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(searched for: Problems in Electric Systems Caused by Harmonics and Solution Proposals)
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Kemal Metin, Huseyin Ceylan, Ertugrul Demirkesen, Kadir Canatan, Mikail Hizli
European Journal of Engineering and Technology Research, Volume 6, pp 137-141; doi:10.24018/ejers.2021.6.1.2343

Abstract:
Together with globalization, factories, companies and even countries can survive by competing with their rivals. Nowadays, technological superiority is one of the most important factors determining competitive power. This situation causes the result of rapid change and development of technology. Due to improvement in technology, humanity dependence on electricity is increasing day by day. Many new devices get in our lives, and both the continuity and quality of electricity comes across as an important issue. Different researches are carried out to make the energy more qualified and efficient. In terms of the stability of the used electrical devices, it is important to keep the harmonic amount in electrical energy under a certain value. Besides this, these unwanted harmonics cause additional energy losses in the energy system and negatively affect energy efficiency, which is an economically important problem. In this exercise, the problems in electrical systems, the damages in electrical devices caused by harmonics have been researched and various solution suggestions have been developed for this problem.
International Journal of Engineering and Advanced Technology, Volume 10, pp 141-147; doi:10.35940/ijeat.b2068.1210220

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G.I. Smelkov, Fgbu Vniipo Emercom Of Russia, V.A. Pekhotikov, A.I. Ryabikov, A.A. Nazarov
Occupational Safety in Industry; doi:10.24000/0409-2961-2020-11-29-36

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Mathieu Jean Pierre Pesdjock, , Daniel Tchiotsop, Marc Rostand Douanla, Godpromesse Kenne
International Journal of Dynamics and Control pp 1-11; doi:10.1007/s40435-020-00718-8

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A.A. Nikolaev, M.V. Bulanov, K.A. Shakhbieva
Vestnik IGEU pp 44-54; doi:10.17588/2072-2672.2020.4.044-054

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C. Boonseng, K. Kularbphettong
2020 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia) pp 1541-1546; doi:10.1109/icpsasia48933.2020.9208616

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Published: 12 April 2020
Applied Sciences, Volume 10; doi:10.3390/app10082666

Abstract:
High-permeability distributed wind power and photovoltaic systems are connected to the distribution network, which exacerbates the volatility and uncertainty of the distribution network. Furthermore, with the increasing demand of heating in winter and environmental protection, the wide use of electric thermal storage heating equipment (ETSHE) can promote distributed renewable energy utilization. However, an unplanned ETSHE connection to the distribution network may cause serious power quality problems. A new method of equipment location and capacity is proposed, which considered the improvement of power quality and load demand characteristics of the distribution network. First, based on heat load portrait technology, the node’s thermal load classification prediction was carried out to provide the data basis for the model solution. Second, the multi-objective optimal location and capacity programming model including harmonic distortion rate, voltage deviation, voltage fluctuation, and ETSHE cost was established. Then, the system nodes were preprocessed based on the sensitivity analysis method to reduce the number of installation nodes to be selected, and a feasible alternative set of installation nodes for the optimal configuration model of ETSHE could be obtained. Finally, the improved multi-objective particle swarm optimization algorithm was used to solve the model, and the data envelope analysis method was used to evaluate the power quality of each access scheme. The analysis of the numerical example shows that it can not only satisfy the user′s heat demand, but also effectively improve the power quality by rationally planning the location and capacity of ETSHE, which achieves the safe and efficient utilization of energy.
Mathematical and Computational Applications, Volume 25; doi:10.3390/mca25010017

Abstract:
One of the effective ways of reducing power system losses is local compensation of part of the reactive power consumption by deploying shunt capacitor banks. Since the capacitor’s impedance is frequency-dependent and it is possible to generate resonances at harmonic frequencies, it is important to provide an efficient method for the placement of capacitor banks in the presence of nonlinear loads which are the main cause of harmonic generation. This paper proposes a solution for a multi-objective optimization problem to address the optimal placement of capacitor banks in the presence of nonlinear loads, and it establishes a reasonable reconciliation between costs, along with improvement of harmonic distortion and a voltage index. In this paper, while using the harmonic power flow method to calculate the electrical quantities of the grid in terms of harmonic effects, the non-dominated sorting genetic (NSGA)-II multi-objective genetic optimization algorithm was used to obtain a set of solutions named the Pareto front for the problem. To evaluate the effectiveness of the proposed method, the problem was tested for an IEEE 18-bus system. The results were compared with the methods used in eight other studies. The simulation results show the considerable efficiency and superiority of the proposed flexible method over other methods.
Published: 9 January 2020
by IEEE
IEEE Access, Volume 8, pp 11991-12000; doi:10.1109/access.2020.2965321

Abstract:
Power factor (PF) is a measure of how effectively electricity is used. The low PF causes considerable power losses along the power supply chain. In particular, it overloads the distribution system and increases the power plant's burden to compensate the expected power losses. Most of the existing PF correction techniques are developed based on capacitor and assuming that power systems are static. However, the power systems are dynamic systems such that their states change over time, necessitating dynamic correction systems. In the emerging smart grid systems, real-time measurements can easily be taken for voltage, current and harmonics. Then, the measured data can be transmitted to a PF controller to reach the desired PF value. However, the problem that may arise in real-time applications is how to determine and adjust the optimal capacitor size that can balance the power factor. In this regard, we propose a real-time correction system based on multi-step capacitor banks to improve PF in co-operation with de-tuned filters to mitigate the harmonics. First, a mathematical model has been formulated for the proposed power factor correction system. The model can be employed to determine the optimal operational settings of the multi-step capacitor and the reactor value that optimize the reactive power while considering the desired PF value and restricting the harmonics. Second, a genetic optimization approach is applied to solve the proposed mathematical model as it can provide accurate solution in a short computational time. A Monte Carlo simulation approach is considered for validating the proposed PF correction system. The simulation results show that the average PF of the randomly generated test instances has improved from 0.7 to 0.95 (35% increase). Furthermore, we conducted real experiments using a PF testbed for experimental validation. The results are found to be consistent with the simulation results, which validate the effectiveness and applicability of the proposed correction system. Furthermore, the saved kVA in one day is estimated to be 26% of total kVA.
Muhammad Hanan, Xin Ai, Salman Azhar, Adnan Azhar, Abubakar Siddique, Waseem Aslam
2019 IEEE 3rd Conference on Energy Internet and Energy System Integration (EI2) pp 2382-2385; doi:10.1109/ei247390.2019.9061905

The publisher has not yet granted permission to display this abstract.
International Journal of Recent Technology and Engineering, Volume 8, pp 458-464; doi:10.35940/ijrte.c4192.098319

Abstract:
Power Quality (PQ) issues and its alleviation techniques are becoming one of the vital research topics, soon after the integration of power electronic devices in power system. The non-linear nature of equipment’s introduces PQ issues such as voltage sag, swell, harmonics, unbalance and transients etc. and cause damage of end user equipment’s. Poor PQ has become a vital issue which affects production and profit of both utilities and consumers. Therefore continuous monitoring and assessment of PQ is essential for finding optimal solution to analyze and mitigate various PQ problems and also maintain quality of power within the prescribed limit. For PQ analysis, it is very difficult to generate power quality events in real life in order to observe the effects or to study their characteristics. Now days, various physical PQ analyzers are available in market to continuously monitor, analyze and record PQ problems. The major drawback of this analyzer is its hardware design, complexity and its cost which limits its usage to many places. Thus online PQ monitoring is a very big challenge for researches. This paper presents modeling and simulation of virtual PQ analyzer using Lab VIEW. Lab VIEW supports a lot of library functions for an acquisition, analysis of data and also the control of instruments. This software is mainly used to model standard real instruments used in laboratories by providing more flexibility. The proposed PQ analyzer is capable of generating, identifying various PQ problems and also measuring PQ parameters RMS Voltage (Vrms), RMS Current (Irms), Total Harmonic Distortion (THD), Real, Reactive and Apparent Power from the test system. Using Lab VIEW software, a complete quality analysis of electric energy can be done online at the user's location. So that the selection of custom power devices and mitigation methods for PQ problems can be done in a perfect manner. This RTPQ analyzer is tested using real time data of hardware are acquired by the construction of test systems such as rectifier with various resistive and inductive loads. ALL PQ parameters measured using proposed PQ Analyzer are also compared with the parameters measured using fluke PQ Analyzer. The response attained has proven that the accuracy and precision of the proposed analyzer can also be used as a very good cost effective tool for online PQ study.
Joao L. Torre, Luis A. M. Barros, Joao L. Afonso, J. G. Pinto
2019 International Conference on Smart Energy Systems and Technologies (SEST) pp 1-6; doi:10.1109/sest.2019.8849010

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Karuna Nikum, Abhay Wagh, Rakesh Saxena, Arshita Singh
2019 IEEE 1st International Conference on Energy, Systems and Information Processing (ICESIP) pp 1-5; doi:10.1109/icesip46348.2019.8938339

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M. A. Noroozi, Mehdi Zarei Tazehkand, S. Hamid Fathi, J. Milimonfared
2018 IEEE 7th International Conference on Power and Energy (PECon) pp 360-365; doi:10.1109/pecon.2018.8684160

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Alejandro G. Yepes, , Hamid Toliyat
2018 IEEE Energy Conversion Congress and Exposition (ECCE) pp 776-783; doi:10.1109/ecce.2018.8558307

The publisher has not yet granted permission to display this abstract.
A. A. Sheinikov, Yu. V. Suchodolov, V. V. Zelenko
ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations, Volume 61; doi:10.21122/1029-7448-2019-61-3-235-245

