Search results for: Power curve

Authors: N.Karpagam, D.Devaraj

Abstract:

Static Var Compensator (SVC) is a shunt type FACTS device which is used in power system primarily for the purpose of voltage and reactive power control. In this paper, a fuzzy logic based supplementary controller for Static Var Compensator (SVC) is developed which is used for damping the rotor angle oscillations and to improve the transient stability of the power system. Generator speed and the electrical power are chosen as input signals for the Fuzzy Logic Controller (FLC). The effectiveness and feasibility of the proposed control is demonstrated with Single Machine Infinite Bus (SMIB) system and multimachine system (WSCC System) which show improvement over the use of a fixed parameter controller.

Keywords: FLC, SVC, Transient stability, SMIB, PIDcontroller.

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Authors: Ahmad Abubakar Sadiq, Mark N. Nwohu, Jacob Tsado, Ahmad A. Ashraf, Agbachi E. Okenna, Enesi E. Yahaya, Ambafi James Garba

Abstract:

Transmission system performance analysis is vital to proper planning and operations of power systems in the presence of deregulation. Key performance indicators (KPIs) are often used as measure of degree of performance. This paper gives a novel method to determine the transmission efficiency by evaluating the ratio of real power losses incurred from a specified transfer direction. Available Transmission Transfer Efficiency (ATTE) expresses the percentage of real power received resulting from inter-area available power transfer. The Tie line (Rated system path) performance is seen to differ from system wide (Network response) performance and ATTE values obtained are transfer direction specific. The required sending end quantities with specified receiving end ATC and the receiving end power circle diagram are obtained for the tie line analysis. The amount of real power loss load relative to the available transfer capability gives a measure of the transmission grid efficiency.

Keywords: Available transfer capability, efficiency performance, real power, transmission system.

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Authors: P. Suryakumari, P. Kantarao

Abstract:

Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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Authors: M. Sreedhar Babu, Vishal Garg, S. B. Akella, Shibu Clement, N. K. S Rajan

Abstract:

Producer gas is a biomass derived gaseous fuel which is extensively used in internal combustion engines for power generation application. Unlike the conventional hydrocarbon fuels (Gasoline and Natural gas), the combustion properties of producer gas fuel are much different. Therefore, setting of optimal spark time for efficient engine operation is required. Owing to the fluctuating tendency of producer gas composition during gasification process, the heat release patterns (dictating the power output and emissions) obtained are quite different from conventional fuels. It was found that, valve lift timing is yet another factor which influences the burn rate of producer gas fuel, and thus, the heat release rate of the engine. Therefore, the present study was motivated to estimate the influence of valve lift timing analytically (Wiebe model) on the burn rate of producer gas through curve fitting against experimentally obtained mass fraction burn curves of several producer gas compositions. Furthermore, Wiebe models are widely used in zero-dimensional codes for engine parametric studies and are quite popular. This study also addresses the influence of hydrogen and methane concentration of producer gas on combustion trends, which are known to cause dynamics in engine combustion.

Keywords: Combustion Duration, crank angle, mass fraction burnt, producer gas, wiebe combustion model, wide open throttle.

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Authors: Hassan Faraji Baghtash

Abstract:

A high-speed current mirror with low-power method of adjusting current gain is presented. The current mirror provides continuous gain adjustment; yet, its gain can simply be programmed digitally, as well. The structure features the ever interesting merits of linear-in-dB gain control scheme and low power/voltage operation. The performance of proposed structure is verified through the simulation in TSMC 0.18 µm CMOS Technology. The proposed tunable gain current mirror structure draws only 18 µW from 0.9 V power supply and can operate at high frequencies up to 550 MHz in the worst case condition of maximum gain setting.

Keywords: Current mirror, current mode, low power, low voltage, tunable circuit, variable current amplifier.

