Non-sinusoidal Currents Research Articles

Geometric Algebra Framework Applied to Single-Phase Linear Circuits with Nonsinusoidal Voltages and Currents

We apply a well known technique of theoretical physics, known as geometric algebra or Clifford algebra, to linear electrical circuits with nonsinusoidal voltages and currents. We rederive from the first principles the geometric algebra approach to the apparent power decomposition. The important new point consists of endowing the space of Fourier harmonics with a structure of a geometric algebra (it is enough to define the Clifford product of two periodic functions). We construct a set of commuting invariant imaginary units which are used to define impedance and admittance for any frequency.

State-of-the-Art Power Factor Correction: An Industry Perspective

On 1 January 2001, the IEC 61000-3-2 regulation became effective. Since then, mitigating current harmonics has been essential to ensure that electronic equipment connected to single-phase power distribution lines conforms to electromagnetic compatibility directives. Today, high-quality rectification, commonly known as power factor correction (PFC), is a well-established technique widely adopted by the industry for powering various devices from the ac line. The topic has been studied by academia and industry since the mid-1980s; thus, an enormous amount of research has been published and countless solutions have been proposed since then. However, only a few of those solutions have encountered wide industrial usage. So, it is not the authors’ intention to provide a comprehensive review, but to take stock of the most used PFC techniques from an industry perspective. This paper will review the power factor theory with non-sinusoidal currents, the practical and regulatory aspects of using PFC, and the most common industry solutions for power factor correction in equipment operated from the single-phase, public, low-voltage supply system, with a special focus on boost PFC pre-regulators, their control methods, design procedures, and issues.

Numerical Simulation on AC Loss in REBCO Stacks and Coils Carrying Non-Sinusoidal Currents

Numerical Simulation on AC Loss in REBCO Stacks and Coils Carrying Non-Sinusoidal Currents

Additional Power Losses Under Non-Sinusoidal Conditions in a 22 kV Overhead Power Line

Non-sinusoidal conditions in the electrical networks cause active power losses at the fundamental frequency, corresponding to the first harmonic, and at harmonic frequencies, which are a multiple of the fundamental frequency. Non-sinusoidal currents flow through network components and create additional active power losses. One of the non-sinusoidal current sources is electronic equipment used in industrial plants to control process equipment. In Vietnam, coal mines use frequency-controlled induction motors when processing coal. The induction motors consume non-sinusoidal current, which creates additional active power losses in the supply network. The harmonic active power does not perform useful work. It causes economic damage to both the supply network and industrial enterprises. The power supply systems in industrial areas of Vietnam, where coal is mined, are characterized by low power quality. Companies engaged in coal mining and processing are forced to pay for additional losses of active power due to the low power quality under non-sinusoidal conditions, which reduces the economic efficiency of the companies' operations. The paper presents a review of the literature on the assessment of additional active power losses in overhead power lines at harmonic frequencies. An example of calculating additional losses of harmonic active power is given for a 22 kV overhead power line, through which electrical energy is supplied to the coal grading plant of the Kua Ong-Vinacomin company. Additional losses are calculated using the measurements of harmonic voltage and current at the point of the supply network connection to the 22 kV overhead power line, through which electrical energy is supplied to the coal mine and the coal grading plant. To assess the influence of the electrical equipment of the coal grading plant on the power quality in the supply network, measurements were carried out on 0.4 kV buses of electrical substation of the coal mine.

Model study of the controlled rectifier of mechatronics systems

The article discusses the types of semiconductor converters for mechatronics systems and the possibilities of their model research using MATLAB software. A model study of a three-phase controlled rectifier as a regulated power source is considered. The rectifier model includes units for measuring the constant component of the load current and measuring the constant component of the load voltage, a unit for measuring the amplitude and phase of the first harmonic of the supply current, a unit for measuring the active supply current, and a unit for measuring the active and average thyristor currents. An important aspect of the research is the ability to perform a spectral analysis, taking into account that the energy conversion process is associated with the distortion of the current and voltage forms. It is possible to quantify these distortions when expanding non-sinusoidal currents and voltages into a Fourier series when performing spectral analysis using MATLAB.

