Frequency AC Voltage Research Articles

(Invited) AFM for Nanoscale Morphology & Property Characterization of Traditional and Emerging Semiconductors and Ferroelectrics

A wide range of characterization methods based upon Atomic Force Microscopy (AFM) can be applied for nanometer scale analysis of semiconductor and electronic materials & devices. The standard capability of AFM to image the surface topography with nanometer scale spatial resolution is augmented with the capability to measure a variety of physical properties: electrical (for example, surface potential, work function, conductivity, carrier density), magnetic, thermal (temperature distribution, thermal conductivity), and mechanical. More recently, this capability has also been expanded to chemical identification at the nanometer scale using AFM-IR imaging and spectroscopy.We will cover a structured overview of these operating modes presenting their capabilities and limitations with case studies in semiconductor, ferro-electrics and general nanoelectrical devices. The operating modes are compared in terms of (i) physical properties characterized (carriers, charges, conductivity, ferro-electricity, dielectric constant, ...), (ii) spatial resolution, (iii) sensitivity, (iv) dynamic range, and (v) quantification potential. The capabilities and limitations of each operating mode are illustrated with examples from Si-based devices as well as compound semiconductors (HEMT and other), organic devices, and 1D & 2D materials.Novel approaches and novel prob & cantilevers focus on improvements in spatial resolution, detection sensitivity and the capability to correlate multiple properties efficiently. One such approach consists of datacube modes where one acquires an electrical or chemical spectrum in every pixel of the image: one of the parameters controlling the electrical measurements (for example DC voltage, AC voltage or AC frequency) is varied between two user defined values in each pixel of the 2D image. When combined with force mapping method, one simultaneously obtains a correlated nano-mechanical data cube holding information on modulus, stiffness, and adhesion. At the same time, one avoids contact mode imaging, thus extending electrical measurements to soft and fragile samples and improving measurement consistency as compared to conventional contact mode operation. Optimization of the force mapping movements and the electrical measurement setup allows one to maintain a relatively high imaging speed (typ. 10-100 ms/pixel). The approach is illustrated by multiple modes: in conductive AFM, I-V spectra in each pixel are acquired by ramping the DC bias. Applied to SCM and sMIM, dC/dV-V and C-V spectra are acquired. In PFM either switching loops or contact resonance spectra are obtained. Investigation of a variety of materials illustrates the capability to reveal sample properties which are not accessible or easily missed in conventional methods where maps at only one or a few discrete settings are acquired. The datacube approach can also be combined with chemical characterization offered by the AFM-IR method, in this way, offering a path to correlated mechanical-chemical analysis.

(Invited) Application of Impedance Spectroscopy to Analysis of Plasma-Surface Interaction

The impedance spectroscopy method is a way to investigate the electrical properties of the target system by applying an AC voltage and measuring the amplitude and phase of the current. From measured impedance spectra and a physics- and/or chemistry-based electrical circuit model, we obtain physical and/or chemical information about the target systems. This methodology has been widely used in electrochemical research fields, such as batteries. It can monitor the degradation of elements in the target system independently by continuously scanning the AC voltage frequency.In this study, we applied impedance spectroscopy to the investigation of electrical properties and degradation features of dielectric materials during plasma exposure. Considering the plasma generation system, which has some critical differences from conventional DUT of impedance spectroscopy, we developed an in-situ impedance spectroscopy system to measure the impedance of materials under plasma exposure.We applied the in-situ impedance spectroscopy system to measure the degradation features of SiO2/Si structures (SiO2 film on Si substrate) exposed to a low-temperature Ar plasma. By analyzing the measured data based on an equivalent circuit model considering the plasma and SiO2/Si structures, we obtained the resistance (R) and capacitance (C) values for the SiO2 film and SiO2/Si interface independently. One example is the sputtering of SiO2 film by high-energy ion irradiation. In addition to the decrease in thickness, we found dielectric-property degradation by ion irradiation based on the variations in the R and C values of the SiO2 film. Another example is the temporal variation of film and interface properties during continuous plasma exposure. The thickness-dependent degradation in the SiO2 film and SiO2/Si interface was analyzed and compared with the results of previous ex-situ measurement studies.Further studies on the in-situ impedance spectroscopy are ongoing. We recently found a way to diagnose not only material properties but also plasma properties by measuring currents at harmonic frequencies of AC voltage. This harmonic spectroscopy method was demonstrated to capture surface oxidation of metal probe and plasma parameters (electron temperature and ion density) simultaneously. These studies have revealed the potential of impedance spectroscopy to contribute to fundamental and application research on plasma-material interaction.

