Search results for: Fast Voltage Stability Index (FVSI)

Authors: Tanapat Brikshavana, Anirut Luadsong

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Keywords: donor-cell scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Xingyuan Qu, Shouming Zhong

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In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: Delay-dependent stability, time-varying delays, Lyapunov functional, linear matrix inequality (LMI).

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Authors: V. Swarnalatha, A. V. Narasimha Rao, P. Pal

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The present research reports the investigation of fast etching of silicon for the fabrication of microelectromechanical systems (MEMS) structures using silicon wet bulk micromachining. Low concentration tetramethyl-ammonium hydroxide (TMAH) and hydroxylamine (NH₂OH) are used as main etchant and additive, respectively. The concentration of NH₂OH is varied to optimize the composition to achieve best etching characteristics such as high etch rate, significantly high undercutting at convex corner for the fast release of the microstructures from the substrate, and improved etched surface morphology. These etching characteristics are studied on Si{100} and Si{110} wafers as they are most widely used in the fabrication of MEMS structures as wells diode, transistors and integrated circuits.

Keywords: KOH, MEMS, micromachining, silicon, TMAH, wet anisotropic etching.

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Authors: Sidhartha Panda, N.P.Padhy, R.N.Patel

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This paper presents a procedure for modeling and tuning the parameters of Thyristor Controlled Series Compensation (TCSC) controller in a multi-machine power system to improve transient stability. First a simple transfer function model of TCSC controller for stability improvement is developed and the parameters of the proposed controller are optimally tuned. Genetic algorithm (GA) is employed for the optimization of the parameter-constrained nonlinear optimization problem implemented in a simulation environment. By minimizing an objective function in which the oscillatory rotor angle deviations of the generators are involved, transient stability performance of the system is improved. The proposed TCSC controller is tested on a multi-machine system and the simulation results are presented. The nonlinear simulation results validate the effectiveness of proposed approach for transient stability improvement in a multimachine power system installed with a TCSC. The simulation results also show that the proposed TCSC controller is also effective in damping low frequency oscillations.

Keywords: Genetic algorithm, TCSC, transient stability, multimachinepower system.

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Authors: Peng Lu, Branimir Radisavljevic, Martin Seeger, Daniel Over, Torsten Votteler, Bernardo Galletti

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CO₂-based gas mixtures exhibit huge potential as the interruption medium for replacing SF₆ in high voltage switchgears. In this paper, the recovery characteristics of dielectric strength of CO₂-O₂ mixture in the post arc phase after the current zero are presented. As representative examples, the dielectric recovery curves under conditions of different gas filling pressures and short-circuit current amplitudes are presented. A series of dielectric recovery measurements suggests that the dielectric recovery rate is proportional to the mass flux of the blowing gas, and the dielectric strength recovers faster in the case of lower short circuit currents.

Keywords: CO2 mixture, high voltage circuit breakers, dielectric recovery rate, short-circuit current, mass flux.

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Authors: Khaled M.EL-Naggar

Abstract:

In power systems, protective relays must filter their inputs to remove undesirable quantities and retain signal quantities of interest. This job must be performed accurate and fast. A new method for filtering the undesirable components such as DC and harmonic components associated with the fundamental system signals. The method is s based on a dynamic filtering algorithm. The filtering algorithm has many advantages over some other classical methods. It can be used as dynamic on-line filter without the need of parameters readjusting as in the case of classic filters. The proposed filter is tested using different signals. Effects of number of samples and sampling window size are discussed. Results obtained are presented and discussed to show the algorithm capabilities.

Keywords: Protection, DC-offset, Dynamic Filter, Estimation.

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization 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 and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: N. Sumathi, R. Srinivasa Rao

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This paper presents the experimental results of 11 kV and 33 kV silicon composite insulators under artificial salt and urea polluted conditions. The tests were carried out under different seasons like summer, winter, and monsoon. The artificial pollution is prepared by properly dissolving the salt and urea in the water. The prepared salt and urea pollutions are sprayed on the insulators and dried up for sufficiently large time. The process is continued until a uniform layer is formed on the surface of insulator. For each insulator rating, four samples were tested. The maximum leakage current and breakdown voltage were measured. From experimental data, performance of test specimen is evaluated by comparing breakdown voltage and leakage current during different seasons when exposed to salt and urea polluted conditions. From these results the performance of the insulators can be predicted when they are installed in industrial, agricultural, and coastal areas. The experimental tests were carried out in the High Voltage laboratory using two stage cascade transformer having the rating of 1000 kVA, 500 kV.