Testing and Analysis of Harmonics at utility Substation

This paper is about auditing electrical quality in substations. A Fluke 1748 Energy Analyze is used for power quality audits. The quality audit will be performed according to IEEE Standard 519 2022. The specific purpose of power quality is the cleanliness of the power supply, including voltage fluctuations and waveform distortion. Harmonics occurs whenever non-sinusoidal currents and/or voltages are generated in a power system. This is commonly referred to as harmonic distortion. The main conditions that cause harmonic problems in power systems are non-linear loading, phase imbalance, high input voltage or current, and resonance. Electrical energy is key to industry, commerce and development, so maintaining the quality of electricity flow is important. Having power quality indicators is very important when identifying hazards and possible defects in electrical installations. Keywords: IEEE 519 2022, Harmonics, Power Quality

Pelican-FOPID Based DSTATCOM for real-time load compensation and harmonics mitigation in three-phase distribution system

Power quality (PQ) explores the issues resulting from current and voltage deviations. Non-sinusoidal currents were drawn from the electric grid by the nonlinear loads. These non-sinusoidal currents contain harmonics and reactive power that lower the system's overall power quality. Distribution Static Compensator (DSTATCOM) emerged as a promising compensator to provide solution for all PQ issues. Yet the controlling strategy of this compensator was still complex to design. Here, an optimization-based Fractional Order Proportional Integral Derivative (FOPID) was introduced to manage the DSTATCOM process to improve PQ in a standard bus system. The optimal problem of FOPID controller was solved through the use of novel optimization approach. The DSTATCOM with FOPID was linked to the weak bus system. The pulse-signal of DSTATCOM was done using the optimal controller, which analyzes the error value of reference voltage and bus voltage to generate-pulses. The proposed model was designed, and the performance was analyzed under two cases, like IEEE 33 bus system and IEEE 13 bus system. The proposed optimal controller-based DSTATCOM performance was validated under various conditions such as interruption, swell, harmonics and sag. The optimal controller offered Total Harmonic Distortion (THD) value at sag, swell, and interruption period was 0.46%, 1.36% and 0.46% in IEEE 13 bus system, and 1.79%, 2.10% and 2.67% THD in IEEE 33 bus system. Moreover, the issues mitigation performance was compared to another present approach. The validated outcome demonstrates the proposed model provides a good mitigation performance in all PQ issues conditions, so it was well fit for real-time implementation.

A robust PQ-controlled three-phase SAPF-based SVM and PI anti-windup for power quality improvement

The use of power electronics devices in electrical energy conversion installations has significantly contributed to improving the performance and efficiency of these systems. On the other hand, static converters have contributed to the deterioration of the quality of current and voltage in distribution networks. These converters consume non-sinusoidal currents, and they behave like harmonic current generators. The power factor and overall system efficiency are weakened by these injected harmonics, reactive power, and other issues. Meanwhile, those loads’ harmonic difficulties must be resolved. The research presented in this paper particularly concerns the study of a shunt active power filter (SAPF) intended to compensate for the harmonic currents generated by nonlinear loads and the compensation of reactive energy. The theory of PQ control is the subject of this research. A robust structure is proposed for that purpose. To sustain the DC-link voltage at the desired interval, a robust PI-regulator-based antiwindup is inserted to ensure active power control. Besides, space vector modulation (SVM) is designed to replace classical pulse width modulation (PWM). The principal benefits of this technique are that it supplies a unitary power factor and sinusoidal network current with no requirement for a PWM generator and fewer harmonics. A comparison between the conventional and the proposed control is established to demonstrate the superiority of the PQ-SVM scheme. The comparison mainly concerns the bus voltage as it is the responsible for the whole system stability Expanded simulation results obtained from the transient and steady-state have demonstrated high performance and have confirmed the robustness and effectiveness of the suggested method.

Limitations of Jiles–Atherton models to study the effect of hysteresis in electrical steels under different excitation regimes

PurposeThe accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.Design/methodology/approachThe different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.FindingsThe paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.Originality/valueThe Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.

