Nonsinusoidal Voltage Source Research Articles

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.

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.

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.

The influence of non-sinusoidal voltage sources on the steady state performance of different NEMA Designs of IMs

Voltage distortion has become one of the most common power quality problems in industrial applications, which has gained a great deal of attention in recent years because of the widespread usage of non-linear loads. Three-phase induction motors are widely used and one of the factors that confirm the reduction of their performance is the presence of harmonics in their voltage supply. In this paper, the impact of non-sinusoidal supply voltages on the steady-state performance of different NEMA designs of squirrel cage induction motors (SCIMs) is presented. It presents the analytical modeling based on the equivalent circuit taking into consideration the skin effect impedance that incorporates the skin effect on the rotor bars, which is used to investigate the motor performance under such conditions. The importance of this study is that it compares all NEMA designs in terms of electromagnetic torque, efficiency, losses, power factor, stator and rotor currents, and derating factor under a distorted supply voltage that is polluted by the most significant odd harmonic orders at adjustable levels in the range of (0–25) % of THDv%. The obtained results are compared and validated with the system employed by using MATLAB/Simulink software.

Source current harmonic mitigation of distorted voltage source by using shunt active power filter

In this paper, three-phase, four-wire shunt active power filter (SAPF) is utilized to mitigate system harmonics of distorted voltage source for unbalanced and nonlinear loads. Basically, the source voltage should be pure sinusoidal waveform to get a good mitigation of source current harmonics. In this under study system, the source voltage is assumed to be harmonic distortion non-sinusoidal voltage source. The phase locked loop (PLL) control circuit is wielded for extracting the fundamental component of the distorted source voltage to use it as an input signal to the SAPF control. Another input signal to the SAPF is the distorted load current. The SAPF control system uses (p-q) theory to calculate the optimum instantaneous current to be injected by the SAPF to mitigate the source current harmonics even the source voltage is harmonic distorted. MATLAB/SIMULINK software package is utilized to simulate the system under study. The effect of SAPF is tested when it’s used with and without the PLL control circuit. The simulation results show that, the THD of source current when using the PLL control circuit is improved to comply with the harmonic limits given in the IEEE 519-1992 and IEC 61000-4-7 standards.

Comparative Performance Analysis Involving a Three-Phase UPQC Operating With Conventional and Dual/Inverted Power-Line Conditioning Strategies

This article deals with a complete evaluating and comparative analysis involving static and dynamic performances of a three-phase unified power quality conditioner (UPQC) controlled to operate using conventional and dual/inverted compensation strategies for performing active power-line conditioning. In the conventional strategy, the series converter of the UPQC operates as a nonsinusoidal voltage source, while the parallel converter operates as a nonsinusoidal current source. Differently, when the UPQC operates with a dual/inverted strategy, the series converter operates as a sinusoidal current source, while the parallel converter is controlled to act as a sinusoidal voltage source. Although, in theory, the results achieved using the mentioned strategies looks similar, in practical applications there are considerable differences in both static and dynamic performances that must be considered for choosing the best compensation strategy to be adopted. Thus, this article addresses aspects related to the mathematical modeling, control and generation of the control references applied to the UPQC, which are implemented using two three-level neutral-point clamped inverters. Furthermore, the performance of the UPQC operating under static disturbances (grid voltage harmonics/unbalances and load current harmonics), as well as dynamic disturbances (voltage sags/swells and load changes) are extensively tested by means of an experimental setup.

Application of Analytic Signal and Smooth Interpolation in Pulsewidth Modulation for Conventional Matrix Converters

This article proposes an alternative and novel approach to the pulsewidth modulation (PWM) duty cycles computation for conventional matrix converters (CMC) fed by balanced, unbalanced, or nonsinusoidal ac voltage sources. The presented solution simplifies the prototyping of direct modulation algorithms. PWM duty cycles are calculated faster by the smooth interpolation technique, using only vector coordinates, without trigonometric functions, and angles. Both input voltages and output reference voltages are expressed by analytic signals in the proposed direct modulation. Input voltages are represented by the rotating vector collection in the 2-D Cartesian coordinate system. All reference output voltages are located inside the triangular surface, named here as the voltage synthesis field, formed by these rotating vectors. A certain degree of reference signals placement freedom allows us to maximize the voltage transfer ratio to 0.866 with less switching compared to the optimum-Venturini direct method. The proposed solution was verified by simulations and experiments for CMC3 × k. The comparison with the optimum-Venturini modulation is included. The proposed PWM duty cycle computation approach can also be applied to multiphase CMC converters for any number of inputs as well as outputs.