Abstract:
The solution of problems of diagnostics of windings of electric machines is associated with the necessity of selection of quasi-periodic test signals against the background noise. In order to highlight useful signals, as a rule, the differences in spectral compositions of signals and noises are used. Ideally, the shape of the optimal filter frequency response should coincide with the shape of the spectrum of the useful signal, which determines the complexity of such a filter. The aim of the research is to increase the accuracy of measurements and simplify the algorithmic support of measuring systems by developing a mathematical tool that makes it possible to uniquely identify and take into account errors caused by the finiteness of the measurement intervals in the processing. Determining a one-to-one relationship between local variations of signal time parameters and alterations in its spectrum parameters is believed to be the reserve of increase of sensitivity of methods of processing of quasi-periodic signals in the conditions of constant growth of computing capabilities of measuring instruments. Variations in the values of the parameters of the signals lead to a violation of the original distribution of the harmonic components, some of the latter being subjected to the greatest alterations changes, and the some other – to the smallest ones. It is proposed to increase the accuracy of measurements due to the replacement the low-sensitivity registration of alterations in the time parameters of signals with the registration of alterations in the parameters of the characteristic harmonic components of the spectrum, which have a maximum sensitivity to deviations of the controlled parameter and a minimum sensitivity to deviations caused by the instability of the measuring equipment. The mathematical tool corresponding to the practice has been developed, that makes it possible to determine unambiguously the errors caused by finiteness of measurement intervals of quasi-periodic signals. Automatic accounting of these errors makes it possible to do without complex correlation processing of quasi-periodic signals that require large computing resources (time and speed of data processing, the amount of RAM) and to ensure the accuracy of measurements.
Renewable and Sustainable Energy Reviews, Volume 88, pp 363-372; doi:10.1016/j.rser.2018.02.011

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Yunfei Wang, Xiaodong Liang, Michael Jackman, Hooman Mazin
2018 IEEE/IAS 54th Industrial and Commercial Power Systems Technical Conference (I&CPS) pp 1-11; doi:10.1109/icps.2018.8369982

The publisher has not yet granted permission to display this abstract.
Published: 3 January 2018
Energies, Volume 11; doi:10.3390/en11010104

Abstract:
Given the increasing integration of wind-based generation systems into the electric grid, efforts have been made to deal with the problem of power quality associated with the intermittent nature of these systems. This paper presents a new modelling approach oriented towards harmonic distortion analysis of the induction machine for wind power applications. The model is developed using companion harmonic circuit modelling, which is a natural approach for analysis of the adverse effects of harmonic distortion in electric power systems, and represents an easier solution method than the well known dynamic harmonic domain, since it solves algebraic equations instead of state-space differential equations. The structure of the companion circuits simplifies both the formulation and solution for power systems with wind-based generation systems. This approach is especially useful for analysis of the harmonic interaction in transient and steady states between the wind power generator and the power system, whose interconnection is made through electronic converters. The proposed model allows us to compute the dynamics of the wind turbine, which are influenced by disturbances such as changes in the wind velocity, voltage fluctuations, electric waveform distortion, and mechanical vibrations, among other factors. Moreover, the cross-coupling between harmonic components at different frequencies is considered. The proposed model represents an integral framework of the electrical and mechanical subsystems of a wind turbine, allowing for analysis of the interactions between them, and understanding power quality degradation behaviour as well as causes and consequences, while also giving useful information on the field of simulation and control. To test the performance of the proposed model, a test power system is used to obtain the behaviour of a wind turbine induction generator in response to typical power quality disturbances, i.e., harmonic distortion, and voltage sags and swells. Then, the dynamics of the variables considering their harmonic interactions are analysed.
Feng Wang
ADVANCES IN MATERIALS, MACHINERY, ELECTRONICS II: Proceedings of the 2nd International Conference on Advances in Materials, Machinery, Electronics (AMME 2018), Volume 1955; doi:10.1063/1.5033756

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Snehal D. Kulkarni, D. B. Kulkarni, S. B. Halbhavi
2017 7th International Conference on Power Systems (ICPS) pp 714-719; doi:10.1109/icpes.2017.8387383

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Qian Yang, Bing Wei, Xinbo He, Minghao Gong
International Journal of Antennas and Propagation, Volume 2017, pp 1-8; doi:10.1155/2017/4971367

Abstract:
The near fields of electric dipole are commonly used in wide-band analysis of complex electromagnetic problems. In this paper, we propose new near field time-domain expressions for electric dipole. The analytical expressions for the frequency-domain of arbitrarily oriented electric dipole are given at first; next we give the time-domain expressions by time-frequency transformation. The proposed expressions are used in hybrid TDIE/DGTD method for analysis of circular antenna with radome. The accuracy of the proposed algorithm is verified by numerical examples.1. IntroductionThe electric dipole is an important unit in electromagnetism; its analytical expressions of the radiation field have been described in a number of works, for example, the expressions of special oriented electric dipole [1–3] and the expressions of arbitrarily oriented electric dipole by using the far-field approximation ‎[4]. But the time-domain expressions of arbitrarily oriented electric dipole are necessary to analyze the time-domain near fields problems. The near field is governed by several type fields, the relationship between and becomes very complex, and special care must be taken when dealing with near fields problems.The hybrid method takes advantage of several methods and is often used to analyze multiscale electromagnetic problems [5–7], like the shortwave antenna in complex environment ‎[8]. In this study, the analytical time-domain expressions of arbitrarily oriented electric dipole are proposed and used in hybrid TDIE/DGTD method for analysis of circular antenna with radome. The numerical results verify the validity of our algorithm.2. The Frequency-Domain Near Fields for an Arbitrarily Oriented Electric DipoleSuppose an electric dipole which along is located at original point; the polar angle and the azimuthal angle of are and , as Figure 1(a) shows. The observation point is located at , and the coordinates of point are , , and , respectively, as Figure 1(b) shows.Figure 1: The arbitrarily oriented electric dipole.The magnetic vector potential produced by the electric current in an infinite medium can be written aswhere , , , , and are the permeability, the position vector of the integrating point, the position vector of the observation point , the distance from the integrating point to the observation point, and the wave number, respectively, as Figure 1(c) shows.A short current source can be seen as an electric dipole; considering the characteristic of the function, we havewhere is defined aswhere the , , and are the unit vector of the rectangular coordinate system. Magnetic field can be evaluated aswhich implies curl elements of (4) can be rewritten asSubstituting (6) into (2), we get expression of magnetic field for the frequency-domain of an arbitrarily oriented electric dipoleThe expression of electric field issubstituting (2) into (8), we havewhere3. The Time-Domain Near Fields for an Arbitrarily Oriented Electric DipoleAn electric dipole consists of a positive charge and an negative charge , distance apart. The dipole moment , so that electric current can be represented asSubstituting (11) into (7),The time-frequency conversion relation and the flourier transformation areThe time-domain expression of (12) can be obtained by (13)The time-domain expression of electric field can be obtained in the same way4. The Hybrid Method Combining DGTD and TDIE for Wire Antenna-Dielectric InteractionTDIE is widely used for analyzing thin-wire antenna (radiation on scattering) problems, but it is difficult to deal with interaction of the antenna and complexity media. The TDIE/FDTD method and the FDTD/FETD/TDIE method have been proposed for complex electromagnetic problems ‎[9, 10]. Discontinuous Galerkin Time-Domain (DGTD) method [11–15] inherits from Finite Element Time-Domain (FETD) the advantage of unstructured grids without solving large linear systems. DGTD is more flexible than Finite Difference Time-Domain (FDTD) method in geometry modeling, but like FDTD, it also becomes resource-consuming dealing with thin-wire structures.Gao et al. proposed the TDIE/DGTD method ‎[16]; in our study, the currents on the antenna can be easily obtained by TDIE. These currents are used to calculate fields on Huygens surface which yields the same radiating fields. The fields are deduced from our new expressions, as shown in Figure 2.Figure 2: The hybrid TDIE/DGTD method.4.1. A Circular AntennaThe antenna is parallel to the XOY plane, the radius of the antenna is 0.5 meter, the excitation wavelength is 0.5 meter, and the time harmonic current is excited at every line element (Figure 3). The normalized results of TDIE/DGTD with our new expressions are shown in Figures 4(a) and 4(b); a good agreement is observed between our algorithm (circle) and analytical solution (solid line) ‎[17].Figure 3: Circular antenna (divided into 35 straight lines).Figure 4: The radiation pattern of a circular antenna.4.2. A Right Angle Antenna with RadomeWe analyzed a right angle antenna located in the center of a dielectric ellipsoid-shell radome (semiprincipal axes meter, meter, and meters); the thickness of the radome is 0.25 meters, the relative electric permittivity is 3.0, and the relative permeability is 1.0. The antenna is parallel to the plane YOZ (Figure 5); each arm of the antenna is 0.2 meters long. Antenna is excited by time harmonic current whose wavelength is 0.5 meters. The results of TDIE/DGTD and DGTD are shown for comparison in Figure 6; a good agreement is observed between two results.Figure 5: Sectional view grid.Figure 6: The radiation pattern of YOZ plane.4.3. A Circular Antenna with RadomeIn this example, the antenna in the example of Section 4.2 is replaced with the circular antenna in the example of Section 4.1; excitation parameters of antenna are the same as the example of Section 4.2 (Figure 7).Figure 7: Sectional view grid.Figure 8(a) is the normalized radiation pattern of circular antenna with radome. It is obvious that the main lobe of the pattern with radome is more intensive than without radome, as Figure 8(a) shows.Figure 8: The radiation pattern of circular antenna with radome.Next, the antenna is excited by a voltage pulse source, as shown in Figure 9, the distribution of currents on antenna is derived from TDIE. The voltage source is defined asFigure 9: Voltage source.Follow the steps in Figure 2(b); the snapshots in Figure 11 of the absolute value of electric field are obtained from the hybrid TDIE/DGTD method. As shown in Figure 11(a), the electric field density is higher in the half-space , because the voltage source is located at the cross point of antenna and axis. The reflection radiation caused by radome can be seen in Figures 11(b), 11(c), and 11(d). The current waveform of source point is shown in Figure 10; the current tends to a value that is not zero.Figure 10: Current of source point.Figure 11: Snapshots of .5. ConclusionThe analytical expressions of time-domain near fields of an arbitrarily oriented electric dipole are derived in this paper; then the expressions are used in hybrid TDIE/DGTD method for analysis of circular antenna with radome. Our study provides a new way to study the time-domain radiation problems of complex medium and structure.Conflicts of InterestThe authors declare that there are no conflicts of interest regarding the publication of this paper.AcknowledgmentsThis work was supported by the National Natural Scientific Foundation of China (61571348; 61231003; 61401344).
International Journal of Antennas and Propagation, Volume 2017, pp 1-6; doi:10.1155/2017/9096217

