Analysis of exact and approximating dependences of active resistance of a conductor on the current frequency based on the influence of skin effect

The operation of semiconductor power converters, which are part of tractionsubstations, frequency-controlled electric drives and other powerful nonlinear loads, cause asignificant emission of higher harmonics of currents to electrical networks. Higher harmonics ofcurrents in electrical networks cause a complex negative effect on the energy efficiency of thenetwork. The increase in power losses in the active resistance under the action of higher harmonicsis due to the increase in the root mean square value of the current and the action of the skin effect.Analytical expressions describing the dependence of the active and impedance of the electricnetwork on the current frequency are determined. Based on them, analytical expressions are obtainedfor the calculation of additional power losses under the action of higher harmonics of currents, whichare due to the skin effect. The dependences of the active resistance of the electric network on thefrequency of higher harmonics are determined on the basis of Bessel equations. The analysis of convergence of the received equations with the data of the international standard IEC 60287-1-1 iscarried out. For the high-frequency zone, simplified approximating dependences are given, whichdetermine the parabolic dependence of the active resistance on the frequency. Simplifiedapproximating dependences of active resistance on the frequency of higher harmonics are obtainedfor engineering calculations. The obtained equations can be used to determine additional powerlosses in the active supports of electrical networks, windings of electric machines, high-frequencytransformers from higher harmonics of currents at different nonlinear loads. In addition, the obtainedexpressions can be used to justify the use of filter-compensating devices.

Inactive capacity compensation device in frequency converters in the composition of electric power systems of marine vehicles

Управление режимами работы гребного электрического двигателя осуществляется полупроводниковыми преобразователями частоты, применение которых значительно ухудшает качество электроэнергии на общих шинах судовых электроэнергетических систем. Основными причинами являются уменьшение коэффициента мощности и появление высших гармоник в потребляемом токе. В результате этого снижается надежность работы потребителей, и увеличиваются потери электроэнергии. Поэтому уменьшение указанных негативных последствий является актуальной задачей. В связи с этим, большое внимание уделяется вопросам, связанным с изучением и разработкой различных методов и устройств обеспечения качества электроэнергии, увеличения коэффициента мощности и фильтрации высших гармоник. В настоящее время, перспективным методов улучшения качества электроэнергии, является применение устройств управления реактивной мощностью и активной фильтрации, т.е. компенсаторов неактивной мощности. Подобные системы можно применять не только для надводных судов, но и в автономных подводных транспортных средствах, в качестве энергетической установки которых выступает батарея топливных элементов. The control of the operating modes of the propulsion electric motor is carried out by semiconductor frequency converters, the use of which significantly degrades the quality of electricity on the common buses of the ship power systems. The main reasons are a decrease in the power factor and the appearance of higher harmonics in the current consumption. As a result, the reliability of the consumers is reduced, and the losses of electricity increase. Therefore, the reduction of these negative consequences is an urgent task. In this regard, much attention is paid to issues related to the study and development of various methods and devices for ensuring the quality of electricity, increasing the power factor and filtering higher harmonics. Currently, a promising method for improving the quality of electricity is the use of reactive power control devices and active filtering, i.e. compensators of inactive power. Such systems can be used not only for surface crafts, but also in autonomous underwater vehicles, the power plant of which is a fuel-cell stack.

Nonlinear load influence on single-phase fault current in shipboard electric networks

Описаны результаты исследований влияния показателей качества электроэнергии на токи однофазных замыканий в судовых электроустановках. Выявлены основные элементы бортовых электроустановок, влияющие на качество электроэнергии. Проанализировано формирование высших гармоник в токе однофазного замыкания. На физической модели электроустановки проведены исследования влияния нелинейной нагрузки на ток однофазного замыкания. Результаты экспериментов подтвердили установленные закономерности. Выявлено, что в установившемся режиме ток однофазного замыкания определяется не только величиной фазной емкости и напряжением сети, но и несинусоидальностью тока нагрузки. Экспериментально показано, что высшие гармоники, присутствующие в токе нагрузки, усиливаются в токе однофазного замыкания. При этом увеличение их амплитуд пропорционально номеру гармоники и ее амплитуде в токе нагрузки. Экспериментально установлено, что формирование высших гармоник в токе однофазного замыкания в результате эмиссии нелинейной нагрузкой приводит к увеличению его действующего значения. The paper represents the research results of the power quality indicators influence on the currents of single-phase ground faults in ship electrical installations. The main elements of on-board electrical installations that affect the quality of electricity are identified. The process of higher harmonics formation in the single-phase ground fault current is analyzed. Studies of the nonlinear load influence on the single-phase fault current are carried out on the physical model of the electrical installation. The experimental results confirmed the established patterns. For the steady-state mode it was discovered that the single-phase ground fault current is determined not only by the phase capacitance value and the mains voltage, but also by the non-sinusoidality of the load current. It has been shown experimentally that the higher harmonics of the load current are amplified in the single-phase ground fault current. In this case, the increase at their amplitudes is proportional to the harmonic number and its amplitude in the load current. It has been experimentally established that the formation of higher harmonics at a single-phase ground fault current as a result of emission by a nonlinear load leads to an increase in its effective value.

