Third-order Harmonic Components Research Articles

A Novel Common-Mode Voltage Suppression Strategy for Current Source Converter

The problem of common-mode voltage (CMV) in current source converter (CSC) has been concerned with the development and application of CSC, such as in the transformerless motor drive system. Using a common-mode choke is a popular solution to suppressing CMV. The high-frequency harmonics of the CMV can be eliminated by the common-mode filter. However, the low-order harmonics cannot be eliminated effectively, especially at low modulation index, which may cause common-mode resonance and increase the size of the choke. In this paper, a novel virtual space vector modulation (VSVM) method is proposed, which constructs virtual space vectors by the original vectors. The average value of the CMV produced by each virtual vector is zero. The proposed method can reduce the amplitude and third-order harmonic component of the CMV. In addition, the number of switching transitions in a switching sequence of the proposed method is the same as the conventional 5-segment SVM. The suppression effects of different methods on the low-order harmonics of CMV are compared through simulation and experiments, and the effectiveness of the proposed methods is verified.

Submodule Capacitor Voltage Ripple Reduction of Full-Bridge Submodule-Based MMC (FBSM-MMC) with Non-Sinusoidal Voltage Injection

The full-bridge submodule (FBSM)-based modular multilevel converter (FBSM-MMC) offers promising performance due to its ability to output negative FBSM voltage. This paper studies this ability of the FBSM-MMC under zero-sequence voltage injection (ZSVI) and second-order harmonic current injection (SHCI). The focus of the research is to redistribute the FBSM powers by injecting an additional power degree of freedom, resulting in a smaller FBSM capacitor voltage ripple, while keeping the maximum AC output voltage for a given fundamental frequency component of the arm voltage reference. Accordingly, a control strategy was developed, based on non-sinusoidal ZSVI, and SHCI is proposed for further improving the performance of the FBSM-MMC. The proposed non-sinusoidal ZSVI contains a higher sinusoidal third-order harmonic component than that of pure sinusoidal third-order voltage injection (THVI) when operating under the same maximum AC output voltage. By implementing this solution, a smaller amplitude of the injected second-order harmonic current can be achieved, producing a lower power loss in the FBSM-MMC. Considering the proposed solution, the relationship of the arm powers and FBSM capacitor voltages are also discussed. Finally, the simulation results and experimental results are presented to verify the effectiveness of the theoretical analysis of the proposed method.

Active Arc Suppression Algorithm for Generator Stator Winding Ground Fault in the Floating Nuclear Power Plant

Electrical equipment of the floating nuclear power plant operates in a long-term vibration environment. Ground faults occur frequently and are often accompanied by arc, a reliable arc suppression algorithm for the generator stator winding is necessary. In this paper, an active arc suppression method is proposed by connecting a controllable voltage source to the generator neutral point. Through regulating the neutral point voltage to be equal in amplitude and opposite in phase to the fault potential, the fault point voltage can be clamped to a low level to achieve arc suppression. Since the generator's phase potential contains certain harmonic components, the controllable voltage source includes fundamental and third-order harmonic components. To accurately calculate the output voltage, online calculation methods for the fault location, fault potential and grounding capacitance are proposed. The accuracy of the fault location method is verified by simulation and dynamic test. And simulation results based on PSCAD/EMTDC software show that the proposed method can achieve effective arc suppression at different ground fault conditions.

Scale Factor Self-Calibration of MEMS Gyroscopes Based on the High-Order Harmonic Extraction in Nonlinear Detection

This article presents a novel self-calibration method to improve the scale factor (SF) stability by the synchronous control on the first-order and third-order harmonic components of nonlinear detection. On the conventional scheme of a drive loop, the readout amplitude of the first-order harmonic component is controlled at a constant value. However, the actual vibration amplitude of drive-mode motion would drift due to the change of circuit gains between the readout amplitude and actual amplitude, thereby resulting in the deterioration of the SF stability. The third-order harmonic component of nonlinear detection shares the same circuit with the vibration signal, indicating that its readout amplitude can track the change in circuit gains in real time. Therefore, this new approach replaces the original fixed reference with the varying readout amplitude of the third-order harmonic component to eliminate the drive-mode vibration error and eventually calibrate the drift of SF. Experiments performed on a honeycomb disk resonator gyroscope (HDRG) have demonstrated the feasibility of the calibration method. The calibration based on the harmonic extraction yields a short-term SF repeatability of 24.9 ppm and a long-term SF repeatability of 30.8 ppm. Allan deviation analysis of the calibrated SF demonstrates a 3.5-ppm precision upon an average of 200 s. The temperature sensitivity of the SF is reduced from 717.3 ppm/°C to 5.02 ppm/°C and the SF repeatability is improved from 15643 ppm to 94.9 ppm over the temperature range of −30 °C to 30 °C.