Charge-Based Separation of Microparticles Using AC Insulator-Based Dielectrophoresis.

Surface charge is an important property of particles. It has been utilized to separate particles in microfluidic devices, where dielectrophoresis (DEP) is often the driving force. However, current DEP-based particle separations based on the charge differences work only for particles of similar sizes. They become less effective and may even fail for a mixture of particles differing in both charge and size. We demonstrate that our recently developed AC insulator-based dielectrophoresis (AC iDEP) technique can direct microparticles toward charge-dependent equilibrium positions in a ratchet microchannel. Such charge-based particle separation is controlled by the imposed AC voltage frequency and amplitude but is nearly unaffected by the size of either type of particle in the mixture except for the time required to achieve an effective separation. This AC iDEP technique may potentially be used to focus and separate submicron or even nanoparticles because of its virtually "infinite" channel length.

Electrified Nano-Gaps Under AC Field: A Molecular Dynamics Study

Solid-Liquid Interfaces (SLIs) hold immense significance in various areas such as materials science, chemistry, physics, biology and medicine [1]. Many studies aim to decipher the molecular details of SLIs through analytical, computational or experimental methods [2]-[3], each optimized for different aspects of SLIs. Analytical methods are mainly based on the mean field approximation and work best for dilute solutions. Computational methods are bound by their maximum accessible time and length scales, while the limitation of experimental approach tend to lie in minimum values accessible of these scales. The concomitant deployment of both the approaches is a powerful tool in studying SLIs.In the current study both the computational and experimental tools are employed to study the interface of silica with aqueous saline solutions under electric fields. Molecular Dynamics (MD) simulation are utilized to investigate the relative response of the ions and waters exposed to an external AC field in a nanoscale silica-elecrolyte-gold system. Complementary experimental measurements are conducted with atomic force microscopy (AFM) which measures the dielectric force exerted on the nanoscale AFM probe. The impact of external factors such as salt concentration, AC voltage frequency and the system size is systematically investigated.Simulations reveal both the transient and stable response of water and ions as the main component of the system to the AC field. In the transient response, the water electric dipole increases monotonically with the voltage at the first cycle while it takes longer for ions to react to the field, limited by their diffusion time. When the ionic response becomes large enough to screen the field, the dipole moment of water molecules decreases and lead the phase of the applied field. The lag in the ionic response is owing to the time required for the ionic diffusion, while the lead in the water response is due to ionic lag.To obtain the stable response through MD simulation, Fourier transform was deployed with the results showing that electric dipole of ions and water have a periodic behavior with a frequency similar to the AC field and waters in lead and ions in lag. The dipole-voltage plots for ions and waters depicted an energy transfer between water and ions in each cycle. Decreasing the frequency to 10MHz, no energy exchange was observed concomitant to the removal of water lead. Besides, in the frequency range of 100MHz-200MHz in which the water phase lead reaches its maximum value, there is also a maximum in the energy exchange. Thus, there is a direct relation between the water-ion energy exchange and lead in the water response.The stable response is affected by various factors including the separation distance between the surfaces, the ionic concentration and the AC frequency. The MD observations of a decrease in the water lead and ionic lag with reducing the electrolyte gap could explain AFM measurements where the dielectric force appears to decrease for small gaps, a counter-intuitive result if bulk electrolyte properties are assumed. The simulation results also show that the sum of the electric dipole of water and ions is always in phase with the applied voltage implying that the field is totally screened by the combination of both of them. To provide the same amount of screening in larger separation distance the electric dipole of ions has to increase to counteract its larger lag which is observed in the ionic dipole values. As the ionic dipole despite water molecules are caused by translational entropy, larger ionic dipole translates to larger forces which is observed in the AFM experiments.[1] Taketoshi et al. Japanese Journal of Applied Physics (2021).[2] T. Fukuma and R. Garcia, ACS nano (2018).[3] J.M. Andanson and A. Baiker, Chemical Society Reviews (2010).