Real Time Harmonic Mitigation Using Fuzzy Based Highly Reliable Three Dual-Buck Full-Bridge APF for Dynamic Unbalanced Load

Abstract This study presents a highly reliable 3-phase 4-wire, three dual-buck full-bridge shunt active power filter (3 DB FB APF) for distribution system. The proposed topology uses three single phase dual buck full bridge inverter sharing the same dc-link capacitor with high utilization of dc-bus voltage. The dual buck inverter circuit composed of one power switch and one diode leg instead of two power switches conventional inverter leg effectually eliminate the undesirable “shoot-through” phenomenon occurs in conventional inverter circuit. The fuzzy and adaptive hysteresis current controller based id-iq control strategy has been adopted to generate optimized switching frequency. For validation, the proposed topology is implemented in the OPAL-RT LAB using OP5142-Spartan 3 FPGA. The dynamic performance of the proposed 3 DB FB APF is assessed for sinusoidal, unbalanced and non-sinusoidal voltage source condition with unbalanced non-linear load that is when both three-phase and single-phase loads are present in the system. Besides, the results with proportional-integral (PI) controller are compared with FLC in terms of harmonic compensation. Furthermore, a comparison has been made between split capacitor dual buck half bridge active power filter (2C DB HB APF) and proposed 3 DB FB APF based on switch power rating.

A Refined Self-Tuning Filter-Based Instantaneous Power Theory Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filters under Non-sinusoidal Source Voltage Conditions

In this paper, a refined reference current generation algorithm based on instantaneous power (pq) theory is proposed, for operation of an indirect current controlled (ICC) three-level neutral-point diode clamped (NPC) inverter-based shunt active power filter (SAPF) under non-sinusoidal source voltage conditions. SAPF is recognized as one of the most effective solutions to current harmonics due to its flexibility in dealing with various power system conditions. As for its controller, pq theory has widely been applied to generate the desired reference current due to its simple implementation features. However, the conventional dependency on self-tuning filter (STF) in generating reference current has significantly limited mitigation performance of SAPF. Besides, the conventional STF-based pq theory algorithm is still considered to possess needless features which increase computational complexity. Furthermore, the conventional algorithm is mostly designed to suit operation of direct current controlled (DCC) SAPF which is incapable of handling switching ripples problems, thereby leading to inefficient mitigation performance. Therefore, three main improvements are performed which include replacement of STF with mathematical-based fundamental real power identifier, removal of redundant features, and generation of sinusoidal reference current. To validate effectiveness and feasibility of the proposed algorithm, simulation work in MATLAB-Simulink and laboratory test utilizing a TMS320F28335 digital signal processor (DSP) are performed. Both simulation and experimental findings demonstrate superiority of the proposed algorithm over the conventional algorithm.

Adaptive hysteresis and fuzzy logic controlled‐based shunt active power filter resistant to shoot‐through phenomenon

This study proposes a novel adaptive hysteresis and fuzzy logic controlled based 3-phase 4-wire full bridge interleaved buck active power filter (FB IB-APF) which eliminates current harmonics without shoot-through phenomenon. Besides mitigating current harmonics, special attention has been given to improve the reliability of the APF by eliminating shoot-through current occurred in the converter circuit. The proposed APF topology consists of three single phase full bridge interleaved buck converter and therefore can be used for high voltage, medium-to-high power application. id –iq control strategy along with fuzzy logic controller (FLC) have been used for reference current generation. The results with PI controller have also been shown to prove the superiority of FLC. The adaptive hysteresis band current controller is being implemented to obtain optimised switching frequency. The performance of the proposed FB IB-APF is evaluated under sinusoidal, unbalanced and non-sinusoidal voltage source condition. Exhaustive simulation results are presented and finally verified with a real time digital simulator. The performance shows that FB IB-APF brings the total harmonic distortion of the source current well below 5% adhering to IEEE-519 standard. A comparison has also been made, based on switch device power between the IB-APFs using for low power and high power application.