Modular Single-Stage Three-Phase Flyback Differential Inverter for Medium/High-Power Grid Integrated Applications.

This paper proposes a single-stage three-phase modular flyback differential inverter (MFBDI) for medium/high power solar PV grid-integrated applications. The proposed inverter structure consists of parallel modules of flyback DC-DC converters based on the required power level. The MFBDI offers many features for renewable energy applications, such as reduced components, single-stage power processing, high-power density, voltage-boosting property, improved footprint, flexibility with modular extension capability, and galvanic isolation. The proposed inverter has been modelled, designed, and scaled up to the required application rating. A new mathematical model of the proposed MFBDI is presented and analyzed with a time-varying duty-cycle, wide-range of frequency variation, and power balancing in order to display its grid current harmonic orders for grid-tied applications. In addition, an LPF-based harmonic compensation strategy is used for second-order harmonic component (SOHC) compensation. With the help of the compensation technique, the grid current THD is reduced from 36% to 4.6% by diminishing the SOHC from 51% to 0.8%. Moreover, the SOHC compensation technique eliminates third-order harmonic components from the DC input current. In addition, a 15% parameters mismatch has been applied between the flyback parallel modules to confirm the modular operation of the proposed MFBDI under modules divergence. In addition, SiC MOSFETs are used for inverter switches implementation, which decrease the inverter switching losses at high-switching frequency. The proposed MFBDI is verified by using three flyback parallel modules/phase using PSIM/Simulink software, with a rating of 5 kW, 200 V, and 50 kHz switching frequency, as well as experimental environments.

Higher-order harmonic induced wave resonance for two side-by-side boxes in close proximity

Wave resonance in a narrow gap formed by two boxes in the side-by-side arrangement is investigated by employing a numerical wave flume based on the OpenFOAM® package. In the present study, the main focus lies in the exploration of the nonlinear resonant behavior induced by the second- and third-order harmonic components which occur around half and one third of the resonant frequencies. A wide range of incident wave frequencies is considered, by which the higher-order harmonic induced wave resonance at lower wave frequencies is discussed. By the harmonic analysis, it is revealed that at the resonant frequency the first-order harmonic component dominates the wave resonance and the second-order effect is minor, which coincides with the conclusion drawn in the previous study. However, around half or one third of the resonant frequencies, the first-order harmonic component is in good agreement with the linear potential flow solutions, but the second- or third-order harmonic component is significant, causing the corresponding higher-order harmonic induced wave resonance. In addition, the numerical results show that the second- and third-order harmonic induced wave resonances only influence the wave properties inside the narrow gap, such as the wave response in the narrow gap and the horizontal wave forces on the boxes. The wave responses around the two-box system, the vertical wave forces on the boxes and the reflection and transmission coefficients are hardly affected by the wave resonance around the corresponding half and one third of the resonant frequencies. The higher-order harmonic induced normalized wave elevation in the narrow gap increases with the increase in incident wave height, implying the increased influence of the free surface nonlinearity.

PWM Strategy to Alleviate Common-Mode Voltage with Minimized Output Harmonic Distortion for Five-Level Cascaded H-Bridge Converters

High-frequency components of common-mode voltage (CMV) induce the shaft voltage and bearing current, which lead to premature failures in motors. In addition, due to non-zero average CMV, the low-frequency components of CMV, particularly the third-order harmonic component, have been reported to cause difficulties in common-mode filter design. Furthermore, the utilization of distant voltage vectors in the pulse-width modulation (PWM) with reduced CMV magnitudes gives rise to high output harmonic distortion compared to PWM ones without CMV reduction. In an attempt to solve the aforementioned issues, this article presents a PWM strategy that features reduced CMV magnitudes, zero average CMV, and improved output harmonic distortion for a five-level cascaded H-bridge (CHB) converter. In addition, the carrier rotation technique based on the phase-leg redundancy of the CHB topology is also combined with the proposed scheme to achieve equal power loss distribution among power switching devices. Both simulation and experimental results confirm that the proposed strategy produces better output harmonic distortion than that of POD-SPWM and APOD-SPWM under the condition of reduced CMV magnitudes, zero average CMV, and equal power loss distribution.