Improvement of AC Conditioning Effect in Vacuum by High Frequency Voltage

To improve the dielectric strength in vacuum, spark conditioning through repetitive breakdowns by AC or impulse voltage is an effective method. AC conditioning at commercial power frequencies has been widely used due to its cost‐effectiveness, but the breakdown voltage after AC conditioning is generally lower compared to impulse conditioning. We have confirmed that multiple breakdowns occur successively in a half cycle of AC voltage application. It is considered that the multiple breakdowns are harmful for conditioning and triggered due to the previous breakdown in the same half cycle. In this paper, we discuss dielectric strength improvement by high frequency AC conditioning and how the multiple breakdowns are induced. We experimentally confirmed that the AC conditioning effect is improved by increasing the frequency of AC voltage for different applied AC conditioning voltages in a sphere‐plane electrode system. We focused on the breakdown position from the light emission images during AC conditioning to investigate whether the multiple breakdowns were induced or affected by the previous breakdown. We found that the multiple breakdowns occurred close to the previous breakdown position. The multiple breakdowns would be induced by the collision of metal particles due to the previous breakdown with the counter electrode. These breakdowns do not contribute to removing protrusion and would lead to damage to the electrode surface. The increasing frequency of AC conditioning would suppress the multiple breakdowns and improve the dielectric strength in vacuum. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

The design of a linear voltage divider based on metal oxide arresters.

In recent years, linearization technology for nonlinear devices has become a hot topic in many fields. In this study, a linear voltage divider based on metal oxide arresters was designed by combining linearization technology and electrical measurement technology to solve the objective problems of online voltage monitoring. These problems include high difficulty in equipment installation, low measurement accuracy, and poor economic benefits. Based on a summary of linearization theory, the sufficient and necessary conditions for the linearization of the voltage divider were deduced in detail. The relevant circuit simulations were conducted, along with voltage divider experiments under power frequency AC voltage, operating overvoltage, and lightning overvoltage. The results revealed that the voltage divider was able to realize linearized measurements and meet the relevant standards of online voltage monitoring. The measurement errors were concentrated in the transition region between the pre-breakdown region (small current region) and the breakdown region (nonlinear region) in the volt-ampere characteristic curve. The main influencing factor of errors was the consistency of the nonlinear characteristics of the high- and low-voltage arms of the voltage divider. The voltage divider designed in this study can be applied in many scenarios, such as power plants, substations, high-voltage electrical equipment manufacturing plants, and high-voltage laboratories.

Solar Induction Cooker

There is no available power grid in the rural areas in many countries in South America, Asia and Africa. st places, Fossil fuel or wood is used for cooking. Besides environmental issues, fossil fuel and wood from trees are being depleted at a fast rate. Solar power is available everywhere during day time in all countries. This solar induction cooker uses a solar panel, which gives a variable dc, to charge a battery. The dc from the battery is converted to a high frequency ac voltage by an inverter circuit. This inverter circuit supplies alternating current to a coil on a magnetic core where alternating flux is produced. This alternating flux produces in the magnetic core Eddy current and Hysteresis ‘losses’ inside the magnetic core. In this application, these losses will produce useful heat. A cooking pot placed on the magnetic core will be used for cooking.

