Non-sinusoidal Voltage Research Articles

Self-starting of induction motors at non-sinusoidal power source voltage

Subject of research: the process of self-starting of asynchronous electric motors in the presence of higher harmonics in the supply voltage network. Purpose of research: analysis of the influence of non-sinusoidal voltage on the duration of self-starting of asynchronous motors and the amount of additional heating during self-starting. Methods and objects of research: modeling of the self-starting mode of an asynchronous motor in the coordinate system α, β, 0; simulation modeling in Matlab Simulink. Main results of research: it has been shown that failure to take into account higher harmonics when the total harmonic distortion (THD) limit values are reached can result in an error in determining the self-start time by more than 20 % and the heating temperature by more than 10 %.

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.

Single-Stage MV-Connected Charger Using an Ac/Ac Modular Multilevel Converter

Modular multilevel converters with non-sinusoidal ac voltage output can reduce cost and volume in medium-voltage-connected electric vehicle battery charging applications. The use of full-bridge submodules in such converters enables single-stage ac/ac voltage conversion, allowing a medium-voltage grid to be directly connected to a medium-frequency isolation transformer. The application of a square wave voltage at the medium-frequency transformer’s single-phase port enhances the converter’s efficiency and power density in comparison to a sinusoidal voltage. This paper presents the analysis and modelling of a modular multilevel converter, comparing its operation with sinusoidal and square wave output voltages. A single control scheme for both output voltage waveforms is proposed for the three-phase and single-phase ac currents, circulating currents, and the energy stored in the submodule capacitors. The control strategy of the three-phase and single-phase port currents is verified through simulation and experiments using a scaled-down prototype, thereby validating its suitability for high-power bidirectional battery chargers.

Compensation of Budeanu’s Reactive and Complemented Reactive Currents in Extended Budeanu Theory in 3-Phase 4-Wire Systems Powered by Symmetrical Nonsinusoidal Voltage Source

The result of continuous efforts in the development of power theory, Budeanu’s power theory was successfully extended. The mathematical description that has been proposed is based on another concept, namely the Currents’ Physical Components (CPC) theory. With CPC theory, it was possible to describe, in the original Budeanu theory, the components of the load current, including the Budeanu distortion current. The Budeanu distortion current can have a maximum of five components associated with different physical phenomena and related to the equivalent parameters of the load. This article discusses passive compensation, which provides compensation for the Budeanu reactive current and the Budeanu complemented reactive current due to the known equivalent load parameters associated with the reactance elements. In addition, the article refers to a very important aspect when determining the parameters of a passive compensator, i.e., choosing parameters in such a way that the compensator simultaneously compensates for the reactive current and the unbalanced current. The article presents five methods relating to the determination of compensator parameters. Two methods are related to the reactive current compensation only for the first harmonic without affecting the unbalanced current. The next three methods relate to the compensation of the Budeanu reactive current and the consideration of the unbalanced current. Calculations and simulations were performed for all five methods, the results of which are presented and analyzed in this publication. The Matlab/Simulink R2023a environment was used as the calculation and simulation software.

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.

Five-phase space vector carrier-based PWM for third harmonic injection

Five-phase AC drives allow a third harmonic voltage to be fed into the stator winding – in addition to the fundamental voltage – to generate a third harmonic magnetic air gap field. This allows the generation of an additional small constant torque. Furthermore, the undesirable saturation harmonics that occur with saturated iron can be compensated. The desired third harmonic voltage is commonly generated via time-consuming space vector PWM algorithms, which are not well-suited for real-time application, or via look-up tables, which require an increased storage capacity. In our case, the desired third harmonic voltage is generated in the five-phase voltages by adding a non-sinusoidal zero-sequence voltage with five times the fundamental frequency to the fundamental voltage reference signals in carrier-based pulse width modulation (PWM) with a constant switching frequency. This is equivalent to a space vector PWM method (SVPWM) and avoids a significantly high calculation effort. The PWM algorithm programmed in MATLAB in real time allows the fast generation of a third harmonic voltage per phase with freely definable amplitude and phase shift without requiring a lot of storage capacity.