A Step-by-Step Design for Low-Pass Input Filter of the Single-Stage Converter

Active power factor correction converters are often introduced as the front stage of power electronic equipment to improve the power factor and eliminate higher harmonics. A Boost or Buck-Boost converter operating in discontinuous current mode is always adopted to achieve high power factor correction. In addition, the input current contains a large amount of higher harmonics, and a low-pass input filter is commonly adopted to filter it out. In this paper, a single-stage high-frequency AC/AC converter is taken as an example to demonstrate the design method of a passive low-pass filter. Firstly, the input side of the grid needs to meet the power factor and harmonic requirements. The preset parameters are set to a range to characterize the performance of the LC filter. The quantitative design method of input filter is proposed and summarized. Moreover, the sensitivity of the filter parameters is analyzed, providing a direction in practical applications. Preset parameters are all proved to conform to the preset range through PSIM simulation. Finally, a 130-W prototype is established to verify the correction of proposed design method. The power factor is around 0.935 and harmonic content in the input current is about 26.4%. All requirements can be satisfied.

Origin of the Solar Rotation Harmonics Seen in the EUV and UV Irradiance

Long-term periodicities in the solar irradiance are often observed with periods proportional to the solar rotational period of 27 days. These periods are linked either to some internal mechanism in the Sun or said to be higher harmonics of the rotation without further discussion of their origin. In this article, the origin of the peaks in periodicities seen in the solar extreme ultraviolet (EUV) and ultraviolet (UV) irradiance around the 7, 9, and 14 days periods is discussed. Maps of the active regions and coronal holes are produced from six images per day using the Spatial Possibilistic Clustering Algorithm (SPoCA), a segmentation algorithm. Spectral irradiance at coronal, transition-region/chromospheric, and photospheric levels are extracted for each feature as well as for the full disk by applying the maps to full-disk images (at 19.3, 30.4, and 170 nm sampling in the corona/hot flare plasma, the chromosphere/transition region, and the photosphere, respectively) from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) from January 2011 to December 2018. The peaks in periodicities at 7, 9, and 14 days as well as the solar rotation around 27 days can be seen in almost all of the solar irradiance time series. The segmentation also provided time series of the active regions and coronal holes visible area (i.e. in the area observed in the AIA images, not corrected for the line-of-sight effect with respect to the solar surface), which also show similar peaks in periodicities, indicating that the periodicities are due to the change in area of the features on the solar disk rather than to their absolute irradiance. A simple model was created to reproduce the power spectral density of the area covered by active regions also showing the same peaks in periodicities. Segmentation of solar images allows us to determine that the peaks in periodicities seen in solar EUV/UV irradiance from a few days to a month are due to the change in area of the solar features, in particular, active regions, as they are the main contributors to the total full-disk irradiance variability. The higher harmonics of the solar rotation are caused by the clipping of the area signal as the regions rotate behind the solar limb.

Research of operating modes of conductors in power supply systems of cranes with induction feed, taking into account the influence of higher harmonics of the current

Purpose. Investigation of the influence of higher harmonics of current on current distribution, voltage and power losses in the supply systems of crane trolleys and development of a calculation method for practical use. Methodology. The analytical method and the results of the modeling method were used for research. Results. Analytical relationships have been obtained that make it possible to determine the current distribution, voltage and power losses in the systems of induction feeding of crane trolleys, taking into account the composition and amplitude of the higher harmonics of the current. Originality. For the first time, analytical dependences are obtained that take into account the effect of changing the trolley parameters on the frequency in the feed systems. Numerical values have been determined for the most commonly used induction feed systems for cranes. It is shown that with an increase in the cross-section of the feed bar there is a decrease in the main, and especially additional, losses. Practical value. Theoretical relationships have been obtained that can be used to calculate the optimization of induction feed systems in the presence of higher harmonic currents arising in power systems during operation of crane semiconductor controlled electric drives.

Experimental studies of single rotors noise of small scale

The work experimentally investigated the characteristics of the noise of large-scale isolated rotors on small-scale models. The experimental rotor model was based on the F7 / A7 design developed by General Electric. The small diameter rotors were 3D printed and powered by brushless DC motors. The studies were implemented at a speed of up to 8500 rpm. Far-field acoustic measurements were performed in a noise-damped anechoic chamber. The noise characteristics of the brushless motors used in the experiments were investigated separately. For brushless motors, the main component is mechanical noise at the speeds of the motor shaft and its harmonics. For a uniaxial electric motor, the mechanical noise at the shaft speed increases with an increase in the rotational speed, while the noise at its higher harmonics decreases. The study of the coaxial electric motor showed an increase in mechanical noise at the higher harmonics of rotation. In experiments with insulated rotors, the tonal and broadband noise content was recorded. The study showed that with an increase in the rotational speed of a single rotor, the noise level rises from 65 to 80 dB. In this case, the maximum sound pressure shifts towards higher frequencies.