Keywords: Silicon composite insulators, Urea pollution, Leakage current, Breakdown voltage, salt pollution, artificial pollution.

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Authors: A. Zeynolabedin, M. A. Olyaei, B. Ghiasi

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Drought is an inevitable part of the earth’s climate. It occurs regularly with no clear warning and without recognizing borders. In addition, its impact is cumulative and not immediately discernible. Iran is located in a semi-arid region where droughts occur periodically as natural hazard. Standardized Precipitation Index (SPI), Surface Water Supply Index (SWSI), and Palmer Drought Severity Index (PDSI) are three well-known indices which describe drought severity; each has its own advantages and disadvantages and can be used for specific types of drought. These indices take into account some factors such as precipitation, reservoir storage and discharge, temperature, and potential evapotranspiration in determining drought severity. In this paper, first all three indices are calculated in Aharchay river watershed located in northwestern part of Iran in East Azarbaijan province. Next, based on two other important parameters which are groundwater level and solar radiation, two new indices are defined. Finally, considering all five aforementioned indices, a combined drought index (CDI) is presented and calculated for the region. This combined index is based on all the meteorological, hydrological, and agricultural features of the region. The results show that the most severe drought condition in Aharchay watershed happened in Jun, 2004. The result of this study can be used for monitoring drought and prepare for the drought mitigation planning.

Keywords: Drought, index variation, regional assessment, monitoring.

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Authors: Abeer A. Abdelhamed

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Background: Diabetic sensorimotor polyneuropathy (DSP) is one of the most common microvascular complications of type 2 diabetes. Loss of sensation is thought to contribute to a lack of static and dynamic stability and increased risk of falling. Purpose: The purpose of this study was to compare the effects of low-level laser (LLL) and monochromatic near-infrared photo energy (MIRE) on pain, cutaneous sensation, static stability, and index of lower limb blood flow in diabetic patients with peripheral neuropathy. Methods: Forty diabetic patients with peripheral neuropathy were recruited for participation in this study. They were divided into two groups: The MIRE group, which contained 20 patients, and the LLL group, which contained 20 patients. All patients who participated in the study had been subjected to various physical assessment procedures, including pain, cutaneous sensation, Doppler flow meter, and static stability assessments. The baseline measurements were followed by treatment sessions that were conducted twice a week for six successive weeks. Results: The statistical analysis of the data revealed significant improvement of pain in both groups, with significant improvement in cutaneous sensation and static balance in the MIRE group compared to the LLL group; on the other hand, the results showed no significant differences in lower limb blood flow between the groups. Conclusion: LLL and MIRE can improve painful symptoms in patients with diabetic neuropathy. On the other hand, MIRE is also useful in improving cutaneous sensation and static stability in patients with diabetic neuropathy.

Keywords: Diabetic neuropathy, Doppler flow meter, –Lowlevel laser, Monochromatic near-infrared photo energy.

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Authors: Tahmine. V. Moghaddam, N. Bigdeli, K. Afshar

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To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure.

Keywords: Fractional controller, Lead compensator, Stabilityregions, Stability boundary locus

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Authors: Elyse Sili, Jean Pascal Cambronne

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In aircraft applications, according to the nature of electrical equipment its location may be in unpressurized area or very close to the engine; thus, the environmental conditions may change from atmospheric pressure to less than 100 mbar, and the temperature may be higher than the ambient one as in most real working conditions of electrical equipment. Then, the classical Paschen curve has to be replotted since these parameters may affect the discharge ignition voltage. In this paper, we firstly investigate the domain of validity of two corrective expressions on the Paschen-s law found in the literature, in case of changing the air environment and known as Peek and Dunbar corrections. Results show that these corrections are no longer valid for combined variation of temperature and pressure. After that, a new empirical expression for breakdown voltage is proposed and is validated in the case of combined variations of temperature and pressure.