A Dual Frequency Tuning Method for Improved Coupling Tolerance of Wireless Power Transfer System

This letter proposes a dual-frequency tuning method for improved coupling tolerance of an inductively coupled wireless power transfer (WPT) system by exploiting the fundamental and third-order harmonic components of a square-wave voltage out of a full-bridge inverter. A dual-frequency hybrid compensation topology is designed to simultaneously utilize the characteristics of series-series (SS) and LCL-S networks under the two different frequencies. Consequently, the output power of the proposed system under a fixed load is maintained approximately constant against coupling variations. A practical hybrid WPT system with a 100 kHz square-wave excitation and a 10.5 Ω resistive load is built to verify the theoretical modeling and analysis. Experimental results show that the system achieves an approximately constant output voltage and power of around 39 V and 150 W against a coupling coefficient variation from 0.52 to 0.72, with maximum fluctuations less than 5% and 10%, respectively.

Theoretical Harmonic Spectra of PWM Waveforms Including DC Bus Voltage Ripple—Application to a Low-Capacitance Modular Multilevel Converter

This article develops a new closed-form analytical solution to the harmonic spectrum of the pulsewidth modulated (PWM) output voltage of the single-phase inverter connected to the dc bus with considerable voltage ripple. The solution is based on a double Fourier series expansion in two variables. As the single-phase inverter forms the basic building block of most converters, the developed expressions can be applied to various topologies. This article first identifies the interactions of a single-frequency sinusoidal modulation signal and the carrier signal with the dc bus voltage harmonics. The dc bus voltage harmonics are constrained in this article to multiples of the inverter output voltage fundamental frequency. The analysis is then extended to include a multifrequency modulation signal. Starting from the general solution, new expressions for the output voltage harmonics of the modular multilevel converter (MMC) are developed. The low-capacitance MMC is chosen in this analysis due to inherent low-frequency voltage oscillations in the converter internal capacitors. The MMC analytical harmonic spectrum can incorporate the effects of the circulating current control and third harmonic injection PWM, by including the second- and third-order harmonic components in the modulation signal, respectively. The MMC analytical harmonic spectrum is benchmarked against the experimental results.

Torque ripple reduction of switched reluctance motor by optimising switch angle based on analytical modelling

To reveal the torque ripple mechanism of switched reluctance motors (SRMs), an analytical instantaneous torque model considering current harmonics is established based on the analysis of the air-gap magnetic field. The results show that torque ripple contains third-order harmonic components in a three-phase SRM and mainly comes from the current harmonic, the rotor slotting, and their interaction. Then, the influence of main current harmonics on the torque ripple is investigated based on an analytical calculation method and it is found that the filtering of the second-order current harmonic is more conducive to reducing the torque ripple. Finally, the influence of the turn-on/turn-off angle on each harmonic current is fully analysed by means of the analytical modelling of current, based on which the second-order current harmonic and torque ripple is reduced by optimising the turn-on/turn-off angle. Also, it is found that the suitable prior turn-on angle and delayed turn-off angle is helpful to reduce the torque ripple.

Scheme of G measurement with large amplitude torsion pendulum

In the recent CODATA-2014 adjustment, the $G$ values obtained by different groups are not in good agreement with each other within respective uncertainties, which may be attributed to the possible unknown or incorrectly evaluated systematic errors in different methods. This paper proposes a scheme to measure $G$ with two independent methods. The first method is the extraction of the $G$ value from the fundamental periods of the torsion pendulum, with the source masses at two positions; the other one determines the $G$ value on the basis of the amplitude of the third-order harmonic component of the torsion pendulum. Both methods are performed with the same setup by using the large-amplitude torsion pendulum. Through theoretical derivation and simulation, the uncertainties of the $G$ values obtained by the two methods are both expected to be within 20 ppm. By comparing the $G$ values from the two methods, we can explore the potential systematic errors in the measurement.