Abstract:
This paper examines system optimization for wirelessly powering a small implant embedded in tissue. For a given small receiver in a multilayer tissue model, the transmitter is ed as a sheet of tangential current density for which the optimal distribution is analytically found. This proposes a new design methodology for wireless power transfer systems. That is, from the optimal current distribution, the maximum achievable efficiency is derived first. Next, various design parameters are determined to achieve the target efficiency. Based on this design methodology, a centimeter-sized neurostimulator inside the nasal cavity is demonstrated. For this centimeter-sized implant, the optimal distribution resembles that of a coil source and the optimal frequency is around 15 MHz. While the existing solution showed an efficiency of about 0.3 percent, the proposed system could enhance the efficiency fivefold.1. IntroductionEfficient wireless power transfer to medical implantable devices is highly desirable. Removal of bulky energy storage components enables the miniaturization of devices and eliminates the need for additional surgeries to replace the battery. Instead of a battery, a receiver on the implant obtains energy provided by external sources. Among various means to deliver power wirelessly, such as using ultrasound, optical, or biological sources, wireless powering through radiofrequency (RF) electromagnetic waves is the most established [1–5].Most studies using electromagnetic waves for powering implantable devices utilize inductive coupling. Under these conditions, a coil structure is most commonly used as the source. In an effort to enhance the efficiency, resonant LC tanks have been used on both coils for impedance matching [4, 6]. Instead of using separate capacitors, one may use extra coils to match the impedance and maintain a high -factor [7].As another effort to increase the efficiency, the size and number of turns of a coil are tuned to maximize the power transfer efficiency [3, 8]. In most studies, the optimization is based on the mutual inductance relation between two coil structures [9]. This approach, however, relies on quasi-static approximation in which the electric field induced by time-varying magnetic field is ignored. Dissipated power loss in tissue due to the presence of electric field, therefore, cannot be correctly accounted for.Recently, optimization of the power transfer efficiency including tissue loss was performed based on full-wave analysis [10, 11]. It showed that, for any given receiver, the power transfer efficiency is upper-bounded because of the tissue loss, and the upper bound is analytically solvable. Specifically, for an implant with a size of few millimeters, the optimal frequency lies in the low gigahertz range [12]. At such a high frequency, the implant is no longer in the near-field regime from the source; hence, inductive coupling alone is not sufficient to explain the performance [13].This finding is the basis for a new design methodology of power delivery systems. For a given receiver, one can readily obtain achievable power transfer efficiency and design the overall system to meet the goal. The power transfer efficiency can often be increased dramatically compared to those of conventional inductive coupling mechanisms [10, 11]. Equipped with this highly efficient power delivery system, a millimeter-sized pacemaker has been built and tested in a rabbit [14].In this work, we apply the optimization technique for a few-centimeters-sized implantable device. This research is novel and important because most implantable devices are still of a size of a few centimeters. This work provides the maximum achievable efficiency for the receivers at a certain depth of tissue composition. As a specific application, the optimization was applied for a neurostimulator inside the cavity of the head [15]. The implant stimulates the sphenopalatine ganglion (SPG), a nerve bundle located behind the nose, to relieve the pain caused by cluster headache. For the same receiver size, our design methodology could improve the efficiency fivefold compared to previous design performance.2. Background Theory2.1. Power Transfer EfficiencyThe power transfer efficiency is defined as the ratio between the received power and the input power to the system.Power efficiency degrades because of various factors, such as ohmic loss due to finite conductivity of the source, radiation loss , and dielectric loss inside the lossy tissue. Among those, the ohmic loss and the dielectric loss often dominate the power loss in a system. The upper bound on for a given receiver structure can be analytically solved [11]. Obviously, this forms the upper bound for the power transfer efficiency.2.2. Tissue, Source, and Receiver ModelWe model the inhomogeneity of the tissue as a planar multilayered medium, as illustrated in Figure 1. Although actual tissue medium is not a strict planar structure, it is known that planar modeling is adequate to predict the power transfer efficiency [16]. The tissue properties are modeled by assigning a dielectric permittivity to each layer. The dependence of with frequency is obtained from the Debye relaxation model [12].Figure 1: The layered medium model for tissue consists of stacked layers, each of which is assigned a dielectric permittivity . The center of the source is positioned at the origin, and the receiver is placed at with the norm of in the layers.Over the planar structure, we look for a source that maximizes the power transfer efficiency. It is difficult, however, to optimize the source, since the shape of the source can be arbitrary in three-dimensional space. The problem can be greatly simplified by invoking the equivalence principle [17], according to which any arbitrary source can be represented by an equivalent surface (tangential) current density, , along a plane between the source and the medium, as shown in Figure 1. For the sake of convenience, is assumed to be placed at .As a result, without loss of generality, we model the source with surface electric current on in the rest of the paper:where . Finally, the receiver of miniature devices is modeled as a magnetic dipole with arbitrary orientation located at (Figure 1):where is the magnetic moment of the dipole and denotes the orientation of the magnetic dipole, which is tilted by from the -axis. For a given and , we want to find and that optimize the power transfer efficiency.2.3. Efficiency OptimizationFor the given magnetic dipole moment , power transfer occurs through the time-varying magnetic field component in the direction of the moment. In a phasor notation, the transferred power iswhere is the magnetic field generated by the source and represents the real part of a complex number . The electric and magnetic fields generated by a time-harmonic current density on the surface of the source conductor can be solved by decomposing the current density into its spatial frequency components. Finally, the efficiency can be written as [14]where and are the electric fields generated by the source and , respectively. Also, represents the imaginary part of a complex number . The above equation of efficiency is intrinsic to the fields in the tissue multilayer structure, excluding any power loss due to radiation or ohmic loss in the source. Therefore, this gives the upper bound on the efficiency that can be obtained. The choice of that maximizes (5) is the key to efficient power transfer. Remarkably, the solution to the optimization problem maximizing can be found in a closed form as a consequence of vector space structure of fields in the multilayer geometry of the medium [11].3. Application: Receiver in Nasal CavityA minimally invasive implantable device demands as small a size as possible. However, if the functions of an implant necessitate large amounts of power, the size of the receiver must reflect this requirement. In some cases, a relatively large implant can utilize a preexisting vacant space inside the human body and thus bypass the need for further miniaturization.A good example of such an occurrence is a commercial neurostimulator inside the head to relieve the pain caused by cluster headache, as shown in Figure 2(a), produced by Autonomic Technologies (ATI) [15]. The implant requires a large amount of power (~50 mW) to provide intense stimulation to the sphenopalatine ganglion (SPG), a nerve bundle located behind the nose. Therefore, miniaturization of the receiver is limited by the device power consumption. Fortunately, exploiting the nasal cavity for the placement of the cm-scale implant, 50 mW of power can be delivered to the cm-scale implant in a relatively noninvasive manner.Figure 2: (a) The neurostimulator implant inside the head to relieve headache pain. (b) Modeling of the receiver occupying the same volume and in the same position as the neurostimulator implant.However, despite the large size of the receiver, the system suffers from low power transfer efficiency. The existing power transfer system attempted minimization of absorption loss in tissue by operating in the range of hundreds of kHz. A Litz wire structure is adopted in the receiver to reduce the ohmic loss of the receiver, as in [7]. Nevertheless, small receiver size and long distance between transceivers reduce the efficiency significantly. As a result, the power transfer efficiency is about 0.3% for the existing wireless powering solution.We are interested in the improvement in power transfer efficiency without increasing receiver size. In order to determine this, we model the receiver as a multiturn loop occupying the same volume as the original receiver and place it at the depth at which the implant will be located, 3.4 cm below the air-tissue interface, as in Figure 2(b). Detailed composition of tissue found from the anatomy of human is tabulated in Table 1. The thickness of the last layer is assumed to be infinite to simplify the calculation. Th
, , António Espírito Santo,
Modelling and Simulation in Engineering, Volume 2017, pp 1-18; doi:10.1155/2017/3258376