Non‐uniform voltage distribution characteristics of metallized film capacitors in flexible HVDC projects

AbstractThe problem of non‐uniform voltage distribution in the internal element of metallized film capacitors in flexible HVDC transmission systems exists, the influence of electrical parameters of dielectric and metal copper row are not considered in the existing metallized film capacitor equivalent circuit model. In this paper, the conductance of biaxially oriented polypropylene film (BOPP) for metalized film capacitors is measured at different electric field intensity and dielectric properties at different frequencies. The current density distribution and voltammetric properties of the metalized film capacitor elements under AC and DC superimposed voltages are calculated by the finite element method, and the voltammetric properties of the copper row considering the skin effect are derived. The equivalent circuit model of the metalized film capacitor under the AC‐DC superposition voltage is proposed. The simulation results of the capacitor equivalent circuit model show that the voltage distribution of the internal elements of the capacitor is uniform at low frequency AC voltages (<102 Hz), and the voltage amplitude and phase difference between the elements of the capacitor gradually increases with increasing AC voltage frequency. At an AC voltage frequency of 105 Hz, the difference in magnitude between the two capacitor elements on the same copper row was up to 2.01% and the phase difference was 13.5%, while the difference in magnitude between capacitors at the same horizontal position on different copper rows was up to 56.8% and the phase difference was 10.44%. The results of this paper provide some guidance for the modeling of the internal components of metalized film capacitors, the calculation of voltage distribution and the structural optimization design.

Bilateral Primary Frequency Support and AC Voltage Regulation of LCC-HVDC Systems for Asynchronously Interconnected Systems

Bilateral Primary Frequency Support and AC Voltage Regulation of LCC-HVDC Systems for Asynchronously Interconnected Systems

BiLSTM-FCN based vibration signal diagnosis of smart grid cables

Abstract Cable faults threaten the safe and stable operation of smart grids, and vibration signal diagnosis research on cables based on artificial intelligence technology can effectively enhance the reliability of smart grids. In order to improve the speed and accuracy of cable defect identification, this paper proposes a partial discharge identification method for cables based on a fully convolutional bidirectional long short-term memory neural network (BiLSTM-FCN). The time-domain characteristics of different working conditions under industrial frequency AC voltage are collected by building a vibration signal-based partial discharge test platform for cables. The Overlap strategy enhances the data set. The BiLSTM layer is introduced to process the one-dimensional time domain waveform signal, and combined with the local detail features extracted by the FCN layer, the data features are more abundant. Thus, a more accurate diagnosis of localized discharge in high voltage cables under different operating conditions. The results show that the diagnostic accuracy based on the BiLSTM-FCN model reaches 92.2%, which is 1.2% and 1.4% higher compared to the FCN model and the BiLSTM model. BiLSTM-FCN model possesses a better recognition effect and faster recognition speed in the identification of partial discharge defects type, which can effectively achieve the automatic detection of abnormal fault nodes of smart grid cables. It is significant for realizing online dynamic evaluation of small portable online monitoring equipment and provides a reference for future related research.

A parallel piezoelectric micro-perforated panel absorber with flexible acoustic characteristics

In this paper, the sound absorption characteristics of a parallel micro-perforated panel absorber (MPPA) fabricated from polyvinylidene fluoride (PVDF) piezoelectric film are studied under an alternating voltage excitation. The simulation and experimental results show that when a certain frequency of AC voltage is applied to the parallel micro-perforated panel, the sound absorption characteristics of the MPPA at the excitation frequency can be improved due to the electrically induced vibration. With an increase in the alternating voltage amplitude, the improvement in sound absorption characteristics is more obvious. Therefore, the sound absorption coefficient of parallel PVDF-MPPA in the target frequency band can be improved by adjusting the parameters of excitation voltage reasonably. Based on the convenience of voltage regulation, this method is very suitable for suppressing the noise of the main frequency fluctuation without changing the structural parameters of the absorber. More importantly, the parallel PVDF-MPPA can apply voltage excitations of different parameters simultaneously, which is beneficial to improve the sound absorption effect in a wider frequency band. This study may provide a reference for the design of intelligent absorbers, especially for noise reduction structures in narrow spaces.