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

Budeanu’s Distortion Power Components Based on CPC Theory in Three-Phase Four-Wire Systems Supplied by Symmetrical Nonsinusoidal Voltage Waveforms

Budeanu’s power theory, in its fundamental version, describes single-phase sinusoidal and nonsinusoidal systems. Over time, this elementary description has been extended to three-phase three-wire and four-wire systems, regardless of power conditions. Initially, three-phase systems were considered as three independent single-phase systems. A distinct approach was introduced by Czarnecki in his power theory (Currents’ Physical Components—CPC). The energy description and reference of the equivalent parameters of the load are comprehensive in the context of three-phase systems; Czarnecki treats such systems as a whole. This paper introduces a mathematical model to expand the basic Budeanu theory for three-phase four-wire (3-p 4-w) systems powered by symmetrical and nonsinusoidal voltage sources. The proposed approach is based on mutual elements between the fundamental Budeanu theory and the CPC theory, treating the 3-p 4-w system as a whole. In the extended Budeanu theory model, equations for the Budeanu reactive current and the Budeanu complemented reactive current are derived. The article also demonstrates their orthogonality concerning the remaining components, indicating that each of the seven components can exist independently of the others. Furthermore, in the extended Budeanu theory, it is possible to identify which equivalent parameters of the load are responsible for the individual currents (powers) and which components are associated with the total distortion power proposed by Budeanu in 1927. All of the calculations were performed in Matlab/Simulink 2023b software.

A Control Strategy for Combined Series-Parallel Active Filter System under Non-Periodic Conditions

In this study, generalized non-active power theory based control strategy is proposed for a 3-phase 4-wire Combined Series-Parallel Active Filter (CSPAF) system using a Three-Dimensional (3D) Space Vector Pulse Width Modulation (SVPWM). The CSPAF system consists of a Series Active Filter (SAF) and a Parallel Active Filter (PAF) combination connected a common Direct Current (DC) link for simultaneous compensating the source voltage and the load current. The generalized non-active power theory was applied in previous studies for the PAF control, in this study the theory is used for the CSPAF system control under non-sinusoidal and nonperiodic current and voltage conditions. The closed loop control algorithm for the proposed CSPAF system has been described to direct control of filtering performance by measuring source currents and load voltages for the PAF and the SAF, respectively. The proposed control strategy has been verified by simulating the CSPAF system in Matlab/Simulink environment.

Coupled Feedforward and Feedback Control Strategy of Parallel Hybrid Filter for Harmonic Mitigation.

The strategy features a small sensitivity against a disturbed supply voltage system and enables us to set grid phase currents in the phase with respective voltages. The expected properties of the PHF control system have been confirmed by experimental tests in the laboratory. The data show that the modified control strategy yields better results than those obtained by using control systems reported previously, especially in case of an unsymmetrical and non-sinusoidal voltage system and the demand of zero reactive power withdrawn from the grid.

ОПРЕДЕЛЕНИЕ ПРОГНОЗИРУЕМЫХ ЗНАЧЕНИЙ НЕСИНУСОИДАЛЬНОСТИ НАПРЯЖЕНИЯ НА ОСНОВЕ СТАТИСТИЧЕСКОГО АНАЛИЗА

A significant problem of ensuring the quality of electricity, including the sinusoidal voltage in the distribution grids of energy systems and power supply grids, arose with the growth and use of equipment with a nonlinear load characteristic. Modernization of production and an increase in its energy efficiency are associated with the use of such electrical equipment. In this regard, in the last decade, the problem of the higher harmonics has become one of the important consequences of global innovative development throughout the world and in Russia in particular. However, the creation of conditions for the operation of all electric receivers in a power system with poor quality of electrical energy causes certain difficulties. (Research Purpose) The research purpose is determining the predicted values of non-sinusoidal voltage based on statistical analysis in distribution grids. (Materials and methods) Methods for analyzing non-sinusoidal voltage and finding deviations from established norms are considered. Studies of non-sinusoidal voltage in distribution grids have been carried out, and critical values of indicators and a constant component have been determined. (Results and discussion) Additional losses from the influence of higher harmonics in distribution electrical grids account for about 4 percent of losses at sinusoidal voltage. In the grids of agro-industrial enterprises, as well as in the grids of traction substations, similar losses reach 17 percent. The maximum value for the entire measurement period is taken as the basis for the measurement result of the harmonic component voltage coefficient, since this approach does not take into account one-time emissions, which in the general structure do not affect the operation mode of electrical equipment. Measurements were carried out in all electric grids on the low and medium voltage side in the Irkutsk region, and the paper presents the results of measurements in the southern electric grids of Irkutsk and its suburbs. (Conclusions) Studies have revealed the presence of a constant component of the coefficient of harmonic components and single emissions exceeding the average operating values. The main regularities of the non-sinusoidal voltage coefficient for the measurement period and the effect on the operating modes of electrical equipment connected to distribution grids are determined.

