Search results for: frequency stability

Authors: Azwadi Mohamad, Pauzi Yahaya, Nadiah Hudi

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Earthing system for high-voltage transmission tower is designed to protect the working personnel and equipments, and to maintain the quality of supply during fault. The existing earthing system for transmission towers in TNB’s system is purposely designed for normal power frequency (low-frequency) fault conditions that take into account the step and touch voltages. This earthing design is found to be inapt for lightning (transient) condition to a certain extent, which involves a high-frequency domain. The current earthing practice of laying the electrodes radially in straight 60 m horizontal lines under the ground, in order to achieve the specified impedance value of less than 10 Ω, was deemed ineffective in reducing the high-frequency impedance. This paper introduces a new earthing design that produces low impedance value at the high-frequency domain, without compromising the performance of low-frequency impedance. The performances of this new earthing design, as well as the existing design, are simulated for various soil resistivity values at varying frequency. The proposed concentrated earthing design is found to possess low TFR value at both low and high-frequency. A good earthing design should have a fine balance between compact and radial electrodes under the ground.

Keywords: earthing design, high-frequency, lightning, tower footing impedance

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Tomotaka Aoki, Isao Tomita

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We examined the on-off ratio and frequency components of output signals from an electron-interference device made of GaAs/AlₓGa₁₋ₓAs by solving the time-dependent Schrödinger's equation on conducting electrons in the channel waveguide of the device. For electron-wave modulation, a periodic voltage of frequency f was applied to the channel. Furthermore, we examined the voltage-amplitude dependence of the signals in time and frequency domains and found that large applied voltage deformed the output-signal waveform and created additional side modes (frequencies) near the modulation frequency f and that there was a trade-off between on-off ratio and side-mode creation.

Keywords: electrical conduction, electron interference, frequency spectrum, on-off ratio

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Authors: Trisiladi Supriyanto

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This study aims to establish a concept of rate of profit on Islamic banking that can create economic justice and stability in the Islamic Financial Market (Banking and Capital Markets). A rate of profit that creates economic justice and stability can be achieved through its role in maintaining the stability of the financial system in which there is an equitable distribution of income and wealth. To determine the role of the rate of profit as the basis of the profit sharing system implemented in the Islamic financial system, we can see the connection of rate of profit in creating financial stability, especially in the asset-liability management of financial institutions that generate a stable net margin or the rate of profit that is not affected by the ups and downs of the market risk factors, including indirect effect on interest rates. Furthermore, Islamic financial stability can be seen from the role of the rate of profit on the stability of the Islamic financial assets value that are measured from the Islamic financial asset price volatility in the Islamic Bond Market in the Capital Market.

Keywords: economic justice, equitable distribution of income, equitable distribution of wealth, rate of profit, stability in the financial system

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Authors: M. Jathaveda, Joben Leons, G. Vidya

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Reentry from orbit is a critical phase in the entry trajectory. For a non-propulsive ballistic entry, static and dynamic stability play an important role in the trajectory, especially for the safe deployment of parachutes, typically at subsonic Mach numbers. Static stability of flight vehicles are being estimated through CFD techniques routinely. Advances in CFD software as well as computational facilities have enabled the estimation of the dynamic stability derivatives also through CFD techniques. Longitudinal static and dynamic stability of a typical reentry body for subsonic Mach number of 0.6 is predicted using commercial software CFD++ and presented here. Steady state simulations are carried out for α = 2° on an unstructured grid using SST k-ω model. Transient simulation using forced oscillation method is used to compute pitch damping derivatives.

Keywords: stability, typical reentry body, subsonic, static and dynamic

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Authors: Kanshio Richard Tyokyaa, Jagadish Singh

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In this paper, we examined the location and stability of Out-Of-Plane Equilibrium points in the elliptic restricted three-body problem of an infinitesimal body when both primaries are taken as oblate spheroids with oblateness up to zonal harmonic J₄. The positions of the Equilibrium points L₆,₇ and their stability depend on the oblateness of the primaries and the eccentricity of their orbits. We explored the problem numerically to show the effects of parameters involved in the position and stability of the Out-Of-Plane Equilibrium points for the systems: HD188753 and Gliese 667. It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable.