Abstract:
This paper addresses the problem of vibrations produced by switched reluctance actuators, focusing on the linear configuration of this type of machines, aiming at its characterization regarding the structural vibrations. The complexity of the mechanical system and the number of parts used put serious restrictions on the effectiveness of analytical approaches. We build the 3D model of the actuator and use finite element method (FEM) to find its natural frequencies. The focus is on frequencies within the range up to nearly 1.2 kHz which is considered relevant, based on preliminary simulations and experiments. Spectral analysis results of audio signals from experimental modal excitation are also shown and discussed. The obtained data support the characterization of the linear actuator regarding the excited modes, its vibration frequencies, and mode shapes, with high potential of excitation due to the regular operation regimes of the machine. The results reveal abundant modes and harmonics and the symmetry characteristics of the actuator, showing that the vibration modes can be excited for different configurations of the actuator. The identification of the most critical modes is of great significance for the actuator’s control strategies. This analysis also provides significant information to adopt solutions to reduce the vibrations at the design.1. IntroductionThe main drawbacks associated with switched reluctance drives (SRD) are the vibrations and the acoustic noise produced in its operation, which are relatively higher than those of the induction machines and permanent magnet synchronous drives. This feature is especially relevant for noise sensitive applications and has received considerable attention over the past two decades. A plethora of studies exists on the analysis of origins and characterization of the mechanical vibrations [1–12], the prediction and mitigation [13–20], and the emitted acoustic noise [11, 20–23]. The majority of published works focuses on the rotational configuration of these type of machines, that is, switched reluctance motor (SRM) drives.When compared to SRM, the linear switched reluctance actuator (LSRA) is a relatively new research and development subject. As a result, the known and published works addressing the vibrations, the force ripple, and the acoustic noise problem for LSRA are relatively scarce [11, 24–28]. Numerous studies identify the primary sources of the acoustic noise as structural vibrations, radiated from the stator, shaft, and bearings and induced by the generated forces. These vibrations vary with the load or the step voltage. Accordingly, several methods have been proposed for either active noise cancellation or new control and optimal driving strategies. For the acoustic noise mitigation, some studies focus on the prediction and characterization of the vibrations. Consequently, several models have been formulated based on the finite element method (FEM), as an alternative to analytical or experimental methods, namely, the hammer test method. Among the reasons that explain the use of FEM are the improvements in computational tools and their performance and also the associated capacity to develop complex mechanical models and achieve high accuracy with the results.The operation of switched reluctance drives is based on the inductance profile of the machine coils,, which is related to the relative positions of its parts and its dimensions. The operation of a three-phase LSRA is based on the same principle as that of SRM and requires the sequential activation of phase coils a, b, and c [29]. If the poles of the stator and the teeth of the translator (or rotor) for any phase are at the unaligned position, the inductance reaches its minimum value. When a phase is activated, the electric current flowing through the coil induces an electromagnetic force that causes the moving parts to move towards the maximum inductance position (minimum magnetic reluctance), that is, to the aligned position. If the movement continues the inductance decreases with the misalignment, due to the increase in the relative displacement towards the minimum inductance. Assuming ideal conditions, the excitation current in the phase coil produces an electromagnetic motoring force that is expressed as [29] (pp. 22)whereis the peak value of the coil excitation current,. At the same time, due to the continuous displacement, regenerative forces,, occur in the regions adjacent to the full alignment position, such that, which are related to the negative variation of the inductance in phase coils b and c, respectively. In general, the regenerative forces superimpose to the motoring force. Repeated activation of the phases in sequence abc moves the translator forward and backwards when the sequence acb is activated. The smoothness of the displacement of the translator depends on the switching positions of the phases, on the duty cycle of the excitation, on the electronics converter topologies, and on the control mode strategies.In real applications, there are imperfections and nonlinearities associated with the inductance profile; besides, the driving currents do not vary linearly either. Moreover, for a given force, the desired excitation current values are achieved by the switching process of the electronics converters and the control strategies, usually modeled by a pulse width modulation signal. The switching regime causes variations to the current that foster ripple in the produced forces. Thus, the nature of the forces generated during the LSRA operation is susceptible to generating vibration whose magnitude can be amplified, especially in the vicinity of the natural frequencies of structural vibrations. The natural modes, the resonant frequencies, and the characteristics of the induced acoustic noise influence or restrict the use of machines, with direct consequences for human well-being and health [30]. On the other hand, the mechanical vibrations are particularly relevant when precise movement is a requirement and can compromise the application of the actuator.The sources of vibrations and the acoustic noise in LSRA are primarily the same as for the rotational configuration, due to their common modes of operation. However, the characteristics of the vibrations in electromechanical linear actuators evidence some unique features. Firstly, the natural modes depend on the structural characteristics of the actuator, which vary according to the relative position of the moving parts. Secondly, while vibrations are usually periodic in rotational configuration, in linear actuators the vibrations are periodic only if the excitation forces and the translation movements are periodic. This phenomenon occurs due to linear displacements in this type of machine, rather than angular movement in the rotational configuration. Also, the vibrations tend to be localized, and the associated displacements depend on the position and the structural configuration. Moreover, the finite length of the machine parts influences the propagation of the mechanical waves along the structure. The reflections at both ends interfere along the actuator structure, forming a stationary wave.The vibrations and the emitted acoustic noise are directly connected with structural aspects of the actuator and its characteristics related to the properties and the dimensions of the materials used. These characteristics dictate the mechanical vibration behavior of the machine and are not an easy issue to deal with from the analytical point of view, in part due to the difficulties encountered in modeling the mechanical structures. Among the structural differences between the rotational and linear configurations of SRD, one can mention the finite length of both the stator and the translator of the latter. On the one hand, the complexity of the mechanical model demands attention to the distribution of masses according to the different positions of the translator. On the contrary, the elastic model denotes results in an increase in complexity, and its analytical solutions are hard to obtain and might be not accurate enough. For these reasons, it is common to use computational simulation tools based on the finite element method (FEM) to model these structures.The FEM is essentially a discretization technique and approximation method for modeling the distributed parameter systems that correspond to its decomposition into several finite elements or building blocks, equivalent to a system discretization technique. When applied to linear systems, the finite element analysis (FEA) allows finding the approximate solutions to the differential equations that describe the physical model [31, 32].This paper presents a simulation study based on the finite element method to obtain the structural vibration modes and frequencies of an LSRA. The focus relies on frequencies within the range up to nearly 1.2 kHz. This band includes the vibration modes considered most relevant and critical to the actuator operation, according to the operation modes as forces profile of the actuator [17, 33]. Moreover, it complements preliminary results of simulations and experiments for frequencies up to 300 Hz [26]. The primary objective of this work is to collect data and establish a framework to characterize the linear actuator fully, regarding the vibrations modes induced due to the regular operation of the machine. Due to the lack of a priori knowledge regarding vibrations, we build a 3D model of the structure and use 3D FEM simulation software to find the natural vibration frequencies. The data obtained support the characterization of the linear actuator focusing on the excited vibrations and mode shapes. The results reveal abundant modes and harmonics and the symmetry characteristics of the actuator. These findings help to identify the vibration modes that can be excited for different configurations of the actuator, according to the position of its moving parts. The gathered
, Shouhui Zhai
Mathematical Problems in Engineering, Volume 2017, pp 1-11; doi:10.1155/2017/6063176