A Step Forward in the Modeling of the Doubly-fed Induction Machine for Harmonic Analysis

This paper develops a doubly-fed induction machine model for steady-state harmonic studies. The model is based on the well-known steady-state induction machine model, considering nonsinusoidal voltage sources on the stator and rotor sides of the machine. The results obtained with the proposed model match those obtained from real lab measurements and with a complete induction machine model for transient studies.

Frequency analysis of DC tolerant current transformers

This article deals with wide frequency range behaviour of DC tolerant current transformers that are usually used in modern static energy meters. In this application current transformers must comply with European and International Standards in their accuracy and DC tolerance. Therefore, the linear DC tolerant current transformers and double core current transformers are used in this field. More details about the problems of these particular types of transformers can be found in our previous works. Although these transformers are designed mainly for power distribution network frequency (50/60 Hz), it can be interesting to understand their behaviour in wider frequency range. Based on this knowledge the new generations of energy meters with measuring quality of electric energy will be produced. This solution brings better measurement of consumption of nonlinear loads or measurement of non-sinusoidal voltage and current sources such as solar cells or fuel cells. The determination of actual power consumption in such energy meters is done using particular harmonics component of current and voltage. We measured the phase and ratio errors that are the most important parameters of current transformers, to characterize several samples of current transformers of both types.

Novel Filter for Stator Harmonic Currents Reduction in Six-Step Converter Fed Multiphase Induction Motor Drives

Multiphase induction motors have a lot of advantages over the conventional three-phase induction motors. But when a motor is supplied with nonsinusoidal voltage source inverter (VSI), it will be found that unwanted harmonic currents substantially exist in stator windings. Focusing on the drawback, a strategy for filtering these kinds of current based on electromagnetic principle is proposed. Actually, the filter is a specially designed inductance that is connected between the multiphase motor and VSI. In this paper, research is carried out on a six-phase induction motor, the most typical multiphase motor being studied at present. Accordingly, the fifth and the seventh harmonic currents in stator should be reduced as the substantial harmonics. Different from the filtering inductances presented earlier, the novel one is of symmetrically round shape. Thus, it is possible to design the construction to be extremely compact. Principle of filter is expounded and considerations are taken for filter design. A prototype of the proposed filter is tested on a multiphase induction motor supplied with a six-step VSI. The experimental results show the validity of the filter as expected.

A Novel Detecting Algorithm for Harmonics and Reactive Currents under Unbalanced and Non-Sinusoidal Source Voltages

Harmonics and reactive currents detected in precision is the key whether active power filters work well. Methods on detecting affect compensation currents and detecting precision. A novel harmonics and reactive currents detecting algorithm in three phase circuit is proposed. It extracts positive fundamentals of source voltages and load currents using three-phase sinusoid and cosine signals with arbitrary phase, and then detects harmonics, reactive and negative currents by accurately separating positive fundamental active component from load currents. Whether waveforms of voltages are non-sinusoidal or unbalanced, the results can not be affected. Furthermore, it is without phase lock loop. Finally, it is proved to be precision and feasibility from simulation.

Analysis of Generalized Non-Active Power Theory for Compensation of Non-Periodic Disturbances

The principle and analysis of usage of the generalized non-active power theory for the parallel compensation of periodic and non-periodic current disturbances is presented in the paper. A non-linear unbalanced load generating periodic as well as non-periodic stochastic currents connected to an unsymmetrical non-sinusoidal voltage source is considered.

A cyclodissipativity characterization of power factor compensation of nonlinear loads under nonsinusoidal conditions

SUMMARYRecently, it has been established that power factor (PF) improvement for nonlinear loads with nonsinusoidal source voltage is equivalent to imposing the property of cyclodissipativity to the source terminals. Using this framework, the classical capacitor and inductor compensators were interpreted in terms of energy equalization. The purpose of this brief note is to extend this approach in three directions. In the result reported in the literature, the supply rate is a function of the load, which is usually unknown, stymieing the applicability of the technique for compensator synthesis. Our first contribution is a new cyclodissipativity condition, which is also equivalent to PF improvement, but whose supply rate is now function of the compensator. Second, we consider general lossless linear compensators, instead of only capacitive or inductive compensators. As a result, we show that the PF is improved if and only if a certain equalization condition between the weighted powers of inductors and capacitors of the load is ensured. Finally, we exhibit the gap between the ideal compensator, namely the one that achieves unitary PF, and the aforementioned equalization condition. This result naturally leads to the formulation of a problem of optimization of the parameters of the compensator. Copyright © 2011 John Wiley & Sons, Ltd.