Keywords: out-of-plane, equilibrium points, stability, elliptic restricted three-body problem, oblateness, zonal harmonic

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Authors: A. Alireza Masjedi, B. Amir Taeedi

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In this research, by placing the two cylindrical piers without roughness and with roughness with riprap around its, they proceeded to a series of tests. Experiments were done by three relative diameters of riprap with density 2.1 and one rate of discharge 27 lit/s under pure water condition. In each experiment, flow depth measured in terms of failure threshold then stability number calculated by using data obtained. The results of the research showed that the riprap stability in pier with roughness is more pier without roughness because of the pier with roughness is sharp-pointed and reduced horseshoe vortex.

Keywords: riprap stability, roughness, river bend, froude number

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Authors: Alireza Masjedi, Amir Taeedi

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In this research, by placing the two cylindrical piers without roughness and with roughness with riprap around its, they proceeded to a series of tests. Experiments were done by three relative diameters of riprap with density 2.1 and one rate of discharge 27 lit/s under pure water condition. In each experiment, flow depth measured in terms of failure threshold then stability number calculated by using data obtained. The results of the research showed that the riprap stability in pier with roughness is more pier without roughness because of the pier with roughness is sharp-pointed and reduced horseshoe vortex.

Keywords: riprap stability, roughness, river bend, froude number

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Authors: Niloufar Ghoreishi, Ali Nekouzadeh

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The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: flight stability, phugoid mode, short period mode, climb phase, damping coefficient

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Authors: B. Y. Danjuma, A. Archibong-Eso, Aliyu M. Aliyu, H. Yeung

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In this experimental investigation, a new data for slugging frequency for high viscosity oil-gas flow are reported. Scale experiments were carried out using a mixture of air and mineral oil as the liquid phase in a 17 m long horizontal pipe with 0.0762 ID. The data set was acquired using two high-speed Gamma Densitometers at a data acquisition frequency of 250 Hz over a time interval of 30 seconds. For the range of flow conditions investigated, increase in liquid oil viscosity was observed to strongly influence the slug frequency. A comparison of the present data with prediction models available in the literature revealed huge discrepancies. A new correlation incorporating the effect of viscosity on slug frequency has been proposed for the horizontal flow, which represents the main contribution of this work.

Keywords: gamma densitometer, flow pattern, pressure gradient, slug frequency

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Authors: Khoshnaw Khalid Hama Saleh, Ergun Ercelebi

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Increasingly complex modern power systems require stability, especially for transient and small disturbances. Transient stability plays a major role in stability during fault and large disturbance. This paper compares a power system stabilizer (PSS) and static Var compensator (SVC) to improve damping oscillation and enhance transient stability. The effectiveness of a PSS connected to the exciter and/or governor in damping electromechanical oscillations of isolated synchronous generator was tested. The SVC device is a member of the shunt FACTS (flexible alternating current transmission system) family, utilized in power transmission systems. The designed model was tested with a multi-machine system consisting of four machines six bus, using MATLAB/SIMULINK software. The results obtained indicate that SVC solutions are better than PSS.

Keywords: FACTS, MATLAB/SIMULINK, multi-machine system, PSS, SVC, transient stability

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Authors: Himanshu J. Bahirat, Apoorva S. Janawlekar

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Plasma actuators are essential for aerodynamic flow separation control due to their lack of mechanical parts, lightweight, and high response frequency, which have numerous applications in hypersonic or supersonic aircraft. The working of these actuators is based on the formation of a low-temperature plasma between a pair of parallel electrodes by the application of a high-voltage AC signal across the electrodes, after which air molecules from the air surrounding the electrodes are ionized and accelerated through the electric field. The high-frequency operation is required in dielectric discharge barriers to ensure plasma stability. To carry out flow separation control in a hypersonic flow, the optimal design and construction of a power supply to generate dielectric barrier discharges is carried out in this paper. In this paper, it is aspired to construct a simplified circuit topology to emulate the dielectric barrier discharge and study its various frequency responses. The power supply can generate high voltage pulses up to 20kV at the repetitive frequency range of 20-50kHz with an input power of 500W. The power supply has been designed to be short circuit proof and can endure variable plasma load conditions. Its general outline is to charge a capacitor through a half-bridge converter and then later discharge it through a step-up transformer at a high frequency in order to generate high voltage pulses. After simulating the circuit, the PCB design and, eventually, lab tests are carried out to study its effectiveness in controlling flow separation.