Abstract:
In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII) for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND) relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.1. IntroductionThe finite-difference time-domain (FDTD) method for Maxwell’s equations, which was first proposed by Yee (see [1], also called Yee’s scheme) in 1966, is a very efficient numerical algorithm in computational electromagnetism (see [2]) and has been applied in a broad range of practical problems by combining absorbing boundary conditions (see [3–7] and the references therein). It is well known from [8] that the Yee Scheme is stable when time and spatial step sizes (, , and for 2D case) satisfy the Courant-Friedrichs-Lewy (CFL) condition , where is the wave velocity. To overcome the restriction of the CFL condition there are many research works on this topic; for example, see [9–17] and the references therein. In [15], two unconditionally stable FDTD methods (named as S-FDTDI and S-FDTDII) were proposed by using splitting of the Maxwell equations and reducing of the perturbation error, where S-FDTDII, based on S-FDTDI (first-order accurate), is second-order accurate and has less numerical dispersion (ND) error than S-FDTDI. However, the second convergence of S-FDTDII was not proved by the energy method.In this letter, by introducing a new method to reduce the error caused by splitting of equations [15] (other methods of reducing perturbation error caused by splitting of differential equations can be seen in [18]), we propose two modified splitting FDTD methods (called MS-FDTDI and MS-FDTDII) for the 2D Maxwell equations. It is proved by the energy method that MS-FDTDI with the perfectly electric conducting boundary conditions is second-order convergent in both time and space. By Fourier method we derive the amplification factors and ND relations of MS-FDTDI and MS-FDTDII. Then, we prove that these two methods are unconditionally stable and that MS-FDTDI has less ND errors than S-FDTDII (or ADI-FDTD [10, 11]). Numerical experiments to compute numerical dispersion errors and convergence orders and to simulate a scattering problem are carried out. Computational results confirm the analysis of MS-FDTDI and MS-FDTDII.2. Modified Splitting FDTD Method for the Maxwell Equations2.1. Maxwell EquationsConsider the two-dimensional Maxwell equations in a lossless and homogeneous medium:where and are the electric permittivity and magnetic permeability of the medium and and for and denote the electric and magnetic fields, respectively. We assume that the spatial domain is surrounded by perfectly electric conductor (PEC). Then the PEC boundary condition below is satisfied:where denotes the boundary of and is the outward normal vector on . The initial conditions are assumed to be where .2.2. Partition of the Domains and NotationsLet be partitioned as Yee’s staggered grids [1]: , and let be divided into equidistant subintervals, , wherewhere and are the spatial step sizes, is the time increment, and , , and are positive integers. For a function and or , we define2.3. Modified Splitting FDTD MethodsDenote by and the approximations to , and , respectively, where, and in what follows, , . Based on the S-FDTDII scheme (see [15]) and the idea of reducing the splitting error, we propose a modified splitting FDTD method (called MS-FDTDI) for (1)–(3).Stage 1. Stage 2. The boundary conditions for (6)–(8) obtained from (2) arewhere or , , .The initial values for (6)–(8) are , and In the implementation of MS-FDTDI, Stage 1 (or Stage 2) can be reduced into a tridiagonal system of linear equations for with (or with ) and a formula for (or ), which can be solved directly.Remark 1. (1) In order to see the difference between MS-FDTDTI and the S-FDTDII method in [15], we give the equivalent forms of the two methods:where (11)–(13) with being the equivalent form of S-FDTDII (Stage 1 of S-FDTDII is the same as (6); Stage 2 of S-FDTDII is (7)-(8) with the last term on the right hand side of (7) removed); (11)–(13) with the case is the equivalent form of MS-FDTDI.By these forms we see that MS-FDTDI is different from the S-FDTDII and ADI-FDTD methods (see [10, 11], where splitting of the equations is not used; however, the equivalent form of S-FDTDII is the same as that of 2D ADI-FDTD).(2) MS-FDTDI has similar perturbation term as the D’yakonov scheme (see [19]). The equivalent form of this scheme is (11)–(13) with and the perturbation term on the right hand side of (12) being removed. In the comparison of these equivalent forms we see that the perturbation term and its location of MS-FDTDI are different from those of the D’yakonov’s scheme. This implies that they are different.Remark 2. Based on S-FDTDII, we propose another modified splitting FDTD method (denoted by MS-FDTDII).Stage 1 of MS-FDTDII.Stage 2 of MS-FDTDII.The boundary and initial conditions of MS-FDTDII are the same as MS-FDTDI.The equivalent form of MS-FDTDII is (11)–(13) withBy these equivalent forms we see that MS-FDTDI and MS-FDTDII are of second-order accuracy.3. Analysis of Stability and Numerical Dispersion ErrorIn this section we first derive the amplification factors and numerical dispersion (ND) relations of MS-FDTDI and MS-FDTDII and then we analyze the stability and ND error.3.1. Stability AnalysisLet the trial time-harmonic solution of the Maxwell equations be where is the unit of complex numbers, , , and are the amplitudes, and are the wave numbers along the -axis and -axis, and is the amplification factor.Substituting the above expressions into the equivalent form of MS-FDTDI and evaluating the determinant of the coefficient matrix of the resulting system of equations for , , and , we get a quadratic equation of . Solving this equation yields the amplification factors for MS-FDTDI:where the coefficients areThe modulus of or is equal to one, implying that MS-FDTDI is unconditionally stable and nondissipative.Similarly, we obtain the amplification factors of MS-FDTDII:where is the same as that in (20), and is That implies that MS-FDTDII is also unconditionally stable and nondissipative.Remark 3. The amplification factors of S-FDTDII, which are the same as those of ADI-FDTD (the derivation is seen in [15]), arewhere is the same as that in (20), and is 3.2. Numerical Dispersion AnalysisLet be the wave speed. Substituting into (20), we obtain the ND relation of MS-FDTDI:where and are defined under (20).Similarly, the ND relation of MS-FDTDII isRemark 4. The ND relation of S-FDTDII is the same as that of ADI-FDTD (see [15]), which isBy using the Taylor expansions of and and the continuous dispersion relation: , we derive the main truncation errors of the ND relations of MS-FDTDI, MS-FDTDII, and S-FDTDII, denoted by , , and , which areBy the second and third terms of truncation errors we see that , implying that the ND error of S-FDTDII or ADI-FDTD is less than that of MS-FDTDII. Noting that we obtain that the ND error of MS-FDTDI is less than that of S-FDTDII (or ADI-FDTD).4. Error Estimates and Convergence of MS-FDTDILet and , where with and denote the values of the exact solution of the Maxwell equations (1)–(3) and with and denote the solution of the MS-FDTDI scheme (6)–(8).Subtracting the equivalent form of MS-FDTDI (11)–(13) from the discretized Maxwell equations (whose form is like (11)–(13) with extra truncation errors), we obtain the following error equations:where with and are the truncation errors, which can be derived by using Taylor formula and discretizing of Maxwell equations. These local truncation error terms are bounded by where and is a constant dependent on norms of the derivatives of the solution of (1)–(3).Multiplying both sides of (31) by , , and , respectively, and applying the summation by parts and the Schwarz inequality we havewhere for and Moreover, if the initial conditions and step sizes satisfythen, by the discrete Growall’s lemma, we haveRemark 5. (1) The convergence of MS-FDTDI requires that with , which is weaker than Courant stability condition: .(2) By the similar method to the above it can not be proved that MS-FDTDII is convergent since the perturbation terms in this scheme are not controlled.5. Numerical ExperimentsWe do some experiments to compute the ND errors of MS-FDTDI and MS-FDTDII, to solve a wave guide problem, and to simulate a scattering problem by the two methods.5.1. Computation of Numerical Dispersion ErrorsLet be the wave length, , and be the number of points per wavelength, and is a multiple of the CFL number (CFL number equals in this case); is the wave propagation angle. Then, by , , , , and the expressions of and (defined in Section 3.1), we see that the amplification or stability factor is a function of , , and ; that is, .The ND errors of MS-FDTDI, MS-FDTDII, and S-FTTDII are computed by the following formula (see [20]): where and denote the imaginary and real parts of the amplification factor . We plot the normalized phase velocity with respect to , and (see Figures 1-2).Figure 1: Normalized phase velocities of MS-FDTDI, MS-FDTDII, and S-FDTDII against wave propagation angle with and .Figure 2: Normalized phase velocities of MS-FDTDI, MS-FDTDII, and S-FDTDII against numbers of points per wavelength with and Figure 1 shows the variation of against the wave propagation with and for MS-
Ahmed Gad
Published: 13 February 2017
by IEEE
2016 Saudi Arabia Smart Grid (SASG) pp 1-9; doi:10.1109/sasg.2016.7849675

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J. H. D. Onaka, A. S. De Lima, A. R. A. Manito, U. H. Bezerra, M. E. L. Tostes, C. C. M. De M. Carvalho, T. M. Soares, D. C. Mendes
2016 17th International Conference on Harmonics and Quality of Power (ICHQP) pp 89-94; doi:10.1109/ichqp.2016.7783363

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P. P. Jadhav, A. S. Patil
2016 International Conference on Global Trends in Signal Processing, Information Computing and Communication (ICGTSPICC) pp 653-656; doi:10.1109/icgtspicc.2016.7955382

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, Lajos Torok, ,
2016 IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC) pp 1-6; doi:10.1109/eeeic.2016.7555689

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Qin Guodong, Pang Quanru,
International Journal of Rotating Machinery, Volume 2016, pp 1-4; doi:10.1155/2016/2573174