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Authors: Nemat Abazari, Ilgin Sager

Abstract:

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, Rigid body motion, Lorentz metric.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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Authors: K. Busko

Abstract:

The aim of the study was to follow changes of powervelocity relationship in female volleyball players during an annual training cycle. The study was conducted on eleven female volleyball players: age 21.6±1.7 years, body height 177.9±4.7 cm, body mass 71.3±6.6 kg and training experience 8.6±3.3 years. Power–velocity relationship was determined from five maximal 10-second cycloergometer efforts with external loads equal: 2.5, 5.0, 7.5, 10.0 and 12.5% of body weight (BW) before (I) and after (II) the preparatory period, after the first (III) and second (IV) competitive season. The maximal power output increased from 9.30±0.85 W•kg–1 (I) to 9.50±0.96 W•kg–1 (II), 9.77±0.96 W•kg–1 (III) and 9.95±1.13 W•kg–1 (IV, p<0,05). The power output at the load of 2.5, 5.0, 7.5, 10.0% BW were statistically significant increased after the first and second competitive season. Power output at load of 12.5% BW was insignificant increased.

Keywords: Female, Force-velocity relationship, Power output, Volleyball

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Authors: B. Sathyanandhi, P. M. Balasubramaniam

Abstract:

This paper presents Buck-Boost converter topology to maintain the input power factor by using the power factor stage control and regulation stage control. Suppose, if we are using the RL load the power factor will be reduced due to the presence of total harmonic distortion in the current wave. To improve the power factor the current waveform should follow the fundamental component of the voltage waveform. These can be achieved by using the high -frequency power converter. Based on the resonant circuit the converter is able to perform the function of Buck, Boost, and buck-boost converter. Here ,we have used Buck-Boost converter, because, the buck-boost converter has more advantages than the boost converter. Here the switching action of the power converter can  take place by using the external zero comparator PFC stage control. The power converter consisting of the resonant  circuit which is used to control the output voltage gain of the converter. The power converter is operated at a very high switching frequency in the range of 400KHz in order to overcome the switching losses of the power converter. Due to  presence of high switching frequency, the power factor will improve. Therefore, the total harmonics distortion present in the current waveform has also reduced. These results has generated in the form of simulation by using MATLAB/SIMULINK software.  Similar to the Buck and Boost converters, the operation of the Buck-Boost has best understood, in terms of the inductor's "reluctance" for allowing rapid change in current, which also reduces the Total Harmonic Distortion (THD) in the input current waveform, which can improve the input Power factor, based on the type of load used.

Keywords: Buck-boost converter, High switching frequency, Power factor correction, power factor correction stage Regulation stage, Total harmonic distortion (THD).

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Authors: S.K. Mazloomi, Nasri b. Sulaiman

Abstract:

By analyzing the sources of energy and power loss in PWM (Pulse Width Modulation) controlled drivers of water electrolysis cells, it is possible to reduce the power dissipation and enhance the efficiency of such hydrogen production units. A PWM controlled power driver is based on a semiconductor switching element where its power dissipation might be a remarkable fraction of the total power demand of an electrolysis system. Power dissipation in a semiconductor switching element is related to many different parameters which could be fitted into two main categories: switching losses and conduction losses. Conduction losses are directly related to the built, structure and capabilities of a switching device itself and indeed the conditions in which the element is handling the switching application such as voltage, current, temperature and of course the fabrication technology. On the other hand, switching losses have some other influencing variables other than the mentioned such as control system, switching method and power electronics circuitry of the PWM power driver. By analyzings the characteristics of recently developed power switching transistors from different families of Bipolar Junction Transistors (BJT), Metal Oxide Semiconductor Field Effect Transistors (MOSFET) and Insulated Gate Bipolar Transistors (IGBT), some recommendations are made in this paper which are able to lead to achieve higher hydrogen production efficiency by utilizing PWM controlled water electrolysis cells.

Keywords: Power switch, PWM, Semiconductor switch, Waterelectrolysis

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Authors: A. Bendarma, T. Jankowiak, A. Rusinek, T. Lodygowski, M. Klósak, S. Bouslikhane

Abstract:

The analysis of the mechanical characteristics and dynamic behavior of aluminum alloy sheet due to perforation tests based on the experimental tests coupled with the numerical simulation is presented. The impact problems (penetration and perforation) of the metallic plates have been of interest for a long time. Experimental, analytical as well as numerical studies have been carried out to analyze in details the perforation process. Based on these approaches, the ballistic properties of the material have been studied. The initial and residual velocities laser sensor is used during experiments to obtain the ballistic curve and the ballistic limit. The energy balance is also reported together with the energy absorbed by the aluminum including the ballistic curve and ballistic limit. The high speed camera helps to estimate the failure time and to calculate the impact force. A wide range of initial impact velocities from 40 up to 180 m/s has been covered during the tests. The mass of the conical nose shaped projectile is 28 g, its diameter is 12 mm, and the thickness of the aluminum sheet is equal to 1.0 mm. The ABAQUS/Explicit finite element code has been used to simulate the perforation processes. The comparison of the ballistic curve was obtained numerically and was verified experimentally, and the failure patterns are presented using the optimal mesh densities which provide the stability of the results. A good agreement of the numerical and experimental results is observed.