Keywords: aircraft propulsion, dielectric barrier discharge, flow separation control, power source

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In this research, the free vibration of a rectangular sandwich nano-plate (SNP) made of three smart layers in the visco Pasternak foundation is studied. The core of the sandwich is a piezo magnetic nano-plate integrated with two layers of piezoelectric materials. First-order shear deformation plate theory is utilized to derive the motion equations by using Hamilton’s principle, piezoelectricity, and modified couple stress theory. Elastic medium is modeled by visco Pasternak foundation, where the damping coefficient effect is investigated on the stability of sandwich nano-plate. These equations are solved by the differential quadrature method (DQM), considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, shear correction factor, damping coefficient, and boundary conditions on the dimensionless frequency of sandwich nano-plate. The results are also compared by those available in the literature, and these findings can be used for automotive industry, communications equipment, active noise, stability, and vibration cancellation systems and utilized for designing the magnetostrictive actuator, motor, transducer and sensors in nano and micro smart structures.

Keywords: free vibration, modified couple stress theory, sandwich nano-plate, visco Pasternak foundation

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Authors: Xize Dai, Jian Hao, Claus Leth Bak, Gian Carlo Montanari, Huai Wang

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Printed Circuit Board (PCB) is a critical component applicable to power electronics systems, especially for high-voltage applications involving several high-voltage and high-frequency SiC/GaN devices. The insulation system of PCB is facing more challenges from high-voltage and high-frequency stress that can alter the dielectric properties. Dielectric properties of the PCB insulation system also determine the electrical field distribution that correlates with intrinsic and extrinsic aging mechanisms. Hence, investigating the dielectric properties in the frequency domain of the PCB insulation system is a must. The paper presents the frequency-dependent, temperature-dependent, and voltage-dependent dielectric properties, permittivity, conductivity, and dielectric loss tangents of PCB insulation systems. The dielectric properties mechanisms associated with frequency, temperature, and voltage are revealed from the design perspective. It can be concluded that the dielectric properties of PCB in the frequency domain show a strong dependence on voltage, frequency, and temperature. The voltage-, frequency-, and temperature-dependent dielectric properties are associated with intrinsic conduction behavior and polarization patterns from the perspective of dielectric theory. The results may provide some reference for the PCB insulation system design in high voltage, high frequency, and high-temperature power electronics applications.

Keywords: electrical insulation system, dielectric properties, high voltage and frequency, printed circuit board

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Authors: E. A. Alshaafi, A. Prakash

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Oil-water emulsions are commonly encountered in various industrial operations and at different stages of crude oil production and processing. Emulsions are often difficult to track and treat and can cause a number of costly problems which need to be avoided. The characteristics of the emulsion phase can vary with crude composition and types of impurities present in oil. The objectives of this study are the development of ultrasonic techniques to track and characterize emulsion phase generated during production and cleaning of crude oil. The position of emulsion layer is monitored with the help of ultrasonic probes suitably placed in the vessel. The sensitivity of the technique and its potential has been demonstrated based on extensive testing with different oil samples. The technique is also being developed to monitor emulsion phase characteristics such as stability, composition, and droplet size distribution. The ultrasonic parameters recorded are changes in acoustic velocity, signal attenuation and its frequency spectrum. Emulsion has been prepared with light mineral oil sample and the effects of various factors including mixing speed, temperature, surfactant, and solid particles concentrations have been investigated. The applied frequency for ultrasonic waves has been varied from 1 to 5 MHz to carry out a sensitivity analysis. Emulsion droplet structure is observed with optical microscopy and stability is examined by tracking the changes in ultrasonic parameters with time. A model based on ultrasonic attenuation spectroscopy is being developed and tested to track changes in droplet size distribution with time.

Keywords: ultrasonic techniques, emulsion, characterization, droplet size

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Authors: L. Maiza, A. Cantagrel, M. Forestier, G. Laucoin, T. Regali

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Evaluation of High Frequency Trading (HFT) impact on financial markets is very important for traders who use market analysis to detect winning transaction opportunity. Analysis of HFT data on tobacco commodity market is discussed here and interesting linear relationship has been shown between trading frequency and difference between averaged trading prices above and below considered trading frequency. This may open new perspectives on markets data understanding and could provide possible interpretation of Adam Smith invisible hand.