Abstract:
Ocean wave energy is a high energy density and renewable resource. High power conversion rate is an advantage of linear generators to be the competitive candidates for ocean wave energy extraction system. In this paper, the feasibility of a wave energy extraction system by linear generator has been verified in an experimental flume. Besides, the analytical equations of heaving buoy oscillating in vertical direction are proposed, and the analytical equations are proved conveniently. What is more, the active power output of linear generator of wave energy extraction system in experimental flume is presented. The theoretical analysis and experimental results play a significant role for future wave energy extraction system progress in real ocean waves.1. IntroductionAccess to wave energy in useful forms has been one of the most important investigations for many years. Wave energy, a renewable resource and high energy density, is therefore promoting the development of global economy under the condition of efficient utilization [1]. There are many technical principles reported in papers and conferences on how to convert wave energy into electric power by linear generators [2–4]. Some of these technical principles have been tested in ocean waves, and the test results were proved to be promising as electric power can be obtained directly from wave energy without complex mechanical transmission [5, 6]. Among these technical principles, two methods of wave energy extraction system have been proposed: design generators such as rotating or linear generators to convert the kinetic energy of waves into electric power [7] and considering the rectification and filtration of the electric power from wave energy to grid connected power [8].Many research studies are focusing on either design generators or electric power conversion to optimise the wave energy extraction system, while few investigate the motion of the heaving buoy, which drives the linear generator to power generation operation. Actually, the operation process of heavy buoy is difficult to describe due to the nonlinear motion of ocean waves.In this paper, the wave energy extraction system includes a heaving buoy and a linear generator is proposed. Considering the effect of radiated potential, the analytical equations of heaving buoy oscillation in vertical are presented. The wave energy extraction system has been tested in an experimental flume, and the tested results indicate that the method of analytical equations is effective. The theoretical analysis and experimental results play a significant role for future wave energy extraction system progress in real ocean waves.2. Theory2.1. Wave Maker in an Experimental FlumeThe wave maker in an experimental flume consists of an oscillating plate at with water of depth , as shown in Figure 1. The oscillating plate () is able to oscillate in horizontal direction. When the oscillating plate oscillates in horizontal direction, a complex amplitude radiated velocity potential is generated, which can be defined aswhere is a coefficient of proportionality and is complex amplitude velocity of oscillating plate [9].Figure 1: Cross section of the experimental flume.In terms of a wave propagation in the positive direction and towards under the circumstance of a given oscillating plate at , it is easy to write down the Laplace equation (2) and the boundary conditions (3) and (4): In the above equations, is the angular frequency and is the acceleration of gravity. Due to (2), (3), and (4), we can also write down the following solution of the boundary-value problem which satisfies the region of and the radiation condition at [10]:Equation (5) resulted from the method of variable separation; is an orthogonal function. is the wave number and is real. In (5), represents evanescent waves which can be negligibly near . Thus in the region of , it can be assumed that2.2. Motion Equation of Heaving BuoyAs shown in Figure 2, the heaving buoy’s water plane area is , submerged volume is (volume of displaced water), wet surface is with unit normal , and the vertical unit vector is . According to the linearised theory and potential theory of waves in the experimental flume, the velocity potential can be expressed aswhere is incident potential, is diffracted potential, and is radiated potential.Figure 2: Heaving buoy in waves.It is assumed that only an incident wave exists and a heaving buoy is restricted to oscillation in the vertical only. The heaving buoy was subject to three forces, namely, the vertical wave force , the radiation force , and the hydrostatic buoyancy force , which can be written as follows:where is the added masses of heaving buoy and is the damping coefficient of heaving buoy.Furthermore, there may be some other additional forces acting on the heaving buoy, such as the viscous force and the friction force . According to Newton’s law, the term of motion equation for the heaving buoy oscillation in vertical may be written aswhere is the weight of heaving buoy, is the acceleration of moving parts, is the heaving buoy position, and is the friction resistance from linear generator.According to , the velocity and position of heaving buoy in the vertical direction can be written as2.3. Wave Energy Absorption by Heaving BuoyThe utilization of wave energy converting into electric energy is still in an initial state of technological development. This section focuses on wave energy absorption by a heaving buoy oscillating in the vertical direction only. The heaving buoy oscillates with a velocity mainly due to vertical wave force produced by an incident wave. According to [9], the power absorption can be manifested as follows:where is the wave power from the incident wave in heave andis the radiated power caused by the heaving buoy. Here is the phase difference between and , and is the radiation resistance.3. Experimental ResultsFor the purpose of verifying that the theory analysis is feasible, a wave energy extraction system is constructed in an experimental flume. The wave energy extraction system includes a three-phase permanent magnet linear generator and a heaving buoy, as illustrated in Figure 3.Figure 3: The wave energy extraction system in an experimental flume.In experiment, the wave maker in experimental flume could provide wave height 0.2~0.3 m and wave period 1.6~2.2 s. Concerning the cogging force of linear generator, from Figure 4 and (10) it is concluded that the more the wave height (wave period is constant 2 s), the more the heaving buoy position and the speed in vertical.Figure 4: Position and speed of the heaving buoy in the vertical direction according to different wave height []; the wave period is 2 s.Figure 5 shows measured three-phase no-load voltages from the three-phase linear generator of wave energy extraction system. In Figure 5, the wave of three-phase no-load voltages is burr, which indicates that some voltage filter and rectifier system is needed before the power energy is ultimately used.Figure 5: The measured no-load voltage of wave energy extraction system.Active power of three-phase linear generator of wave energy extraction system under incident wave power, radiated wave power, and floating buoy absorbed power for one buoy stroke is presented in Figure 6. As seen from Figures 4 and 6, the active power, incident wave power, radiated wave power, and floating buoy absorbed power are zero corresponding to the upper and lower buoy positions, where the buoy speed is zero. In case of harmonic time variation, the speed of linear generator is not constant; therefore the active power of linear generator of wave energy extraction system is also not constant.Figure 6: The heaving buoy absorbed power, incident wave power, radiated wave power, and active power of linear generator for one buoy stroke.4. ConclusionsAnalytical equations of a heaving buoy oscillation in the vertical direction and a three-phase linear generator have been proposed for wave energy extraction system in this paper. The feasibility of analytical equations is proved, and experimental results indicate a possibility to extract electric power from wave power directly by three-phase linear generator. In the experimental results, the curves of three phase no-load voltages are burr, and the speed of linear generator is not constant. Therefore, some methods are needed to optimise the properties of linear generator, and an optimal control method is also needed to improve the operation process of wave energy extraction system.Competing InterestsThe authors declared that they have no conflict of interests regarding the publication of this paper.AcknowledgmentsThis work was financially supported by the Normal Scientific Research Project from Zhejiang Province (Y201533835).
Sanjit Kumar Kaper, Niraj Kumar Choudhary
2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES) pp 1-6; doi:10.1109/icpeices.2016.7853065

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Mathieu Morati, Daniel Girod, Franck Terrien, Virginie Peron, , Shahrokh Saadate
Published: 17 December 2015
by IEEE
IEEE Transactions on Power Delivery, Volume 31, pp 2494-2501; doi:10.1109/tpwrd.2015.2508498

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Aziz Boukadoum, Tahar Bahi, , Abla Bouguerne, Sofiane Oudina
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Volume 34, pp 1896-1916; doi:10.1108/compel-11-2014-0303

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Jianshuo Li, , Kai Wang, Xin Shi, Shan Liang, Min Gao
Mathematical Problems in Engineering, Volume 2015, pp 1-11; doi:10.1155/2015/610490

Abstract:
Microwave heating has been the research hot spot for many years. It has the capability of volumetric heating, which makes it save energy and time compared to traditional heating by conduction. A lot of work has been done to easily and exactly describe power distribution in the heating material. Maxwell’s equations and Lambert’s law are the most common ways. Maxwell’s equation is complicated and hard to apply, while Lambert’s law ignores the temperature influence. For material thickness less than penetration depth, only Maxwell’s equation can accurately solve power distribution. For large thickness material, Lambert’s law combined with regional temperature proposed in this paper can be more precise than only Lambert’s law. But there also exist some differences. To precisely control the heating process and make the whole process safe, this paper proposes the use of model predictive control (MPC) algorithm to make the maximum temperature follow a preset reference trajectory. The simulation results demonstrate that the algorithm can well control the heating process with little difference between the reference trajectory and the practical output.1. IntroductionMicrowave heating has been widely used in our lives, from domestic utilized microwave oven to industrial high-power applications. Compared with traditional heating method, microwave heating saves energy and time and is easier to control. But there exist two main problems holding back its wide applications. Firstly, during the heating process, due to the microwave’s inhomogeneous heating, temperature distribution nonuniformity will make the heating results unsatisfied. Secondly, at some parts of the heating material, sharp temperature rising may happen. Then it may lead to thermal runaway, which is very dangerous in practical applications. It may cause reactants burning or even blow them up.Maxwell’s equation and Lambert’s exponential law form the basis for modeling microwave assisted heating process. According to Lambert’s law, microwave power decays exponentially by the penetration depth into the material. The correctness to calculate power distribution for large thickness material has been proved. While Maxwell’s equation is based on space and time, its calculation characterizes the exact microwave propagation behavior. But the calculation process is complex and needs exact temperature distribution.Maxwell’s equation is commonly used to theoretically explain some phenomenon or validate proposed models, for example, the simulation analysis of the heating process in microwave ovens [1, 2], the relationship between the emerging of resonance and material thickness [3, 4], the temperature field distribution during the thawing process [5], and the verification of impulse microwave on making heating process temperature distribution uniform [6]; those researches help people know microwave heating characteristic. But, in practical applications, the exact microwave distribution is hard to obtain. Microwave field distribution is influenced by material permittivity, which directly relates to temperature. The usual way to obtain temperature is by optical fiber thermometer, infrared thermometer, or infrared camera [7]. Those methods are suitable for detecting surface or point temperature. Another way to detect temperature is by ultrasonic sensors, which can obtain the temperature field in the heating material. But there are some problems unsolved to be applied in practical applications [8]. Because of the incomplete temperature field, the exact microwave distribution is basically unknown during the heating process. So, Maxwell’s equation cannot be used to solve power distribution in real time practical applications.Lambert’s law is the common way to calculate power distribution in actual applications, such as food heating, thawing, and drying process [9–13]. But it disregards the influence of temperature which directly relates to permittivity and makes the power distribution quite different with reality. This paper uses Lambert’s law combined with material temperature to analyze power distribution. It makes up the shortcoming of ignoring material regional permittivity. Although Lambert’s law combined with temperature can have a better solution to solve power distribution, there still exist some differences. So, to make the heating process safe and avoid thermal runaway, some control methods have been proposed by former researchers, for example, the global linearizing control of multiple-output-multiple-input microwave assisted thawing process [14] and the automatic control of microwave heating process [15]. But because of the lacking of power distribution information, some problems remain unsolved to exactly control the heating process.Model predictive control (MPC), an advanced model based control strategy, is well dedicated to solve this constrained problem of ordinary differential equation systems [16–18]. MPC or receding horizon control is used to predict and optimize process performance. The main idea is to solve the manipulated variable input value over a finite prediction horizon at each sampling time. The procedure is reiterated at the next sampling time with the updated process measurements and model parameters. Today, MPC has become an advanced control strategy widely used in industry.According to the above, to analyze microwave assisted heating process and guarantee its safety, MPC algorithm based on Lambert’s law combined with temperature is proposed in this paper. This paper is organized as follows. In Section 2, it mainly deals with the difference among the three ways (Maxwell’s equation, Lambert’s law, and Lambert’s law combined with local temperature) to calculate power distribution. Section 3 introduces the way how control algorithm can be applied in the proposed model to control the heating process. At last, the simulation results of this model and the effect of the control algorithm are revealed.2. Model BuildingThe power distribution model applied in this analysis is shown in Figure 1. The heating material is placed in free space, with permittivity and permeability , which are varying with temperature. is the free space dielectric constant, and is the free space permeability. Assuming that a plane, time harmonic electromagnetic wave of frequency impinges normally upon an isotropic material which fills the region , the transverse electric (TE) wave propagates along the -direction, with perpendicular electric () along the -direction and magnetic () along the -direction. The wave satisfies the first order Mur absorbing boundary condition. The electromagnetic field satisfies the following formulas:Figure 1: Wave propagation model.To solve the electric field within the sample, the solutions of following coupled Maxwell’s equations are required. The heating sample may be made by material with different permittivity. Let us set it to have layers, so each layer can be represented bywhere and . Here denote the interface position. is the propagation constant which depends on dielectric constant and dielectric loss . is the material permeability, which equals one for nonmagnetic heating material. Let us assume each layer has a constant dielectric property; therefore, the solutions of (2) can be represented by propagation and reflection wave asThe electric and magnetic field are continuous at the interface between different layers. That is as follows:By using the interface conditions, the general solution coefficients can be obtained via solving the set of algebraic equations:Let us denote by the incident power, which is the control variable in actual applications. Then the electric amplitude at can be calculated bywhere is the velocity of light.Based on (5) and (6), the absorbed power in the th layer, calculated by Poynting vector theorem, iswhere the superscript “” denotes the complex conjugate.2.1. Case of Lambert’s LawLambert’s law is valid for semi-infinite material, and the power absorbed by the material per unit volume can be represented by [19]where represents the penetration coefficient calculated by the sampling temperature on material surface and represents attenuation factor:2.2. Case of Lambert’s Law Combined with Regional TemperatureThe main characteristic of Lambert’s law combined with regional temperature is that it considers the regional permittivity and attenuation factor. The algorithm uses electric amplitude attenuation instead of power attenuation. The eclectic amplitude in each layer can be calculated by (10) and (11). The penetration depth of each layer is calculated by the corresponding permittivity, and the power dissipation in the material can be solved by (12). The use of this equation needs to sample material temperature. Space distribution of temperature sensors can be set as demanded: 2.3. The Comparison among the Three Methods2.3.1. Material with Constant PermittivityThe permittivity and thermophysical properties of the heating material are referred to in Table 1. The microwave frequency used in this analysis is chosen to be 2.45 Ghz. The initial material temperature is set to be 280 K. The surrounding material is filled with air. The penetration depth can be calculated by , equal to 3.64 cm. For the entire material with the same temperature, the calculation of Lambert’s law and Lambert’s law combined with temperature has the same value. So Maxwell’s equation and Lambert’s law are utilized to calculate the difference in power distribution. As Figure 2(a) shows, for small thickness material, power distribution calculated by Lambert’s law has a huge difference with Maxwell’s equation. That means Lambert’s law cannot be utilized to material thickness less than penetration depth. For thickness a little larger than penetration depth, as shown in Figure 2(b), Lambert’s law can approximately describe power distribution. But it cannot reveal the phenomenon of power fluctuation. For thickness much larger than penetration depth, seeing Figur
Jian-Wei Yang, Man-Feng Dou, Zhi-Yong Dai
Journal of Electrical and Computer Engineering, Volume 2015, pp 1-9; doi:10.1155/2015/168786