Keywords: Aluminum alloy, ballistic behavior, failure criterion, numerical simulation.

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Authors: Jae-Kyung LEE, Byung-Hak CHO, Kyung-Nam Jang, Sun-Chul Jung, Ki-Yong OH, Joon-Young PARK, Jong-Seog Kim

Abstract:

The cables in a nuclear power plant are designed to be used for about 40 years in safe operation environment. However, the heat and radiation in the nuclear power plant causes the rapid performance deterioration of cables in nuclear vessels and heat exchangers, which requires cable lifetime estimation. The most accurate method of estimating the cable lifetime is to evaluate the cables in a laboratory. However, removing cables while the plant is operating is not allowed because of its safety and cost. In this paper, a robot system to estimate the cable lifetime in nuclear power plants is developed and tested. The developed robot system can calculate a modulus value to estimate the cable lifetime even when the nuclear power plant is in operation.

Keywords: Autonomous robot, Cable Inspection, Indenter, Nuclear Power Plant

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Authors: Mohammad Javad Dehghani

Abstract:

In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.

Keywords: Power quality, S-Transform, Short Time FourierTransform , Wavelet Transform, instantaneous sag, swell.

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Authors: Dana M. Ragab, Jasim A. Ghaeb

Abstract:

The three-phase power system suffers from different challenging problems, e.g. voltage unbalance conditions at the load side. The voltage unbalance usually degrades the power quality of the electric power system. Several techniques can be considered for load balancing including load reconfiguration, static synchronous compensator and static reactive power compensator. In this work an efficient neural network is designed to control the unbalanced condition in the Aqaba-Qatrana-South Amman (AQSA) electric power system. It is designed for highly enhanced response time of the reactive compensator for voltage balancing. The neural network is developed to determine the appropriate set of firing angles required for the thyristor-controlled reactor to balance the three load voltages accurately and quickly. The parameters of AQSA power system are considered in the laboratory model, and several test cases have been conducted to test and validate the proposed technique capabilities. The results have shown a high performance of the proposed Neural Network Control (NNC) technique for correcting the voltage unbalance conditions at three-phase load based on accuracy and response time.

Keywords: Three-phase power system, reactive power control, voltage unbalance factor, neural network, power quality.

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Authors: A. B.Bhattacharyya, B. S.K.Goswami

Abstract:

This paper presents Genetic Algorithm (GA) based approach for the allocation of FACTS (Flexible AC Transmission System) devices for the improvement of Power transfer capacity in an interconnected Power System. The GA based approach is applied on IEEE 30 BUS System. The system is reactively loaded starting from base to 200% of base load. FACTS devices are installed in the different locations of the power system and system performance is noticed with and without FACTS devices. First, the locations, where the FACTS devices to be placed is determined by calculating active and reactive power flows in the lines. Genetic Algorithm is then applied to find the amount of magnitudes of the FACTS devices. This approach of GA based placement of FACTS devices is tremendous beneficial both in terms of performance and economy is clearly observed from the result obtained.

Keywords: FACTS Devices, Line Power Flow, OptimalLocation of FACTS Devices, Genetic Algorithm.

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Authors: Talam K. E, Kainkwa R. M.