Keywords: financial market, high frequency trading, analysis, impacts, Adam Smith invisible hand

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Authors: Azeddine Ghodbane, David Bensoussan, Maher Hammami

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An innovative approach for controlling unstable and invertible systems has demonstrated superior performance compared to conventional controllers. It has been successfully applied to a levitation system and drone control. Simulations have yielded satisfactory performances when applied to a satellite antenna controller. This design method, based on sensitivity analysis, has also been extended to handle multivariable unstable and invertible systems that exhibit dominant diagonal characteristics at high frequencies, enabling decentralized control. Furthermore, this control method has been expanded to the realm of adaptive control. In this study, we introduce an alternative adaptive architecture that enhances both time and frequency performance, helpfully mitigating the effects of disturbances from the input plant and external disturbances affecting the output. To facilitate superior performance in both the time and frequency domains, we have developed user-friendly interactive design methods using the GeoGebra platform.

Keywords: control theory, decentralized control, sensitivity theory, input-output stability theory, robust multivariable feedback control design

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Authors: Eti Dwi Wiraningsih, Folashade Agusto, Lina Aryati, Syamsuddin Toaha, Suzanne Lenhart, Widodo, Willy Govaerts

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This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs-domestic dogs-human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh-Hurwitz test to analyze the stability of the Disease-Free Equilibrium and Endemic Equilibrium of this model.

Keywords: stability analysis, rabies model, vaccination effect, culling in dogs

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

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Authors: Yufu Yin, Tao Lin, Shanghong Zhao, Zihang Zhu, Xuan Li, Wei Jiang, Qiurong Zheng, Hui Wang

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In this paper, a frequency-dependent and tunable phase shifter is proposed and numerically analyzed. The key devices are the dual-polarization binary phase shift keying modulator (DP-BPSK) and the fiber Bragg grating (FBG). The phase-frequency response of the FBG is employed to determine the frequency-dependent phase shift. The simulation results show that a linear phase shift of the recovered output microwave signal which depends on the frequency of the input RF signal is achieved. In addition, by adjusting the power of the RF signal, the full range phase shift from 0° to 360° can be realized. This structure shows the spurious free dynamic range (SFDR) of 70.90 dB·Hz^2/3 and 72.11 dB·Hz^2/3 under different RF powers.

Keywords: microwave photonics, phase shifter, spurious free dynamic range, frequency-dependent

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Authors: Vladimir Mantsevich, Natalya Maslova, Petr Arseyev

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We investigated the tunneling current peculiarities in the system of two coupled by means of the external field quantum dots (QDs) weakly connected to the electrodes in the presence of Coulomb correlations between localized electrons by means of Heisenberg equations for pseudo operators with constraint. Special role of multi-electronic states was demonstrated. Various single-electron levels location relative to the sample Fermi level and to the applied bias value in symmetric tunneling contact were investigated. Rabi frequency tuning results in the single-electron energy levels spacing. We revealed the appearance of negative tunneling conductivity and demonstrated multiple switching "on" and "off" of the tunneling current depending on the Coulomb correlations value, Rabi frequency amplitude and energy levels spacing. We proved that Coulomb correlations strongly influence the system behavior. We demonstrated the presence of multi-stability in the coupled QDs with Coulomb correlations when single value of the tunneling current amplitude corresponds to the two values of Rabi frequency in the case when both single-electron energy levels are located slightly above eV and are close to each other. This effect disappears when the single-electron energy levels spacing increases.

Keywords: Coulomb correlations, negative tunneling conductivity, quantum dots, rabi frequency

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Authors: M. Meenasaranya, S. Saravanan

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Nonlinear stability analysis is carried out to determine the effect of surface temperature modulation in an infinite horizontal porous layer heated from below. The layer is saturated by an electrically conducting, viscous, incompressible and Newtonian fluid. The Brinkman model is used for momentum equation, and the Boussinesq approximation is invoked. The system is assumed to be bounded by rigid boundaries. The energy theory is implemented to find the global exponential stability region of the considered system. The results are analysed for arbitrary values of modulation frequency and amplitude. The existence of subcritical instability region is confirmed by comparing the obtained result with the known linear result. The vertical magnetic field is found to stabilize the system.