Measurement and analysis of electric power quality indicators with targeted identification of the perpetrators of non-compliances on the example of the Belarusian energy system

The existing problems of ensuring the established [1] standards of electric power quality indicators (EPQI) in electric networks of different nominal voltage are considered. The authors' practical experience in identifying the perpetrators of non-compliances in terms of non-sinusoidal voltage with the determination of their actual contributions (AC) based on the results of measurements made by their own accredited electrotechnical laboratory is summarized.

Применение методологической базы исследования для определения кондуктивной низкочастотной электромагнитной помехи по коэффициенту n-й гармонической составляющей напряжения

With the help of the methodological base of the study (the foundations of probability theory and mathematical statistics), the processing of the experiment conducted at the research object is carried out. This object is the mechanical workshop of CJSC Sibgazstroydetal, which is engaged in providing for the needs of the gas, oil and energy industries. In this paper, the issue of determining the conductive low-frequency electromagnetic interference (EMI) by the coefficient of the n-th harmonic component of the voltage (K U(n) ) is studied in detail. Harmonic distortion is a constant phenomenon in electrical networks. Higher harmonics have a negative impact on the electrical network, including on electric consumers (reduced service life, productivity, etc.). The problem of non-sinusoidal voltages has been studied for quite a long time and the results obtained during these studies confirm the presence of a large number of damages to electricity consumers who are in operation. The probability of occurrence of conductive low-frequency EMF by K U(n) at the research site is determined. The paper analyzes the results obtained with the help of the conducted research. According to the results of the analysis, the relevant conclusions are presented.

STUDY OF INFLUENCE OF HIGHER HARMONICS ON RELIABILITY CABLE NETWORKS

This study is devoted to the analysis of the cable network of industrial enterprises with a significant number of cable lines with a voltage of 10 kV. A feature of this electric power supply unit is a powerful direct current valve electric drive for rolling production. The schematic diagram of the cable network is shown in the figure, the total length of the cables is more than 20 km. The results of previous experimental studies made it possible to determine the magnitude and spectrum of harmonics in this node, namely: in 5 harmonics do not exceed 1.5%, but abnormal n = 22—40 determine the value of the non-sinusoidal voltage coefficient within the limits of 5.5—8.9%, which exceeds the 5% norm. The plans of the conducted research also included the measurement of single-phase ground fault currents, which gave the following results for workshop substations: PS-4 — 24.2 A; PS-5 — 17.3 A; PS-5 — 14.8 A. Analyzing the problem of the reliability of cable networks, it is necessary to take into account one more indicator — the value of the leakage currents. A significant number of high-voltage cables are insulated with cable paper impregnated with oil-rosin mastic. Such insulation contains gas inclusions that, under the influence of high-frequency electric shocks, are ionized with subsequent neutralization, which leads to its local damage. Oscillograms of the supply voltage show a sharp shape of the curve as a result of the presence of higher harmonics, which causes the aging of the insulation due to the acceleration of physicochemical processes in the dielectric. Thus, the results of theoretical and experimental studies made it possible to substantiate the main factors that determine the operational reliability of cables, namely: the dynamics of leakage currents, the value of the coefficient of non-sinusoidal voltage caused by abnormal harmonics. Analysis of the specified characteristics allows you to assess the current state of the cable network and predict the reliability of work in the future.