Abstract:

In this study, a field testing has been carried out to assess the power characteristics of some small scale wind turbines fabricated by one native technician from Tanzania. Two Horizontal Axis Wind Turbines (HAWTs), one with five and other with sixteen blades were installed at a height of 2.4m above the ground. The rotation speed of the rotor blade and wind speed approaching the turbines were measured simultaneously. The data obtained were used to determine how the power coefficient varies as a function of tip speed ratio and also the way in which the output power compares with available power in the wind for each turbine. For the sixteen-bladed wind turbine the maximum value of power coefficient of about 0.14 was found to occur at a tip speed ratio of around 0.65 while for the five bladed, these extreme values were respectively attained at approximately 0.2 and 1.7. The five bladed-wind turbine was found to have a higher power efficiency of about 37.5% which is higher compared to the sixteen bladed wind turbine whose corresponding value was 14.37%. This is what would be expected, as the smaller the number of blades of a wind turbine, the higher the electric power efficiency and vice versa. Some of the main reasons for the low efficiency of these machines may be due to the low aerodynamic efficiency of the turbine or low efficiency of the transmission mechanisms such as gearbox and generator which were not examined in this study. It is recommended that some other researches be done to investigate the power efficiency of such machines from different manufacturers in the country. The manufacturers should also be encouraged to use fewer blades in their designs so as to improve the efficiency and at the same time reduce materials used to fabricate the blades. The power efficiency of the electric generators used in the locally fabricated wind turbines should also be examined.

Keywords: Tip speed ratio, Power coefficients and power efficiency.

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Authors: Badr M. Alshammari, Mohamed A. El-Kady

Abstract:

The paper presents new results of a recent industry supported research and development study in which an efficient framework for evaluating practical and meaningful power system reliability and quality indices was applied. The system-wide integrated performance indices are capable of addressing and revealing areas of deficiencies and bottlenecks as well as redundancies in the composite generation-transmission-demand structure of large-scale power grids. The technique utilizes a linear programming formulation, which simulates practical operating actions and offers a general and comprehensive framework to assess the harmony and compatibility of generation, transmission and demand in a power system. Practical applications to a reduced system model as well as a portion of the Saudi power grid are also presented in the paper for demonstration purposes.

Keywords: Power systems, Linear programming, Quality assessment, Reliability.

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Authors: M. Zamin Khan, Yanjie Wang, R. Raut

Abstract:

A 1V, 1GHz low noise amplifier (LNA) has been designed and simulated using Spectre simulator in a standard TSMC 0.18um CMOS technology.With low power and noise optimization techniques, the amplifier provides a gain of 24 dB, a noise figure of only 1.2 dB, power dissipation of 14 mW from a 1 V power supply.

Keywords:

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Authors: Wenjuan Du, Jingtian Bi, Tong Wang, Haifeng Wang

Abstract:

Grid connection of a large-scale wind farm affects power system small-signal angular stability in two aspects. Firstly, connection of the wind farm brings about the change of load flow and configuration of a power system. Secondly, the dynamic interaction is introduced by the wind farm with the synchronous generators (SGs) in the power system. This paper proposes a method to assess the two aspects of the effect of the wind farm on power system small-signal angular stability. The effect of the change of load flow/system configuration brought about by the wind farm can be examined separately by displacing wind farms with constant power sources, then the effect of the dynamic interaction of the wind farm with the SGs can be also computed individually. Thus, a clearer picture and better understanding on the power system small-signal angular stability as affected by grid connection of the large-scale wind farm are provided. In the paper, an example power system with grid connection of a wind farm is presented to demonstrate the proposed approach.

Keywords: power system small-signal angular stability, power system low-frequency oscillations, electromechanical oscillation modes, wind farms, double fed induction generator (DFIG)

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Authors: Idris Elfeituri

Abstract:

In the current study, energy and exergy analysis of a 65 MW steam power plant was carried out. This study investigated the effect of variations of overall conductance of the super heater on the performance of an existing steam power plant located in Derna, Libya. The performance of the power plant was estimated by a mathematical modelling which considers the off-design operating conditions of each component. A fully interactive computer program based on the mass, energy and exergy balance equations has been developed. The maximum exergy destruction has been found in the steam generation unit. A 50% reduction in the design value of overall conductance of the super heater has been achieved, which accordingly decreases the amount of the net electrical power that would be generated by at least 13 MW, as well as the overall plant exergy efficiency by at least 6.4%, and at the same time that would cause an increase of the total exergy destruction by at least 14 MW. The achieved results showed that the super heater design and operating conditions play an important role on the thermodynamics performance and the fuel utilization of the power plant. Moreover, these considerations are very useful in the process of the decision that should be taken at the occasions of deciding whether to replace or renovate the super heater of the power plant.