Metrological support of digital electronic voltage transformers and low-power voltage transformers

Metrological support of digital electronic voltage transformers and low-power voltage transformers (sensors) is represented. The methods and reference measuring instruments of the State primary special standard of units of the ratio error and the phase displacement of AC electric voltage of power frequency in the range from to and units of electric capacitance and tangent of loss dissipation factor at AC voltage of power frequency in the range from 1 to 500 kV – GET 175-2023, used for metrological support of the measuring instruments mentioned above. The results of research of GET 175-2023 are presented. The expanded uncertainties of GET 175-2023 when reproducing the units of the ratio error and the phase displacement of AC electric voltage of power frequency for metrological support of analog low-power voltage transformers (sensors) include the budget of the uncertainties of the current comparator, low-voltage (reference) and high-voltage measuring measures, the high-voltage MVE-01 bridge (SA7400MA1 amplifi er) and are respectively 9.62·10–5 and The expanded uncertainties of GET 175-2023 when reproducing the units of the ratio error and the phase displacement of AC electric voltage of power frequency for metrological support of electronic digital voltage transformers and digital low-power voltage transformers (sensors) include the budget of uncertainties of the converter «high voltage – current», converter «current – low voltage», converter «low voltage – a digital copy of voltage», a digital comparison device and constitutes 10.8·10–5 and respectively. GET 175-2023 allows solving the problems of metrological support of electronic digital voltage transformers and digital low-power voltage transformers (sensors).

Harmonic filtering and fault ride‐through of diode rectifier unit and modular multilevel converter based offshore wind power integration

AbstractThe diode rectifier unit (DRU) is promising in offshore wind power integration due to its reliability and economy. Offshore AC voltage control is the key technology of the DRU‐based scheme. In this paper, a low‐cost offshore wind power integration system based on the DRU and the modular multilevel converter (MMC) in parallel on the rectifier side is proposed. The low‐capacity MMC rectifier is controlled to establish the offshore AC voltage amplitude and frequency, maintain all offshore wind active power transmitted by the DRU, and provide reactive power compensation and AC harmonic filtering for the DRU. Besides, the fault ride‐through strategies of both the offshore fault and the onshore fault are proposed. Moreover, the calculation method of the rated capacity of the MMC rectifier is derived. The time domain simulations of the hybrid system under typical operating conditions are investigated in PSCAD/EMTDC, and the feasibility of the proposed scheme is verified.

Identification of Electrical Tree Aging State in Epoxy Resin Using Partial Discharge Waveforms Compared to Traditional Analysis.

Electrical treeing is one of the main degradation mechanisms in high-voltage polymeric insulation. Epoxy resin is used as insulating material in power equipment such as rotating machines, power transformers, gas-insulated switchgears, and insulators, among others. Electrical trees grow under the effect of partial discharges (PDs) that progressively degrade the polymer until the tree crosses the bulk insulation, then causing the failure of power equipment and the outage of the energy supply. This work studies electrical trees in epoxy resin through different PD analysis techniques, evaluating and comparing their ability to identify tree bulk-insulation crossing, the precursor of failure. Two PD measurement systems were used simultaneously-one to capture the sequence of PD pulses and another to acquire PD pulse waveforms-and four PD analysis techniques were deployed. Phase-resolved PD (PRPD) and pulse sequence analysis (PSA) identified tree crossing; however, they were more sensible to the AC excitation voltage amplitude and frequency. Nonlinear time series analysis (NLTSA) characteristics were evaluated through the correlation dimension, showing a reduction from pre- to post-crossing, and thus representing a change to a less complex dynamical system. The PD pulse waveform parameters had the best performance; they could identify tree crossing in epoxy resin material independently of the applied AC voltage amplitude and frequency, making them more robust for a broader range of situations, and thus, they can be exploited as a diagnostic tool for the asset management of high-voltage polymeric insulation.