Decomposition of the Voltages in a Three-Phase Asymmetrical Circuit with a Non-Sinusoidal Voltage Source

This article presents the concept of a mathematical description of a three-phase, four-wire asymmetrical electric circuit in decomposition into Voltages’ Physical Components (VPC), associated with distinctive physical phenomena in the load. This is an alternative method of mathematical description to the Currents’ Physical Components (CPC) still being developed since the end of the last century. According to previous studies, the improvement of the power factor in three-phase systems is possible by observing several components. Compensation for the scattered power is possible only by using a reactive compensator connected in series with the load. Thanks to the presented analytical method, it is possible to design compensators connected in series with the load. The VPC power theory opens the possibility of improving the power factor in three-phase networks for loads with asymmetry between phases. Due to the unfavorable impact of high currents on the compensator branches, the method proposed in the article can improve the energy quality in local low-power grids. However, the possibility of its practical use in high-power industrial networks is questionable.

A modified hysteresis current controller with DFCEA for current harmonic mitigation using PV-SHAPF

ABSTRACT A Modified Hysteresis Current Controller (MHCC) with Dual Fundamental Component Extraction Algorithm (DFCEA) is presented in this paper. Its purpose is to improve the current harmonics mitigation performance of a three-level T-type inverter-based Shunt Active Power Filter (SHAPF) while operating under non-sinusoidal voltage conditions. The DFCEA is responsible for isolating the fundamental voltage and current components that are necessary for synchronizing each phase and producing the reference current. The existing dual fundamental component extraction technique is updated in order to create the optimized reference currents that are required by the proposed PV-linked T-Type inverter-based Shunt Active Power Filter (PV-SHAPF). This was done in order to meet the requirements of the PV-SHAPF. It is also anticipated that it is excellent at extracting reference currents even under situations of voltage that are not optimum. To maintain the dc-link capacitor voltage at 600 V, a control algorithm of the dc-link capacitor known as the ‘DC link voltage controller’ is used. Both control algorithms are tested in a three-phase T-Type inverter-based PV-SHAPF by simulating them in a MATLAB/Simulink environment. The performance of the MHCC-DFCEA that was designed to mitigate current harmonics was proven by the findings that were gathered.

Разработка мероприятий по устранению резонансных явлений на частотах высших гармоник на линии электропередачи 35 кВ

One of the problems to ensure the quality of electricity and reliability of the network is significant deviation of the voltage curve from sinusoidal in some active electricity transmission lines of the energy system of the Irkutsk region. The purpose of the research is to develop organizational and technical measures to eliminate resonance phenomena at higher harmonics that occur in the active 35 kV electrical line connected to a traction power substation. The object of the research is non-sinusoidal mode of the 35 kV electric power transmission line connected to the medium voltage winding of the three-winding traction transformer. The authors have used technological research methods of calculation using an equivalent circuit of the existing linear circuit of an electrical power system with a traction substation. The software “Calculation program of non-symmetric and non-sinusoidal modes of the electric power system” and Microsoft Excel are used for the research. The authors have developed a 110–35–10 kV “Consumer 1 – Consumer 2 – Consumer 3” model using the software “Calculation program of non-symmetric and non-sinusoidal modes of the electric power system”. The calculation results are processed using Microsoft Excel. Non-sinusoidal electrical modes of the equivalent circuit of the electrical power system and the power transmission lines are calculated. Calculation of non-sinusoidal modes of a 35 kV line is carried out to show the distribution of higher harmonic voltages along the line. It is established that the quality indicators of electricity in terms of non-sinusoidal voltages in most nodes of the 35 kV power transmission line do not comply with GOST 32144-2013. Calculation and analysis of non-symmetric and non-sinusoidal modes of the network have shown resonance voltage increase along the line on the odd harmonics frequencies and elimination of resonance factor when installing the compensation reactor at the beginning of the 35 kV line. Based on the calculation results, the diagrams of harmonics power-voltage curve from 3 to 39 are compiled. Based on the results obtained, the authors have proposed technical measures such as installation of a compensation reactor at the beginning of the electrical power system line to prevent resonance factor to improve the electrical power quality in terms of voltage unsinusoidality in the consumers busbars connected to the 35 kV line. The proposed measures will improve the electrical power quality in busbars of consumers and satisfy the requirements of GOST 32144-2013.