Keywords: Gas breakdown, gas density, Paschen curve, temperature effects

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Authors: Zhengisbek Tolen, Kubash Mengdigali, Dinara Akbolat, Elnura Assyltaeva, Aliya Alimzhanova

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In the article the historical formation of interethnic and interconfessional agreement policy in Kazakhstan and their developing features at present time will be analyzed. The successfully pursued by Kazakhstan at the present in the direction of ethnic and confessional policy is regarded as a major factor in promoting stability for the country.

Keywords: Political stability, interethnic relationship, interconfessional agreement, tolerance.

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Authors: Ti-An Tsai, Chun-Chih Wang, Hung-Wen Wang, I-Ling Chang, Lien-Wen Chen

Abstract:

In this study, we demonstrate a high-resolution refractive index sensor based on a Magnetic Photonic Crystal (MPC) composed of a triangular lattice array of air holes embedded in Si matrix. A microcavity is created by changing the radius of an air hole in the middle of the photonic crystal. The cavity filled with gyrotropic materials can serve as a refractive index sensor. The shift of the resonant frequency of the sensor is obtained numerically using finite difference time domain method under different ambient conditions having refractive index from n = 1.0 to n = 1.1. The numerical results show that a tiny change in refractive index of  Δn = 0.0001 is distinguishable. In addition, the spectral response of the MPC sensor is studied while an external magnetic field is present. The results show that the MPC sensor exhibits a dramatic improvement in resolution.

Keywords: Magnetic photonic crystal, refractive index sensor, sensitivity, high-resolution.

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Authors: Nawang Chhunid, Gagnesh Kumar

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On-chip memories consume a significant portion of the overall die space and power in modern microprocessors. On-chip caches depend on Static Random-Access Memory (SRAM) cells and scaling of technology occurring as per Moore’s law. Unfortunately, the scaling is affecting stability, performance, and leakage power which will become major problems for future SRAMs in aggressive nanoscale technologies due to increasing device mismatch and variations. 3T1D Dynamic Random-Access Memory (DRAM) cell is a non-destructive read DRAM cell with three transistors and a gated diode. In 3T1D DRAM cell gated diode (D1) acts as a storage device and also as an amplifier, which leads to fast read access. Due to its high tolerance to process variation, high density, and low cost of memory as compared to 6T SRAM cell, it is universally used by the advanced microprocessor for on chip data and program memory. In the present paper, it has been shown that 3T1D DRAM cell can perform better in terms of fast read access as compared to 6T, 4T, 3T SRAM cells, respectively.

Keywords: DRAM cell, read access time, tanner EDA tool write access time and retention time, average power dissipation.

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Authors: Yu-Wei Chen, Li-Ren Han

Abstract:

In this paper, we employ the approach of linear programming to propose a new interactive broadcast method. In our method, a film S is divided into n equal parts and broadcast via k channels. The user simultaneously downloads these segments from k channels into the user-s set-top-box (STB) and plays them in order. Our method assumes that the initial p segments will not have fast-forwarding capabilities. Every time the user wants to initiate d times fast-forwarding, according to our broadcasting strategy, the necessary segments already saved in the user-s STB or are just download on time for playing. The proposed broadcasting strategy not only allows the user to pause and rewind, but also to fast-forward.

Keywords: Broadcasting, Near Video-on-Demand (VOD), Linear Programming, Video-Cassette-Recorder (VCR) Functions, Waiting Time.

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Authors: Saeed H. Nasiri, Rahim Faez, Bita Davoodi, Maryam Farrokhi

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Bode stability analysis based on transmission line modeling (TLM) for single wall carbon nanotube (SWCNT) interconnects used in 3D-VLSI circuits is investigated for the first time. In this analysis, the dependence of the degree of relative stability for SWCNT interconnects on the geometry of each tube has been acquired. It is shown that, increasing the length and diameter of each tube, SWCNT interconnects become more stable.