Dynamic measurement of magnetic characteristics of switched reluctance motor

Introduction. Switched reluctance motor (SRM) is a type of electric motor featuring nonlinear magnetic characteristics. The flux linkage or inductance profile of SRM is usually required for the purpose of high control performance, and can be normally obtained through conventional static test by using DC or AC method when the rotor is locked. Problem. However, it is not practical to use the conventional method of measurement when the specific apparatus for locking the rotor is unavailable. Besides, due to the magnetic nonlinearity of SRM, the saturation effect makes it difficult to obtain the saturated magnetic characteristics, and the conventional static AC test fails to address this problem. Novelty. In this paper, a dynamic measurement method of the magnetization curves of SRM is proposed which allows the measurement take place while the motor is running with load. Methodology. Based on the conventional static AC test, the proposed measurement handles the saturation problem successfully by introducing a DC offset in the high frequency AC voltage. Phase inductance with different rotor positions and currents can be obtained by analyzing simple equivalent circuit. Practical value. Simulation is conducted in MATLAB/Simulink environment and the results have verified that the proposed dynamic measurement can effectively obtain the magnetic characteristics of SRM.

A Multipurpose and Power Quality Improved Electric Vessels Charging Station for the Seaports

To avoid air and noise pollution on seaports, the use of electric vessels and shore-to-ship power supply based charging station on seaports are in trend, which is also known as cold ironing (CI) infrastructure. In the starting stage, electric vessels charging stations are being implemented on the most busiest commercial ports, where modern electronic devices are used to serve different types of vessels. These devices only take care of the quality of output power. However, on the input side, it creates a serious harmonic issue. During CI, megawatt range of power is supplied to the ships, so generated harmonics and interharmonics in the high-power supply based charging system become more dangerous for the grid. In this article, we propose a novel power quality improved cold ironing (PQICI) system (charging mechanism) to overcome this issue. Moreover, due to inherent multipurpose useability, this novel PQICI is able to supply different types of power to various types of vessels, such as ac power, dc power, 50 Hz frequency, 60 Hz frequency, single phase, three phases, three-wire network, four-wire network, five-wire network, and different ac and dc voltages. Furthermore, this PQICI supply system is capable of serving four vessels at a time. In every type of loading condition with different kinds of power supply mode, the PQICI maintains the power quality on the input side, with fulfilling the varieties of the power demand of vessels. The capability of the developed “PQICI” system is tested for different types of ships and vessels on the simulation platform as well as through real-time hardware-in-the-loop experimentation. On IEEE standard 519, satisfactory test results on both platforms show the efficiency of the developed system and its control mechanism.

Dual, Three-Level, Quasi-Z-Source, Indirect Matrix Converter for Motors With Open-Ended Windings

In this paper, a novel variable-voltage, variable-frequency, dual, three-level, quasi-Z-source, indirect matrix converter topology is proposed, including a detailed description of a modulation method and a control strategy for three-phase motors with open-ended windings. The proposed power drive system (PDS) supports bidirectional power flow and has a combined control of DC-link voltage and output AC voltage frequency. Experimentally validation was performed on a 4-kW PDS. For a given supply voltage amplitude and the same power switch voltage rating in the DC/AC converter, the proposed PDS can double the voltage output gain, thus being an interesting solution for high-power applications with motors designed for higher voltages. The proposed PDS topology, modulation method and motor control strategy can reduce the common-mode component, low-order harmonic content, peak values and d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</i> /d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> of the motor phase voltage, ultimately leading to lower winding insulation voltage stress at low-speed, low-voltage operation, lower harmonic losses in the motor, and ride-through capability over voltage sags in the mains, which are important advantages.

Computational study on the discharge dynamics of atmospheric pressure He plasma driven by high frequency AC voltage