MULTIFUNCTIONAL GRID CONNECTED INVERTER BY WIND ENERGY CONVERSION SYSTEM

Non-conventional mode of generation of electricity has several advantages over conventional sources of generation. It is eco-friendly, cost effective, damage free, long lasting and more over harmless. Electricity generation through wind energy is considered as socially beneficial and economically feasible for several applications. Domestic and industrial devices use more and more circuits having a non- linear behaviour. They create non-sinusoidal currents causing high harmonic currents in the distribution networks. In the proposed method, a three-phase multifunctional grid-connected inverter interfaced with a wind energy conversion system (WECS) is introduced. This system consists of a permanent magnet synchronous generator (PMSG) based wind turbine, a rectifier and a three-phase voltage source inverter connected to the utility at the point of common coupling. To ensure the multifunctional feature, we propose a direct power control (DPC) which is applied to eliminate line current harmonics, compensate reactive power and feeding wind power into the utility. The simulation results show that the control algorithm of system is effective for eliminating harmonic currents, reactive power compensation and inject the active power available from the PMSG wind turbine into the load and/or grid. Key Words: Wind Energy Conversion System, Double Fed Induction Generator, Self-Excited Induction Generator, Self- Excited Induction Generator, Permanent Magnet Synchronous Generator, Shunt Active Power Filter, Static Compensator, Voltage and Frequency Controller, Photo Voltaic Generator.

Winding Loss Suppression in Inverter-Fed Traction Motors via Hybrid Coil Materials and Configurations

In a typical inverter-fed AC drive system, the stator windings carry a current with a large harmonics content, resulting in an increased AC loss. In this paper, the additional copper losses caused by non-sinusoidal currents are investigated for different magnet wire topologies, including the flat conductor, stranded, and litz wires. Also, a two-slot simplified model is introduced for accurate prediction of the AC losses at high frequency. It is found that one of the major issues of the conventional copper coil is that the losses are not uniformly distributed across the slot, and over 70% of the losses are concentrated near the slot opening. Moreover, using the transient finite element method, different winding topologies and arrangements are simulated at the stranded level to evaluate the losses and current density for each strand under highly distorted currents. Furthermore, different coil samples are prototyped for the same slot geometries to compare their performance under the same pulse-width modulation (PWM) waveforms for a wide range of frequencies. Finally, new hybrid coil topologies are proposed, which employ different magnet wires or materials within the same slot. The results demonstrate that utilizing a mixed wire configuration can effectively mitigate the adverse effects of eddy current losses. This approach can yield up to 16–41% lower losses while also achieving a weight savings of 36–70%.

Design and Implementation of a Low Losses Current-Fed Portable Induction Furnace

This research is concentrated on the practical design of a portable Induction Heating Furnace (IHF) composed of a Current-Fed Parallel Resonance Inverter (CFPRI) as a power supply of an Induction Coil (IC) and its specimen. The design is intended to reduce the losses in both the switches of the inverter and those due to non-sinusoidal currents in the conductors connecting the power supply components. The IC was connected in parallel to a suitable capacitor to form a tank load in this furnace. Detailed design steps for each implemented part are represented in this research. The implemented power supply tested practically on certain load. The practical results were compared with that obtained from the simulation for this system using the (Plecs) computer package. The practical results agreed with the simulation.

AC Loss Analysis in Superconducting Cables Carrying Characteristic and Noncharacteristic Harmonic Currents

Harmonic distortions - especially in current waveform - are the inherent nature of any power system such as urban grids, wind farms, electric aircraft, and other electrified transportation units that could change the AC loss value in High Temperature Superconducting (HTS) cables. The aim is to investigate the impact of non-sinusoidal currents with different integer-harmonics, inter-harmonics, and sub-harmonics on the AC loss characteristics of a 22.9 kV, 50 MVA HTS cable. This was accomplished by using an Equivalent Circuit Model (ECM). To do so, current waveforms containing different harmonic components were passed to the ECM of HTS cable. For evaluating the impact of distorted current waveforms on the AC loss of the HTS cable, the ECM was validated by means of Finite Element Method (FEM) in tape level. The results of validation phase have shown a good agreement between the AC loss value derived by ECM and those calculated by FEM published in literature. The results showed that when current waveform was distorted by harmonics, the value of AC loss was changed significantly with respect to variations of harmonic phase angle, order, and amplitude. Results also indicated that 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonic order has the highest impact on the AC loss value and could increase 6% to 80% of AC loss in comparison to pure sinusoidal current. Sub-harmonics and inter-harmonics could also increase the AC loss value to maximum 88% and 64% higher than that of sinusoidal condition.