Abstract:
Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.1. IntroductionOwing to high torque-to-current ratio, large power-to-weight ratio, high efficiency, high-power factor, high fault tolerance, robustness, and so forth, multiphase PMSMs have been paid more attention in high-power and high-reliability applications [1–3]. Compared with the traditional three-phase PMSM, with the added phase number, the fault tolerance of the multiphase PMSM is enhanced, and thus the reliability of the multiphase PMSM is improved. Therefore, multiphase PMSMs are widely used in fault-tolerant control systems [4, 5].Fault diagnosis is the foundation of the fault-tolerant control of the electrical machines. In PMSMs, the usual faults include electrical faults, mechanical faults, and magnetic faults [6]. In electrical faults, short circuit faults form 21% of the faults occurring in electrical machines. The stator winding ITSC fault is the commonest short circuit fault in PMSMs. It always occurs due to insulation failures but develops into more serious faults very quickly [7]. So it is meaningful to research the effective fault diagnosis methods of stator winding interturn short circuit for PMSMs.The current existing detection and diagnosis methods of ITSC fault can be commonly divided into off-line methods and on-line methods [8]. Compared to the off-line methods, in on-line methods, the PMSMs do not have to be taken out of service and predicting health condition and detecting faults at an incipient stage are made easier [9]. In recent years, with the application of neural network, fuzzy logic and particle swarm optimization (PSO), the artificial intelligence (AI) on-line fault detection, and diagnosis methods have drawn the attention of many authors [10]. The AI methods improve the robustness and efficiency of the fault diagnosis and have no need to interpret the collected data in relation to the occurring fault.In some AI fault detection and diagnosis methods, such as literature [11], in order to detect and diagnose the severity of the stator winding interturn short circuit fault of PMSM, a mathematical model that can describe both healthy and fault conditions is needed first. Literature [12] built power losses model of five-phase PMSM with ITSC fault and analyzed the changes in power losses due to faults occurrence by finite elements simulations. However, this fault model is not suitable for AI fault diagnosis based on parameter optimization. Literature [13] and literature [14] proposed two mathematical models of PMSM with ITSC fault for fault diagnosis. Unfortunately, these models are all about three-phase PMSM and relatively complex. If the fault model of five-phase PMSM was built by the way shown in literature [13] and literature [14], the model would be more complex, and the calculation for the subsequent fault diagnosis based on parameter optimization would increase greatly. Thus, the efficiency of fault diagnosis would be affected. Therefore, it is meaningful to establish a relatively simple five-phase PMSM model with ITSC fault for fault diagnosis.After the establishment of the fault model, in order to diagnose fault severity of the fault motor, the parameters associated with fault severity need to be identified. However, for the complex distribution of the parameters in the fault model, the identification problem is extremely difficult for nonlinear identification techniques. To overcome this difficulty, the fault diagnosis problem is transformed into a corresponding optimization problem and then solved by intelligent algorithm [15]. In recent years, many authors focus on PSO parameter optimization to deal with this problem, such as that shown in literature [16] and literature [17]. PSO is an evolution computation technique based on swarm intelligent methodology. PSO is initialized as a swarm of arbitrary particles (arbitrary solution), and then the optimal solution is discovered by iteration. However, the PSO algorithm creates the problems of partial convergence and precocious convergence when the particles’ diversity is decreasing. Therefore, finding a better parameter optimization algorithm for five-phase PMSM fault diagnosis is essential.In this paper, relatively simple mathematics models of the five-phase PMSM under both healthy and ITSC fault situations are established, respectively. Furthermore, a novel fault diagnosis method of ITSC based on the trust region algorithm is proposed for five-phase PMSM. With the aid of the trust region algorithm which is global convergence, the interturn short circuit ratio is estimated with a short time transient. The simulation and experimental results have validated both the correction of the established models and the effectiveness of the proposed parameter estimation method.2. Model Analysis2.1. Five-Phase PMSM Healthy ModelIn order to establish the healthy model of five-phase PMSM, without loss of generality, the following assumptions are as follows:(1)The magnetic circuit is linear. It is, in turn, that the magnetic circuit is not saturation.(2)The stator winding current is sinusoidal, symmetrical, and without harmonics. The air gap magneto motive force (MMF) is sinusoidal.(3)The rotor MMF is sinusoidal and the slot effect is neglected.(4)The five-phase PMSM is nonsalient pole structure.(5)Eddy currents and hysteresis losses are negligible.With these assumptions, the five-phase PMSM model can be provided byEquation (1) is the voltage balance equation, (2) is the flux equation, and (3) is the torque equation, where the stator phase voltage vector ; the stator phase current vector ; the stator winding resistance ; the stator flux vector ; the rotor flux vector ( is the rotor electrical angle and ); is the stator inductance matrix; is the differential operator; is the number of pole pairs; and is the electromagnetic torque.Because of adding two-phase windings, compared to traditional PMSM, the stator inductance matrix of five-phase PMSM is more complex and it can be represented bywhere is the self-inductance of phase winding A (B, C, D, and E) and is the mutual- inductance between phase windings A and B (C, D, and E). Actually, the mutual-inductances can be expressed by , , , and .2.2. Five-Phase PMSM Fault ModelWithout loss of generality, assume that phase winding A causes ITSC fault and the rest of the phase windings is in healthy state. The five-phase PMSM with ITSC is shown in Figure 1. Note that a short circuit loop current , which gives birth to braking torque, is produced in phase winding A. And thus the braking torque affects the motor performance seriously. Besides, the effective turns number of phase winding A is reduced, and the values of the phase winding resistance, the self-inductance, the mutual-inductance, and the flux linkage are all changed accordingly.Figure 1: The schematic of five-phase PMSM with interturn short fault.In the ITSC fault model of five-phase PMSM, one of the most important parameters is the interturn short circuit ratio , which is defined as the ratio of the shorted turns number to the total turns number. When the ITSC fault occurs in phase winding A, depending on the physical relationship of the windings, the equivalent circuit of five-phase PMSM with ITSC fault is shown in Figure 2, where is the resistance of phase winding A (B, C, D, and E); is the short circuit winding resistance; is the self-inductance of phase winding A (B, C, D, and E); is the self-inductance of the short circuit winding; is the self-inductance of phase winding under normal conditions. Actually, the resistance and the inductances can be expressed byFigure 2: The equivalent circuit of five-phase PMSM with interturn short circuit fault.Besides, there are also three kinds of mutual-inductances existing. The first is the mutual- inductance between the remaining normal winding of phase A and other phase (B, C, D, and E) windings, where . The second is the mutual-inductance between the remaining normal winding of phase A and the short circuit winding of phase A, where . The third is the mutual-inductance between the short circuit winding of phase A and other phase (B, C, D, and E) windings, where . Since the phase windings B, C, D, and E are healthy, the mutual-inductances of the phase windings B, C, D, and E remain the values of the healthy model.When phase winding A causes ITSC fault, the fluxes between the windings and the rotor can be derived asAccording to the equivalent circuit and the analysis above, the voltage balance equation renders asThe voltage balance equation (7) can be rewritten aswhereThe electromagnetic torque equation of five-phase PMSM isThe mechanical motion equation of five-phase PMSM iswhere is the electromagnetic torque; is the load torque; is the rotational inertia; is the viscous friction coefficient; is the mechanical angular velocity.3. F
S. S. Anan’Ev, A. N. Golubev, V. A. Martynov, V. D. Karachev, A. V. Aleinikov
Russian Electrical Engineering, Volume 86, pp 264-269; doi:10.3103/s106837121505003x