ЕФЕКТИВНІСТЬ ЗАСТОСУВАННЯ МАКСИМАЛЬНОГО СТРУМОВОГО ЗАХИСТУ В ПІДЗЕМНИХ МЕРЕЖАХ

The article considers the use of maximum current protection in underground mine electrical networks, which disables short-circuit currents with an absolute value greater than the starting currents of powerful electric motors. It was determined that these protections have a number of disadvantages. The article reveals that the protection with the current-time characteristic is more perfect than the maximum current protection, but in the case of arcing short circuits, the values of which can be less than the starting ones in absolute value, the protection activation time significantly exceeds the permissible value. Protection with filters of symmetrical components of currents and voltages reduces the sensitivity to two-phase short circuits with a connected load, protection at the level of the third harmonic in the event of a short circuit has a limited range of action and requires duplication. It was investigated that with the use of valve converters and thyristor schemes for controlling the drives of lifting installations and conveyor transport in underground networks, the level of higher harmonic currents increased. In the practice of work of domestic and foreign enterprises, it has been proven that capacitor banks, which are installed to compensate for reactive power, have protection against overcurrents and shortcircuit currents, but with non-sinusoidal voltage, in a number of cases, they quickly fail because they are overloaded with higher harmonics. The article shows that with the increase in the power of the engines of the underground district networks and the manifestation of the asymmetry of the air gap, the higher harmonics given exceed the permissible values. Therefore, the article presents the most promising directions for the construction of systems for the protection of mine distribution underground networks and electrical installations

A FEM in frequency domain for a transient electric field in non-sinusoidal steady state under the non-sinusoidal periodic voltage

PurposeThis paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation.Design/methodology/approachFirstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin’s method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given.FindingsThe FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs’ code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs.Originality/valueThe FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant.

DETERMINATION OF ABNORMAL HARMONICS AND HARMONIC COMPOSITION COEFFICIENTS OF NON-SINUSOIDITY IN A 10 kV NETWORK WITH A VALVE ELECTRIC DRIVE OF DIRECT CURRENT

The operation process of the electric valve drive is accompanied by the generation of higher harmonics — canonical and non-canonical. Limitation of the level of canonical harmonics is carried out by power resonance filters, however, in the case of asymmetry of the control pulses of the thyristors of the converters, non-canonical harmonics are generated — both even and odd harmonics. The composition of non-canonical harmonics can be determined in the case of harmonic analysis of non-sinusoidal current and voltage coefficients. The conducted harmonic analysis makes it possible to determine the composition of the filter-compensating device in the case of its design.
 The article examines the operation of a power supply unit with a powerful valve electric drive powered by controlled six-phase converters. Experimental measurement of higher harmonics showed the following: canonical harmonics ν £ 13 do not exceed 1—1.5 %, while the non-sinusoidal voltage coefficient exceeds the standard by 5 % (equal to 5.5—8.2 %). Such a situation is possible in the presence of high-order abnormal harmonics, which can be explained by the asymmetry of thyristor opening pulses e ³ 3 el. deg. 
 This study is devoted to the analysis of the operation of the power supply unit with a powerful DC valve electric drive powered by controlled six-phase converters. Measurements showed an insignificant level of canonical harmonics (up to 1.5 %), while harmonics ν = 21—39 exceeded 2.5—3.5 %. Such a situation can be explained by the presence of abnormal harmonics of a high order, when the asymmetry of the opening pulses of the thyristors of the converters exceeds 3 el. deg. The analysis of the non-sinusoidal coefficients as a random process and its decomposition into a Fourier series made it possible to determine the harmonic composition of the current and voltage non-sinusoidal coefficients. Thus, the task of the research is defined in the calculation of the harmonic composition of non-sinusoidal coefficients and the analysis of abnormal harmonics