Keywords: Exergy, super-heater, fouling, steam power plant, off-design.

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Authors: Sidhartha Panda, C. Ardil

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, real-coded genetic algorithm (RCGA) optimization technique is applied to design robust power system stabilizer for both singlemachine infinite-bus (SMIB) and multi-machine power system. The design problem of the proposed controller is formulated as an optimization problem and RCGA is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: Theerawut Jinayim, Somchai Arunrungrasmi, Tanes Tanitteerapan, Narong Mungkung

Abstract:

Although White LED lighting systems powered by solar cells have presented for many years, they are not widely used in today application because of their cost and low energy conversion efficiency. The proposed system use the dc power generated by fixed solar cells module to energize White LED light sources that are operated by directly connected White LED with current limitation resistors, resulting in much more power consumption. This paper presents the use of white LED as a general lighting application powered by tracking solar cells module and using pulse to apply the electrical power to the White LED. These systems resulted in high efficiency power conversion, low power consumption, and long light of the white LED.

Keywords: Efficiency, lighting, light-emitting diode, pulse, Solar, white LED.

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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

Abstract:

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

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

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Authors: Wiem Gadri

Abstract:

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral characteristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, Formal power series, Minimal polynomial degree.

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Authors: Saad Mutashar, M. A. Hannan, S. A. Samad, A. Hussain

Abstract:

This paper deals with the modified wireless power transmission system for biomedical implanted devices. The system consists of efficient class-E power amplifier and inductive power links based on spiral circular transmitter and receiver coils. The model of the class-E power amplifier operated with 13.56 MHz is designed, discussed and analyzed in which it is achieved 87.2% of efficiency. The inductive coupling method is used to achieve link efficiency up to 73% depending on the electronic remote system resistance. The improved system powered with 3.3 DC supply and the voltage across the transmitter side is 40 V whereas, cross the receiver side is 12 V which is rectified to meet the implanted micro-system circuit requirements. The system designed and simulated by NI MULTISIM 11.02.

Keywords: Wireless Transmission, inductive coupling, implanted devices, class-E power amplifier, coils design.

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Authors: Hiroaki Sumi, Kiichiro Hayashi

Abstract:

Now, the use of renewable energy power generation has been advanced. In this paper, we compared the usable amount of resource for photovoltaic power generation which was estimated using the NEDO formula and the expansion support policy of photovoltaic power generation which was researched using Internet in the municipality level in Hokkaido and Aichi Prefecture, Japan. This paper will contribute to grasp the current situation especially about the policy. As a result, there were municipalities which seemed to be no consideration of fitting the amount of resources. We think it would need to consider the suitability between the resources and policies.

Keywords: Photovoltaic power generation, expansion support policy, amount of resources, Japan.

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Authors: Lucjan Setlak, Emil Ruda

Abstract:

The subject of this paper is to review, comparative analysis and simulation of selected components of power electronic systems (PES), consistent with the concept of a more electric aircraft (MEA). Comparative analysis and simulation in software environment MATLAB / Simulink were carried out on the base of a group of representatives of civil aircraft (B-787, A-380) and military (F-22 Raptor, F-35) in the context of multi-pulse converters used in them (6- and 12-pulse, and 18- and 24-pulse), which are key components of high-tech electronics on-board power systems of autonomous power systems (ASE) of modern aircraft (airplanes of the future).

Keywords: Converters, electrical machinery, more electric aircraft, MEA, power electronics systems, PES.

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Authors: H. Abaali, M. T. Lamchich, M. Raoufi

Abstract:

There are a variety of reference current identification methods, for the shunt active power filter (SAPF), such as the instantaneous active and reactive power, the instantaneous active and reactive current and the synchronous detection method are evaluated and compared under ideal, non sinusoidal and unbalanced voltage conditions. The SAPF performances, for the investigated identification methods, are tested for a non linear load. The simulation results, using Matlab Power System Blockset Toolbox from a complete structure, are presented and discussed.

Keywords: Shunt active power filter, Current perturbation, Non sinusoidal and unbalanced voltage conditions.

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Authors: Nemat Abazari, Ilgin Sager

Abstract:

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, rigid body motion, Lorentz metric.

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