Keywords: Bode stability criterion, Interconnects, Interlayer via, Single wall carbon nanotubes, Transmission line method, Time domain analysis

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Authors: O. S. Ebrahim, M. A. Badr, A. S. Elgendy, K. O. Shawky, P. K. Jain

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This paper demonstrates an improved Loss Model Control (LMC) for a 3-phase induction motor (IM) driving pump load. Compared with other power loss reduction algorithms for IM, the presented one has the advantages of fast and smooth flux adaptation, high accuracy, and versatile implementation. The performance of LMC depends mainly on the accuracy of modeling the motor drive and losses. A loss-model for IM drive that considers the surplus power loss caused by inverter voltage harmonics using closed-form equations and also includes the magnetic saturation has been developed. Further, an Artificial Neural Network (ANN) controller is synthesized and trained offline to determine the optimal flux level that achieves maximum drive efficiency. The drive’s voltage and speed control loops are connecting via the stator frequency to avoid the possibility of excessive magnetization. Besides, the resistance change due to temperature is considered by a first-order thermal model. The obtained thermal information enhances motor protection and control. These together have the potential of making the proposed algorithm reliable. Simulation and experimental studies are performed on 5.5 kW test motor using the proposed control method. The test results are provided and compared with the fixed flux operation to validate the effectiveness.

Keywords: Artificial neural network, ANN, efficiency optimization, induction motor, IM, Pulse Width Modulated, PWM, harmonic losses.

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Authors: Sherif. S. Nafee, Ameer. K. Al-Ramady, Salem. A. Shaheen

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The analytical prediction of the decay heat results from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team from King Abdulaziz University (KAU), Saudi Arabia, and supervised by Argonne National Laboratory (ANL) has collaborated with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic comparisons with the measurements reported by the University of Tokyo, in YAYOI reactor.

Keywords: Decay heat, fast neutron fission, and Numerical Solution of Linear Differential Equations.

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Authors: Hanan A. M. Abd Alla, Lilac A. E. Al-Safadi

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In this paper, a novel multi join algorithm to join multiple relations will be introduced. The novel algorithm is based on a hashed-based join algorithm of two relations to produce a double index. This is done by scanning the two relations once. But instead of moving the records into buckets, a double index will be built. This will eliminate the collision that can happen from a complete hash algorithm. The double index will be divided into join buckets of similar categories from the two relations. The algorithm then joins buckets with similar keys to produce joined buckets. This will lead at the end to a complete join index of the two relations. without actually joining the actual relations. The time complexity required to build the join index of two categories is Om log m where m is the size of each category. Totaling time complexity to O n log m for all buckets. The join index will be used to materialize the joined relation if required. Otherwise, it will be used along with other join indices of other relations to build a lattice to be used in multi-join operations with minimal I/O requirements. The lattice of the join indices can be fitted into the main memory to reduce time complexity of the multi join algorithm.

Keywords: Multi join, Relation, Lattice, Join indices.

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Authors: Rizwan Ullah, Abdar Ali, Zahid Ullah

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This paper illustrates the study of three isolated zero voltage switched (ZVS) PWM full bridge (FB) converters to charge the high voltage battery in the charger of electric vehicle (EV). EV battery chargers have several challenges such as high efficiency, high reliability, low cost, isolation, and high power density. The cost of magnetic and filter components in the battery charger is reduced when switching frequency is increased. The increase in the switching frequency increases switching losses. ZVS is used to reduce switching losses and to operate the converter in the battery charger at high frequency. The performance of each of the three converters is evaluated on the basis of ZVS range, dead times of the switches, conduction losses of switches, circulating current stress, circulating energy, duty cycle loss, and efficiency. The limitations and merits of each PWM FB converter are reviewed. The converter with broader ZVS range, high efficiency and low switch stresses is selected for battery charger applications in EV.

Keywords: Electric vehicle, PWM FB converter, zero voltage switching, circulating energy, duty cycle loss, battery charger.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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Authors: Fashad Amini, Lin Li

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High performance turf reinforcement mat (HPTRM) is one of the most advanced flexible armoring technologies for severe erosion challenges. The effect of turbulence on the slope stability of an earthen levee strengthened by high performance turf reinforcement mat (HPTRM) is investigated in this study for combined storm surge and wave overtopping conditions. The results show that turbulence has strong influence on the slope stability during the combined storm surge and wave overtopping conditions. Among the surge height, peak wave force and turbulent force. The turbulent force has the ability to stabilize the earthen levee at the large wave force the turbulent force has strongest effect on the FS. The surge storm acts as an independent force on the slope stability of the earthen levee. It just adds to the effects of the turbulent force and wave force on the slope stability of HPTRM strengthened levee.