Keywords: Brinkman model, energy method, magnetic field, surface temperature modulation

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Authors: Kreangkri Ratchagit

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This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: O. S. Omorogiuwa, E. J. Omozusi

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The monitoring of spectrum usage and signal identification, using cognitive radio, is done to identify frequencies that are vacant for reuse. It has been established that ‘internet of things’ device uses secondary frequency which is free, thereby facing the challenge of interference from other users, where some primary frequencies are not being utilised. The design was done by analysing a specific frequency spectrum, checking if all the frequency stations that range from 87.5-108 MHz are presently being used in Benin City, Edo State, Nigeria. From the results, it was noticed that by using Software Defined Radio/Simulink, we were able to identify vacant frequencies in the range of frequency under consideration. Also, we were able to use the significance of energy detection threshold to reuse this vacant frequency spectrum, when the cognitive radio displays a zero output (that is decision H0), meaning that the channel is unoccupied. Hence, the analysis was able to find the spectrum hole and identify how it can be reused.

Keywords: spectrum, interference, telecommunication, cognitive radio, frequency

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Authors: Seyed Mohammad Nasir Mousavi, Amir Mashayekh, Pasha Hejazi, Sanaz Kanani Zadeh Khalkhali

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To determine the stability of the oil percent canola varieties, an experiment was done in a randomized complete block design with four replications in four research stations of the country Shahrood, Esfahan, Kermanshah, Varamin. Analysis of variance showed that there is cultivars considerable variability in the percentage of oil. The results showed that the coefficient of variation of oil Hyola 401 and Hyola308 stability and flexibility are high. Cultivars Cooper and Likord are minimum variance Shukla that stable for the percentage of oil Based on the chart AMMI 1, cultivars Zarfam and Hyola 401 are of oil percentage than other varieties had higher stability. On the chart AMMI2, cultivars Karun and Hyola 308 are identified as stable, also location Isfahan is stable

Keywords: canola, stability, AMMI, variance Shukla

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Authors: Puneet Chawla, Balwinder Singh

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Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper, P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton-Raphson method. Using Q-V curves, the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: voltage stability, reactive power, power flow, weakest bus, STATCOM

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Authors: Mohamed Ayoub

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The structures and energetics of various isomeric hydrogen bonded dimers, such as (FH…OC, FH…CO), (FH…CNH, FH…NCH), (FH…N2O, FH…ON2), and (FH…NHCO, FH…OCNH) have been investigated using DFT B3LYP with aug-cc-pVTZ basis set and by natural bond orbital (NBO) analysis. For each isomeric pair we calculated: H-bond energy (ΔEB…H), charge-transfer (QCT), where B is atom bearing lone-pairs in CO, CNH, NCH, N2O, and NHCO, H-bond distances (RB…H), the elongation of HF bond (ΔRHF) and the red-shift of HF stretching frequency (ΔVHF). We conclude that the principle difference in the relative stability between each isomeric pair is attributed to distinctive interaction of carbon and oxygen lone pairs of CO, carbon and nitrogen lone-pairs of CNH and NCH, and nitrogen and oxygen lone pairs of N2O and NHCO into the unfilled antibond on HF (σ*HF).

Keywords: charge transfer, computational chemistry, isomeric hydrogen bond, natural bond orbital

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Authors: Umair Ashraf, Kjetil Uhlen, Sverre Eriksen, Nadeem Jelani

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Although advancement in technology has increased the reliability and ease of work in ship power system, but these advancements are also adding complexities. Ever increasing non linear loads, like power electronics (PE) devices effect the stability of the system. Frequent load variations and complex load dynamics are due to the frequency converters and motor drives, these problem are more prominent when system is connected with the weak grid. In the ship power system major consumers are thruster motors for the propulsion. For the control operation of these motors variable frequency drives (VFD) are used, mostly VFDs operate on nominal voltage of the system. Some of the consumers in ship operate on lower voltage than nominal, these consumers got supply through step down transformers. In this paper the vector control scheme is used for the control of both rectifier and inverter, parallel operation of the synchronous generators is also demonstrated. The simulation have been performed with induction motor as load on VFD and parallel RLC load. Fault analysis has been performed first for the system which do not have VFD and then for the system with VFD. Three phase to the ground, single phase to the ground fault were implemented and behavior of the system in both the cases was observed.