Performance evaluation of different line current shaping controllers of shunt active power filters

This paper deals with the performance evaluation of three different control methods for line current shaping in single-phase system using shunt active power filter (APF). The first two methods are indirect current control based on source current sensing and the last one is a direct current control based on load current sensing. The method I is investigated with an aim to compensate only customer generated harmonics and reactive power to attribute the responsibilities of the utility and customer at the point of common coupling (PCC). The inventing feature of method I is its realisation without the use of source voltage signal. The methods II and III are presented with an objective to compensate customer as well as utility generated harmonics and reactive power. The detailed mathematical modelling of all three controllers is presented. The performance of these controllers is investigated for rapidly varying load under sinusoidal and non-sinusoidal source voltage conditions. The total harmonic distortion (TH...

Present point of view about the instantaneous reactive power theory

The instantaneous reactive power theory has been the most used in nonlinear load compensation with active power filters (APF). Its application to APF control allows constant source power to be obtained after compensation in a simple way. It works optimally with balanced and sinusoidal source voltage, but not so good with unbalanced or non-sinusoidal source voltage. Although the p–q theory obtains constant source power in all the cases, in the second one the source current obtained is not balanced and sinusoidal. On the other hand, some researches argue that it is not a complete power theory because it does not assign a physical meaning to the power terms. Necessary modifications in the original formulation to treat compensation under any condition of voltage supply are discussed. Moreover, here, it is reformulated in phase coordinates, which allows a simpler treatment for analysing the different compensation strategies. On the other hand, from the power point of view, it is proved that the introduction of instantaneous imaginary power makes p–q formulation a formal theory of electric power in three-phase system. Finally, compensation strategies are applied to a practical power system and the results are presented.

Analysis and Application of Particular Current Signatures (Symptoms) for Cage Monitoring in Nonsinusoidally Fed Motors With High Rejection to Drive Load, Inertia, and Frequency Variations

In this paper, some original and effective fault indicators for broken-bar detection in power squirrel-cage induction motors are presented. A motor phase-current signature analysis can be performed by evaluating the typical ratios I (7 - 2s)f /I 5f and I (5 + 2s)f I 7f, I (13 - 2s)f /I 11 f and I (11 + 2s)f /I 13f , etc., which appear in the phase-current spectrum of faulted motors fed by nonsinusoidal voltage sources. The main advantages of the new indicators are the following: (1) accentuate insensitivity to disturbs such as load torque, drive inertia, and frequency variations; (2) low dependence with respect to machine parameters (except the pole number); and (3) linear dependence on fault gravity. They can be directly applied on motors fed by open-loop low-switching frequency gate turn-off/thyristor converters. Railway traction drives are possible targets. Application to mains-fed motors can be tried too, if suitable harmonics are present in the plant supply. A detailed analytical formulation for fault indicators is furnished, based on the multiphase symmetrical component theory; theoretical results have been supported by experimental work, performed by using a motor with an appositely prepared cage, and successively, method validation was achieved on three other industrial motors.

Genetic algorithm-based optimal design of shunt compensators in the presence of harmonics

This paper presents a genetic algorithm (GA)-based approach for the optimal design of passive shunt compensators when a nonideal, nonsinusoidal voltage source supplies a linear load. In contrast to traditional optimization techniques, the proposed GA has the following combined advantages: it allows both topological structure and component sizes of a compensator of any complexity to be optimized by introducing variable-length chromosomes. It is easy to change constraints or apply new ones using a death penalty or an adaptive penalty scheme for handling constraints. No preliminary calculations are necessary to identify resonant conditions in advance. Simulation results on an example system show the way and the extent to which the various apparent power components and other significant quantities are affected by compensation. An almost unity power factor is possible using a Foster form compensating circuit.