Numerical simulation on AC loss in REBCO tapes carrying non-sinusoidal currents

AC loss is one of the greatest obstacles for high-temperature superconducting (HTS) applications. In some HTS applications, coated conductors carry non-sinusoidal currents. Thus, it is important to investigate the effect of various waveforms on AC loss in coated conductors. In this work, transport AC loss in a 4 mm - wide REBCO coated conductor carrying sinusoidal and non-sinusoidal currents, is numerically investigated. The current amplitudes, the frequency of the transport current, and n-value are varied. Non-sinusoidal transport current waveforms studied include square, five types of trapezoidal, and triangular waveforms. Simulated results show that, for a given current amplitude, AC loss for the square current waveform is the greatest, that for the triangular waveform is the smallest. The sequence of AC loss in the conductor for different current waveforms coincides with the penetration depth, which implies the penetration depth determines the AC loss of the coated conductor. Furthermore, the transport AC loss in the conductor was found to decrease with frequency as f-2/n for non-sinusoidal transport current.

Harmonic Analysis of Non-sinusoidal Currents During Heating of Transformers

The results of the analysis of currents in the transformer windings when heated by low-frequency short-circuit currents are presented, for the description of which the Fourier series expansion of piecewise exponential functions is used. This makes it possible to mathematically model the heating process and solve the issues of the ratio of the power released in the electric and magnetic circuits of the transformer.

Investigations of the variable magnetic moment automatic compensation efficiency improving possibility of three-phase electrical equipment currents

An analysis and review of known parametric systems for automatic compensation of electrical equipment the external magnetic field was carried out. It was found that the known parametric electrical equipment automatic compensation systems of the external magnetic field do not take into account the change in the order of alternating power phases when the level of the external magnetic field changes, which reduces the effectiveness of the three-phase electrical equipment magnetic field compensation by two to three times. The parametric system of three-phase electrical equipment sinusoidal currents magnetic moment automatic compensation with the phase alternation order sensor was improved, the distinguishing features of which are the preliminary determination of the phases alternation order in the power circuit of three-phase electrical equipment and the formation electromagnets compensators currents taking into account this order, which allows to increase the efficiency of three-phase electrical equipment currents magnetic moment compensation and use such a system in a three-phase distribution device containing a plurality of three-phase feeders. The system parameters bench adjustment method of the sinusoidal currents magnetic moment automatic compensation of three-phase electrical equipment with the phase alternation order sensor has been improved, which differs from known methods in that the phases order in the power circuit is determined in advance and the currents of the electromagnets compensators are formed taking into account this order and only then the power is supplied in turn, in each independent circuit of the electrical equipment power circuit an electromagnet compensator oriented along the selected axis is simultaneously turned on, the component of the total magnetic moment along the same axis is measured, and depending on its value, the magnitude and phase of the compensation currents signals are adjusted, then the sequence of alternating phases is changed and the rest of the operations are repeated. It is recommended to improve the non-sinusoidal currents magnetic moment system automatic compensation of three-phase electrical equipment with the phases alternating order sensor to ensure high efficiency of the magnetic moment compensation and the external magnetic field regardless of the power supply phases alternating order of three-phase electrical equipment.

Examination of Non-Sinusoidal Current Drive in Direct Current excited Reluctance Motor

A Direct Current excited Reluctance Motor (DCRM) powered by three-phase sinusoidal currents is expected to have a higher torque density than a Switched Reluctance Motor (SRM) powered by unipolar currents because they can achieve a greater angular variation of magnetic co-energy even in the magnetic saturation region. In this study, a non-sinusoidal current drive method for DCRM is proposed to increase torque. The non-sinusoidal current waveform is defined by a Fourier series function, and the optimum coefficients of the current function are solved using nonlinear programming. According to simulation results, the average torque of a DCRM driven by optimized non-sinusoidal current waveform is increased. Furthermore, the current balance between the armature coil and the excitation coil is investigated. As a result, the average torque is increased by up to about 25% when compared to conventinal sinusoidal current drive.