Keywords: non-linear load, power electronics, parallel operating generators, pulse width modulation, variable frequency drives, voltage source converters, weak grid

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Authors: Der Chyan Lin

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Since the early introduction by Ormondroyd and Den Hartog, vibration absorber (VA) has become one of the most commonly used vibration mitigation strategies. The strategy is most effective for a primary plant subjected to a single frequency excitation. For continuous systems, notable advances in vibration absorption in the multi-frequency system were made. However, the efficacy of the VA strategy for systems under multi-frequency excitation is not well understood. For example, for an N degrees-of-freedom (DOF) primary-absorber system, there are N 'peak' frequencies of large amplitude vibration per every new excitation frequency. In general, the usable range for vibration absorption can be greatly reduced as a result. Frequency modulated harmonic excitation is a commonly seen multi-frequency excitation example: f(t) = cos(ϖ(t)t) where ϖ(t)=ω(1+α sin⁡(δt)). It is known that f(t) has a series expansion given by the Bessel function of the first kind, which implies an infinity of forcing frequencies in the frequency modulated harmonic excitation. For an SDOF system of natural frequency ωₙ subjected to f(t), it can be shown that amplitude peaks emerge at ω₍ₚ,ₖ₎=(ωₙ ± 2kδ)/(α ∓ 1),k∈Z; i.e., there is an infinity of resonant frequencies ω₍ₚ,ₖ₎, k∈Z, making the use of VA strategy ineffective. In this work, we propose an absorber frequency placement strategy for SDOF vibration systems subjected to frequency-modulated excitation. An SDOF linear mass-spring system coupled to lateral absorber systems is used to demonstrate the ideas. Although the mechanical components are linear, the governing equations for the coupled system are nonlinear. We show using N identical absorbers, for N ≫ 1, that (a) there is a cluster of N+1 natural frequencies around every natural absorber frequency, and (b) the absorber frequencies can be moved away from the plant's resonance frequency (ω₀) as N increases. Moreover, we also show the bandwidth of the VA performance increases with N. The derivations of the clustering and bandwidth widening effect will be given, and the superiority of the proposed strategy will be demonstrated via numerical experiments.

Keywords: Bessel function, bandwidth, frequency modulated excitation, vibration absorber

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Authors: Nikolai Bertelsen, Robert A. Alphinas, Klaus B. Orskov

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The shortest possible tool stickout has been the traditional go-to approach with expectations of increased stability and productivity. However, experimental studies at Danish Advanced Manufacturing Research Center (DAMRC) have proven that for some tool stickout lengths, there exist local productivity optimums when utilizing the Stability Lobe Diagrams for chatter avoidance. This contradicts with traditional logic and the best practices taught to machinists. This paper explores the vibrational characteristics and behaviour of a milling system over the tool stickout length. The experimental investigation has been conducted by tap testing multiple endmills where the tool stickout length has been varied. For each length, the modal parameters have been recorded and mapped to visualize behavioural tendencies. Furthermore, the paper explores the correlation between the modal parameters and the Stability Lobe Diagram to outline the influence and importance of each parameter in a multi-mode system. The insights are conceptualized into a tool tuning approximation solution. It builds on an almost linear change in the natural frequencies when amending tool stickout, which results in changed positions of the Chatter-free Stability Lobes. Furthermore, if the natural frequency of two modes become too close, it will onset of the dynamic absorber effect phenomenon. This phenomenon increases the critical stable depth of cut, allowing for a more stable milling process. Validation tests on the tool tuning approximation solution have shown varying success of the solution. This outlines the need for further research on the boundary conditions of the solution to understand at which conditions the tool tuning approximation solution is applicable. If the conditions get defined, the conceptualized tool tuning approximation solution outlines an approach for quick and roughly approximating tool stickouts with the potential for increased stiffness and optimized productivity.

Keywords: milling, modal parameters, stability lobes, tap testing, tool tuning

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