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Anand Singh, Prashant Baredar, Ashutosh Singh
2014 International Conference on Advances in Engineering & Technology Research (ICAETR - 2014) pp 1-5; doi:10.1109/icaetr.2014.7012836

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Le Ge, Xiaodong Yuan, Zhong Yang
Mathematical Problems in Engineering, Volume 2014, pp 1-6; doi:10.1155/2014/864989

Abstract:
To rely on joint active disturbance rejection control (ADRC) and repetitive control (RC), in this paper, a compound control law for active power filter (APF) current control system is proposed. According to the theory of ADRC, the uncertainties in the model and from the circumstance outside are considered as the unknown disturbance to the system. The extended state observer can evaluate the unknown disturbance. Next, RC is introduced into current loop to improve the steady characteristics. The ADRC is used to get a good dynamic performance, and RC is used to get a good static performance. A good simulation result is got through choosing and changing the parameters, and the feasibility, adaptability, and robustness of the control are testified by this result.1. IntroductionThe proliferation of nonlinear loads caused by more and more modem electronic equipments results in deterioration of power quality in power transmission or distribution systems. Harmonic, reactive, negative sequence and flickers are the reasons of various undesirable phenomena in the operation of power system. In order to solve these problems, the concept of active power filter (APF) was presented. Active power filters, which compensate harmonic and reactive current component for the power supplies, can improve the power qualities and enhance the reliabilities and stabilities on power utility [1–3]. In recent 30 years from APF presented, the continual innovation of control strategies mainly impels the APF techniques to be developed rapidly [4–7].Active disturbance rejection control (ADRC) is a robust control method that is based on extension of the system model with an additional and fictitious state variable, representing everything that the user does not include in the mathematical description of the plant [8–11]. Different from other disturbances and states estimation [12–15], this virtual state (sum of internal and external disturbances, usually denoted as a “total disturbance”) is estimated online with a state observer and used in the control signal in order to decouple the system from the actual perturbation acting on the plant. This disturbance rejection feature allows user to treat the considered system with a simpler model, since the negative effects of modeling uncertainty are compensated in real time. As a result, the operator does not need a precise analytical description of the system, as one can assume the unknown parts of dynamics as the internal disturbance in the plant. Robustness and the adaptive ability of this method make it an interesting solution in scenarios where the full knowledge of the system is not available.Repetitive control is a control method developed by a group of Japanese scholars in 1980s. It is based on the Internal Model Principle and used specifically in dealing with periodic signals, for example, tracking periodic reference or rejecting periodic disturbances. The repetitive control system has been proven to be a very effective and practical method dealing with periodic signals [15–18]. Repetitive control has some similarities with iterative learning control.This paper addresses the electric current tracking control problem for shunt APF. The control law is joint ADRC and RC which can deal with the static and dynamic performance. The rest of this paper is organized as follows. In Section 2, a brief description of the ADRC is presented. In Section 3, main results of ADRC + RC control technique are developed. In Section 4, simulation results are presented to show the effectiveness of the proposed control technique. Finally, some conclusions are made in Section 5.2. Active Disturbance Rejection ControlIn ADRC, the tracking differentiator (TD) is used to deal with the reference input and the extended state observer (ESO) is used to deal with the output of controlled system. Then the ADRC control law can be selected through the appropriate nonlinear combination of state errors. The general structure of ADRC is shown in Figure 1. In Figure 1 of ADRC, the transient profile generator is used to obtain each order derivative of reference trajectory . Next, brief description of ADRC is given as follows.Figure 1: Block diagram of the ADRC.Consider a class SISO nonlinear system as Equation (1) also can be described as where is unknown function, is unknown disturbance, and is control input.Construct the following ESO for nonlinear systems (2): Let , so we can obtain the following conclusion: through selecting appropriate nonlinear function . Defining that is the estimation value of , we can obtain .From the above brief description of ESO, it can be seen that ESO can be used to estimate the states and the sum of model uncertainty and disturbance . So, ESO is such a link, which uses the output of plant to get each order derivative signal and estimation value of disturbance.Using from ESO and from TD, we get the state errors as So the following nonlinear combination can be gotten by state errors (5): where , , and are adjustable parameters. And nonlinear function is defined as follows: Using the nonlinear state errors feedback (6) and estimation value , the ADRC law can be given by 3. Main ResultsShunt APF circuit schematic is shown in Figure 2; the upper and lower arm of the shunt APF can be considered as ideal switch from the APF working principle. The equivalent circuit of APF is shown in Figure 3. Since the switching operation can control voltage size of the AC side. So shunt APF can be considered as a controllable voltage source and a parallel impedance in the circuit, and to compensate harmonic current and reactive current can be achieved.Figure 2: Block diagram of shunt APF.Figure 3: Equivalent circuit of shunt APF.So we can obtain the model of shunt APF as follows: Define PWM as a proportional part, namely, , where is modulation amount. Let be the control input of system. is voltage of DC side. For the supply current, we know Substituting (10) into (9), we have Designed system controller can be considered by a DC voltage outer-loop control and an inner-loop current control. Since the response speed of inner-loop is much faster than the DC voltage outer-loop, it can be considered that DC voltage is constant when the inner current controls. Ignore the impedance of the power line; we let ; system (11) can be written as The APF is a first-order system. ADRC does not need to detect the load current and supply voltage and only uses them as unknown disturbances. A PI controller is used to control the outer-loop DC voltage, which is order to obtain a given current value . can be seen as the reference input of ADRC. The control objective is to make the supply current able to track the given current value through controlling the modulation amount of PWM. Set an order TD output as where , , and are selected parameters. Construct of the following formula ESO: where , , , and are selected parameters. So we can obtain the ADRC law as where , , and are also selected parameters. All selected parameters of ADRC controller must try to get in simulation.RC is mainly used in continuous processes for tracking or rejecting periodic exogenous signals. In most cases, the period of the exogenous signal is known. The internal model principle is the theoretical foundation of RC. According to internal model principle, to track or reject a certain signal without steady-state error, the signal can be regarded as the output of an autonomous generator that is inside the control system.Although RC system can still get a good static performance, it cannot get a good dynamic performance of the system. RC is usually used to meet up with other control strategies. Actually, RC is only used to restrain the tracking error. But ADRC can improve the rapid response of the system. After being coupled with the repetitive controller, controller can detect the tracking error and accumulate a correction on the basis of the original command to reduce the error. Repetitive controller can be seen as an embedded component, so this system is called embedded repetitive control system (ERCS). Figure 4 is a block diagram of a parallel ADRC with RC. Next, how to select the controller parameters of RC is shown as follows.(1)Cycle delay factor N: is sampled beat number of sinusoidal cycle and can be described as fundamental frequency and the switching frequency .(2)Compensation link : characterizes the steady precision of repetitive controller. In general, is a constant. When , the open-loop gain of system is infinite, and steady-state error is zero. But this may likely cause system instability. So we usually select a constant that is less than but close to 1. is also preferably chosen zero phase low pass filter.(3)Compensation link of plant: is used to reform the controlled plant. After reformation, the amplitude-frequency characteristics of the plant has zero gain in the low frequency band. Generally, the series correction part is first selected to correct the low-frequency gain of controlled plant. Then, in order to improve system stability, the second-order low-pass filter is selected to attenuate high frequency gain.(4)Phase compensation factor : the aim of phase compensation factor is to compensate phase lag for reformed controlled plant in the low frequency.(5)Repetitive controller gain : is used to ensure the stability of the system in the high frequency band. The smaller can cause the better stability, but the speed of convergence will become slow and the steady-state error will increase. In general, is chosen to be close to 1 as possible under maintaining the well stability of the RC.Figure 4: Block diagram of a parallel ADRC with RC for shunt APF.4. Simulation ResultsIn this section, we use Matlab/Simulink for testing and verifying the proposed APF control method. The parameters of chosen APF are H, , μs, and kHz. The ADRC controller parameters are designed as , , , , , , , , , and . The RC controller parameters are designed as , , , , , and . First, we consi
I. Shakra, Th. Ellinger, U. Radel, C. Sauerbrey, J. Petzoldt
2013 15th European Conference on Power Electronics and Applications (EPE) pp 1-11; doi:10.1109/epe.2013.6631744

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, Luca Consolini, Emilio Lorenzani
IEEE Transactions on Industrial Electronics, Volume 60, pp 4403-4414; doi:10.1109/tie.2012.2213562

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V. Lakshmi Devi, T. Phanindra
International Journal of Smart Sensor and Adhoc Network. pp 90-94; doi:10.47893/ijssan.2011.1020

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Wensheng Song, Keyue Smedley, Xiaoyun Feng, Pengju Sun
IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society pp 2346-2351; doi:10.1109/iecon.2010.5674930

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Deepak Balkrishna Kulkarni,
Published: 14 June 2010
by IEEE
IEEE Transactions on Power Delivery, Volume 25, pp 1978-1985; doi:10.1109/TPWRD.2010.2040293

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Prince M Anandarajah, H. Shams, P. Perry,
2010 12th International Conference on Transparent Optical Networks pp 1-3; doi:10.1109/icton.2010.5549156

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