A two dimensional self-consistent fluid model has been established to investigate the discharge dynamics of double-ring electrode He atmospheric pressure plasma jet (APPJ) driven by high frequency AC voltage. The difference of the internal stream and external jet and the influence of the change of applied voltage polarity on plasma discharge characteristics has been discussed. It has been discovered that the capacitive breakdown characteristic of the double ring electrode significantly enhances the intensity of the APPJ. The discharge intensity of the external jet is stronger than that of the internal stream and the propagation speed of the external jet is faster than that of the internal stream due to the ionization and Penning ionization of N2 and O2. Therefore, the density of reactive species in the external jet is greater than that in the internal stream. When the negative voltage is applied to the downstream electrode, the propagation direction of the internal stream changes to the downstream electrode. The ionization of the external jet is also concentrated near the downstream electrode and in the streamer head. The radial propagation distance of the external jet on the dielectric surface continues to increase and the peak value of the radial electric field is concentrated at the streamer head. When the applied voltage changes from negative to positive, the propagation direction of the internal stream turns to the upstream electrode and the upstream jet is formed above the electrode. At the beginning of the positive cycle, the radial propagation distance of the external jet is shortened due to the effects of the electron attachment of O2 and the radial electric field. With the increase of applied voltage, the ionization in the streamer head gradually increases, which promoted the radial propagation of external jet.

Smooth frequency change effects in electrical circuits: explained by the Fresnel integral

The paper presents the problem of the relation between ac voltage frequency supplying a circuit and the resulting current frequency in that circuit in the case when the voltage frequency changes smoothly following a {f}_{{v}}left(tright) function. Contrary to the expectations, the resulting current frequency fc(t) changes in a different way that this of the voltage. One can say that the current frequency variations are considerably amplified compared with these of the supply voltage. This problem is important because we have to deal with voltage frequency changes that are introduced deliberately, like in case of starting ac motors, and voltage frequency variations that result from external influences, like in case of electrical grids with significant component from wind generating units. Paper solves this problem in analytical way by presenting a relation between supply voltage frequency variations {f}_{v}left(tright) and resulting current frequency fc(t). It also contains solution of the inverse problem which can find the frequency function of the supply voltage that will result in a required frequency of the current. According to the best author’s knowledge, this problem was not reported and examined before and potentially has a number of practical implications, one of which – the induction motor frequency starting – is presented as for example purposes in the paper. The significance of the problem discussed in this paper has still to be examined and established, since frequency variations apply to many engineering branches and until now were counteracted by frequency control without a comprehensive identification of the problem.Article HighlightsThe supply voltage frequency variations have an important effect on the respective current frequency of the loads. One can forecast that a frequency of the current changes so that it follows exactly the frequency change of the supply voltage. However, in reality the situation looks much different. The frequency of the current changes occur much more intensively than the frequency in the supply voltage, that is the frequency changes of the current amplify the variations of the supply voltage. This phenomenon has neither been examined nor described in technological literature yet, according to best author’s knowledge.The paper presents, explains and solves the problem in an analytical way. It presents a formula to calculate the frequency of a current when a function of the frequency of the supply voltage is given. The paper also contains a solution of the inverse of the problem described above. There is presented general form of an ordinary differential equation that serves to find a supply voltage frequency function which results in required frequency of the current in a circuit. Presented solutions are general and hold for any lumped parameters circuits: single phase, multi-phase as well as for ac electrical motors supply. In the paper this is demonstrated for single phase circuit supplied by the three exemplary voltage frequency functions as well as for the case of induction motor frequency starting.

Cooperative Control Strategy of Fundamental Frequency Modulation-Based Current Source Converters for Offshore Wind Farms

The actively commutated current source converter (CSC) does not need large energy storage capacitors and can realize the black start of wind farms, which provides a practicable scheme for the lightweight offshore wind power DC transmission system. However, resulted from utilizing pulse width modulation, the existing CSC has the disadvantages of high DC harmonics and high switching loss. To solve this problem, an offshore wind power transmission system based on the current source converter with fundamental frequency modulation employed (FFM-CSC) is investigated. Firstly, the topology and mathematical model are analyzed. Then, a steady-state control strategy coordinated by the offshore CSC and the onshore CSC is put forward, and the power operating range is researched. A black start control strategy for wind farms is also proposed. Finally, the offshore wind power transmission system is tested by simulation in PSCAD/EMTDC. The results demonstrate that the FFM-CSC-based offshore wind power transmission system can smoothly realize the black start, stably control the frequency and amplitude of AC voltage, adapt to output changes of wind turbines, and realize the fault ride-through.