Study on determination of an asynchronous motor’s reactive power by the current-to-voltage converter

This article presents a method for determining the primary currents, non-sinusoidal and asymmetrical currents flowing through the stator windings of an asynchronous motor based on the signal in the form of the output voltage from the current converter loops placed in each phase between the poles of the asynchronous motor stator and in the arrangement of the stator windings. Differences and characteristics of output signals are researched based on independent, series and opposite (bifilar) connection schemes of asynchronous motor current converter loops of measuring coil. In order to determine the value of the currents generated in each phase of the asynchronous motor stator windings, the output signals of the current converter with independent loop and loops connected in series were mutually analyzed. Measuring non-sinusoidal and asymmetrical currents, according to the opposite (bifilar) connection scheme, the loops of measuring coils are placed in the inter-pole grooves of each phase of the stator in the order corresponding to the three-phase stator windings, the current converter measuring coils each consists of two loops, bifilarly connected to each other. The end of loops of the measuring coils has two exits. Diodes and phase meter-regulators are placed on the first outputs of the loops, and they are oppositely connected to the microprocessor unit for measuring and controlling the asymmetry. The second outputs of the loops are connected directly opposite to the microprocessor unit for measuring and controlling non-sinusoidal currents. This type of current converter is important for determining the non-sinusoidal and asymmetrical currents generated in asynchronous motors, it increases the functional capabilities and accuracy of the current converter, and based on the determined results, it simplifies theoretical calculations, and at the same time, the dynamic and it will be possible to determine the static characteristics through theoretical differential equations. As a result of the research, practical and theoretical results were compared.

Analysis of the impact of non-sinusoidal voltage levels in the power grid of apartment buildings on the reliability and efficiency of transformers

The effects of mass implementation of energy-saving lighting on the permissible level of loading of the supply transformer were analyzed. The influence of non-sinusoidal voltages and currents on transformer wear was analyzed. Distortions of sinusoidal shape of voltages and currents lead to additional power losses in transformer. They cause heating of the insulation and windings of the transformer, increased losses and accelerated wear and tear. Higher harmonic components of voltage and current in a 0.4 kV network are caused by the presence of various energy-saving lighting lamps with non-linear volt-ampere characteristic, which include compact fluorescent and LED light sources. As a result, the transformer designed to operate at a frequency of 50 Hz experiences an additional adverse effect in the form of power losses and accelerated wear of electrical insulation, which leads not only to the deterioration of its technical and economic performance characteristics, but also to a significant decrease in reliability associated with the influence of higher harmonic components of voltage and current on equipment failure. It is shown that the lack of power factor correction schemes for low-power compact fluorescent and LED lamps causes the growth of nonsinusoidal voltage and current as they spread, which in turn causes the need to adjust the limit load of transformers to ensure their rated thermal mode. One way to maintain operational reliability under such conditions is to limit the transformer load depending on the level of higher harmonics in the network, as well as to predict the residual life of the operating transformer. Measuring the values of current transformer load and current levels of higher harmonic components of voltage and current will allow not only to calculate an acceptable load factor of the transformer (for the condition of insulation wear), but also to estimate the current residual life of transformer equipment using a neural network model.

Reactive Power and Energy Instrument’s Performance in Non-Sinusoidal Conditions Regarding Different Power Theories

Abstract It is important to conduct the examination of reactive power and energy instruments in normal operating conditions, due to their place in the regulated trade of electrical energy. The challenge arises when the normal operating conditions encompass non-sinusoidal voltages and currents, for two main reasons: the fact that the term reactive power/energy is not unambiguously defined in case of harmonically polluted environment and the fact that the measurement algorithm implemented in the meter is usually not explicitly presented by the producer. Different algorithms provide the same result in case of sinusoidal signals, while in case of harmonics the instrument’s performance may vary significantly, when different power theories are adopted. In the paper, a commercially available reactive energy electricity meter is tested with harmonically distorted voltage and current signals, and an analysis of its output is performed from the perspective of the implemented measuring algorithm, which is not known a priori. The tests encompass alteration of different waveform parameters and the instrument’s output is analyzed from the perspective of several reactive power theories. The conclusion of the analysis results in the meter’s performance feature illustration in correlation with different harmonic parameters and different reference conditions.