid urbanization need to be offset. Eco-roofs are one way to achieve this; this study presents the energy savings and environmental benefits of the implementation of eco-roofs in subtropical climates. An experimental set-up was installed at Rockhampton campus of Central Queensland University, where two shipping containers were converted into small offices, one with an eco-roof and one without. These were used for temperature, humidity and energy consumption data collection. In addition, a computational model was developed using Design Builder software (state-of-the-art building energy simulation software) for simulating energy consumption of shipping containers and environmental parameters, this was done to allow comparison between simulated and real world data. This study found that eco-roofs are very effective in subtropical climates and provide energy saving of about 13% which agrees well with simulated results. 

Keywords: Climate Change, Eco/Green roof, Energy savings, Subtropical climate.

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Authors: A. J. Nazari, S. Honma

Abstract:

This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21^st, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.

Keywords: Fractional flow, oil displacement, relative permeability, simultaneously flow.

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Authors: Saeed Hosseini, Ali Reza Tahavvor

Abstract:

Sound processing is one the subjects that newly attracts a lot of researchers. It is efficient and usually less expensive than other methods. In this paper the flow generated sound is used to estimate the flow speed of free flows. Many sound samples are gathered. After analyzing the data, a parameter named wave power is chosen. For all samples the wave power is calculated and averaged for each flow speed. A curve is fitted to the averaged data and a correlation between the wave power and flow speed is found. Test data are used to validate the method and errors for all test data were under 10 percent. The speed of the flow can be estimated by calculating the wave power of the flow generated sound and using the proposed correlation.

Keywords: Flow generated sound, sound processing, speed, wave power.

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Authors: P. Azimi, B. Behtoiy

Abstract:

One of the most famous techniques which affect the efficiency of a production line is the assembly line balancing (ALB) technique. This paper examines the balancing effect of a whole production line of a real auto glass manufacturer in three steps. In the first step, processing time of each activity in the workstations is generated according to a practical approach. In the second step, the whole production process is simulated and the bottleneck stations have been identified, and finally in the third step, several improvement scenarios are generated to optimize the system throughput, and the best one is proposed. The main contribution of the current research is the proposed framework which combines two famous approaches including Assembly Line Balancing and Optimization via Simulation technique (OvS). The results show that the proposed framework could be applied in practical environments, easily.

Keywords: Assembly line balancing problem, optimization via simulation, production planning.

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Authors: Malika.D Kedir-Talha, Mohamed Mehenni

Abstract:

In order to be able to automatically differentiate between two modes of permanent flow of a liquid simulating blood, it was imperative to put together a data bank. Thus, the acquisition of the various amplitude spectra of the Doppler signal of this liquid in laminar flow and other spectra in turbulent flow enabled us to establish an automatic difference between the two modes. According to the number of parameters and their nature, a comparative study allowed us to choose the best classifier.

Keywords: Doppler spectrum, flow mode, pattern recognition, permanent flow.

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Authors: Mohammad Syuhaimi Ab-Rahman, Boonchuan Ng, Kasmiran Jumari

Abstract:

This paper presented a new approach for centralized monitoring and self-protected against fiber fault in fiber-to-the-home (FTTH) access network by using Smart Access Network Testing, Analyzing and Database (SANTAD). SANTAD will be installed with optical line terminal (OLT) at central office (CO) for in-service transmission surveillance and fiber fault localization within FTTH with point-to-multipoint (P2MP) configuration downwardly from CO towards customer residential locations based on the graphical user interface (GUI) processing capabilities of MATLAB software. SANTAD is able to detect any fiber fault as well as identify the failure location in the network system. SANTAD enable the status of each optical network unit (ONU) connected line is displayed onto one screen with capability to configure the attenuation and detect the failure simultaneously. The analysis results and information will be delivered to the field engineer for promptly actions, meanwhile the failure line will be diverted to protection line to ensure the traffic flow continuously. This approach has a bright prospect to improve the survivability and reliability as well as increase the efficiency and monitoring capabilities in FTTH.

Keywords: Fiber fault, FTTH, SANTAD, transmission surveillance, MATLAB.

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Authors: Nor Maniha Abdul Ghani, Faradila Naim, Tan Piow Yon

Abstract:

This project focuses on the development of a line follower algorithm for a Two Wheels Balancing Robot. In this project, ATMEGA32 is chosen as the brain board controller to react towards the data received from Balance Processor Chip on the balance board to monitor the changes of the environment through two infra-red distance sensor to solve the inclination angle problem. Hence, the system will immediately restore to the set point (balance position) through the implementation of internal PID algorithms at the balance board. Application of infra-red light sensors with the PID control is vital, in order to develop a smooth line follower robot. As a result of combination between line follower program and internal self balancing algorithms, we are able to develop a dynamically stabilized balancing robot with line follower function.

Keywords: infra-red sensor, PID algorithms, line followerBalancing robot

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Authors: M. Tahar Bouzaher

Abstract:

This study involves a numerical simulation of the flow around a NACA2415 airfoil, with a 15°angle of attack, and flow separation control using a rod, It reposes inputting a cylindrical rod upstream of the leading edge in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The viscous, non-stationary flow is simulated using ANSYS FLUENT 13. Our results showed a substantial modification in the flow behavior and a maximum drag reduction of 51%.

Keywords: CFD, Flow separation, Active control, Boundary layer, rod, NACA 2415.

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Authors: S. Berjozkina, A. Sauhats, V. Bargels, E. Vanzovichs

Abstract:

There are various solutions for improving existing overhead line systems with the general purpose of increasing their limited capacity. The capacity reserve of the existing overhead lines is an important problem that must be considered from different aspects. The paper contains a comparative analysis of the mechanical and thermal limitations of an existing overhead line based on certain calculation conditions characterizing the examined variants. The methodology of the proposed estimation of the permissible conductor temperature and maximum load current is described in detail. The transmission line model consists of specific information of an existing overhead line of the Latvian power network. The main purpose of the simulation tasks is to find an additional capacity reserve by using accurate mathematical models. The results of the obtained data are presented.

Keywords: capacity of an overhead line, mechanical conditions, permissible conductor temperature, thermal conditions.

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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