Keywords: Slope stability, strength reduction method, HPTRM, levee, overtopping.

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Authors: Reza Sharifian, Vagharshak Belubekyan

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This paper is concerned with an investigation into the localized non-stability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and different boundary conditions, clamped, hinged, sliding contact and free on the other edge, are considered. The mathematical model is used and a general solution is presented the conditions under which localized solutions exist are investigated.

Keywords: Localized, Non-stability, Orthotropic, Semi-infinite

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Authors: R. Srinivasa Rao

Abstract:

Individually Network reconfiguration or Capacitor control perform well in minimizing power loss and improving voltage profile of the distribution system. But for heavy reactive power loads network reconfiguration and for heavy active power loads capacitor placement can not effectively reduce power loss and enhance voltage profiles in the system. In this paper, an hybrid approach that combine network reconfiguration and capacitor placement using Harmony Search Algorithm (HSA) is proposed to minimize power loss reduction and improve voltage profile. The proposed approach is tested on standard IEEE 33 and 16 bus systems. Computational results show that the proposed hybrid approach can minimize losses more efficiently than Network reconfiguration or Capacitor control. The results of proposed method are also compared with results obtained by Simulated Annealing (SA). The proposed method has outperformed in terms of the quality of solution compared to SA.

Keywords: Capacitor Control, Network Reconfiguration, HarmonySearch Algorithm, Loss Reduction, Voltage Profile.

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Authors: Changjin Xu

Abstract:

In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.

Keywords: Two-neuron system, delay, stability, Hopf bifurcation.

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Authors: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen

Abstract:

In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.

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Authors: Siti Khairunniza-Bejo, Yusnida Yusoff, Nik Salwani Nik Yusoff, Idris Abu Seman, Mohamad Izzuddin Anuar

Abstract:

Most of the oil palm plantations have been threatened by Basal Stem Rot (BSR) disease which causes serious economic impact. This study was conducted to identify the healthy and BSRinfected oil palm tree using thirteen color indices. Multispectral and thermal camera was used to capture 216 images of the leaves taken from frond number 1, 9 and 17. Indices of normalized difference vegetation index (NDVI), red (R), green (G), blue (B), near infrared (NIR), green – blue (GB), green/blue (G/B), green – red (GR), green/red (G/R), hue (H), saturation (S), intensity (I) and thermal index (T) were used. From this study, it can be concluded that G index taken from frond number 9 is the best index to differentiate between the healthy and BSR-infected oil palm trees. It not only gave high value of correlation coefficient (R=-0.962), but also high value of separation between healthy and BSR-infected oil palm tree. Furthermore, power and S model developed using G index gave the highest R2 value which is 0.985.

Keywords: Oil palm, image processing, disease, leaves.

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Authors: A. Maamoun, Y. M. Alsayed, A. Shaltout

Abstract:

The paper presents a space-vector pulse width modulation (SVPWM) inverter feeding a permanent-magnet synchronous motor (PMSM). The SVPWM inverter enables to feed the motor with a higher voltage with low harmonic distortions than the conventional sinusoidal PWM inverter. The control strategy of the inverter is the voltage / frequency control method, which is based on the space-vector modulation technique. The proposed PMSM drive system involving the field-oriented control scheme not only decouples the torque and flux which provides faster response but also makes the control task easy. The performance of the proposed drive is simulated. The advantages of the proposed drive are confirmed by the simulation results.

Keywords: permanent-magnet synchronous motor, space-vectorPWM inverter, voltage/frequency control.

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Authors: Boualem Chetti

Abstract:

In this paper, the dynamic characteristics of a threelobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory .The finite difference technique has been used to determine the solution of the modified Reynolds equation. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show that the three-lobe bearing lubricated with micropolar fluid exhibits better stability compared with that lubricated with Newtonian fluid. According to the results obtained, the effect of the parameter micropolar fluid is remarkable on the dynamic characteristics and stability of the three-lobe bearing.

Keywords: Three-lobe bearings, Micropolar fluid, Dynamic characteristics, Stability analysis.

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