Family of DTMRC‐based DC–DC converters with an RZP

This study presents a novel family of dual-transformer multi-resonant DC–DC converters (DTMRCs) with a resonant zero point (RZP). The limitations of the conventional LLC resonant converter and its fundamental harmonic approximation (FHA) method are firstly discussed. On this basis, a unique RZP is combined with the dual-transformer architecture. As a result, both of the output voltage regulation capability and the over-current protection feature are promoted. Then, an extended describing modelling method is presented to improve the calculative accuracy of the FHA method. Moreover, by means of the appropriate placement of all three resonant frequencies, the fundamental and the third-order harmonic components are employed to transmit active power to the load simultaneously. The zero-voltage soft-switching characteristic is acquired for all the primary-side switches. Meanwhile, the preferable zero-current soft-switching feature is obtained for diodes both at the turn-on and turn-off moments. Therefore, the switching losses are significantly reduced for the proposed converters. Finally, with the employed SiC metal–oxide–semiconductor field-effect transistors, a 500-W half-bridge DTMRC prototype is built as an example, based on the P-type multi-resonant network. The experimental results demonstrate the validity and correctness of the theoretical analyses.

Photonic triangular waveforms generation based on nonlinear polarization rotation using a highly nonlinear fiber

We propose a photonic approach to generate triangular waveforms based on nonlinear polarization rotation (NPR) effect in a highly nonlinear fiber. A continuous wave probe light is polarization rotated by an intensity-modulated control light through the NPR effect. By tuning the cascaded polarization controller, the undesired second-order harmonic is well suppressed after photodetection. A 90-deg hybrid coupler is used to compensate the phase mismatch between the fundamental and third-order harmonic components, so that triangular waveforms are generated successfully. The proposed approach is theoretically analyzed and experimentally verified. Triangular waveforms at repetition rates of 3, 4, and 5 GHz with full-duty cycle are experimentally generated.

A <inline-formula> <tex-math notation="LaTeX">$V$ </tex-math> </inline-formula>-Band Wide Locking Range Divide-by-4 Injection-Locked Frequency Divider

A novel $V$ -band divide-by-4 injection-locked frequency divider (ILFD) topology involving an injection loop and an output loop coupled by a two-port LC -tank has been proposed. With the specially designed LC -tank, the third-order harmonic component can be enhanced in the injection loop, so that the mixing using the second-order nonlinearity can be used to realize divide-by-4, and thus, the locking range can be improved. Simultaneously, the output loop excites the oscillation at the fundamental frequency and suppresses the third-order harmonic components, facilitating a stable oscillation at the fundamental frequency and avoiding the effects of third-order harmonic on the following stages. Fabricated in a 65-nm CMOS technology, the proposed ILFD demonstrates a wide locking range of 60.2–69.9 GHz (14.9%) while consumes 4.8 mW from a 0.75-V supply.

Study of Wireless Power and Information Transmission Technology Based on the Triangular Current Waveform

Wireless power and information transmission (WPIT) technology can realize simultaneous wireless transmission of power and information. In this paper, the fundamental component of the triangular current waveform is employed to transfer power, and its third-order harmonic component is selected to transfer information. The Fourier decomposition method is conducted to analyze the triangular current waveform; two equivalent circuit models of the proposed WPIT system are established based on the relationship between the fundamental component and the third-order harmonic component. Harmonic components have an enlargement effect on the deviation of the fundamental frequency; this feature is used to realize the weakly coupled control between the information transmission and the efficiency of wireless power transfer. Based on the proposed harmonic communication method, the transient process and the maximum communication speed of the circuit are discussed. To achieve the high signal-to-noise ratio (SNR) communication, different space positions of the signal receiving winding are compared. Experimental results show that the proposed method provides a new solution for designing the WPIT system.

Analysis of Noncharacteristic Harmonics Generated by Voltage-Source Converters Operating Under Unbalanced Voltage

This paper deals with an analytical model to evaluate the noncharacteristic harmonics that are generated by three-phase three-wire voltage-source converters (VSCs) operating under unbalanced sinusoidal voltage conditions. This model permits the calculation of the oscillating current on the VSC dc side by considering the unbalanced voltages on its ac side. It can be used to prove that the use of dc voltage control techniques to eliminate VSC dc-side double frequency voltage ripple necessarily creates three-phase currents with undesirable low-frequency harmonic components on the VSC ac side. In this paper, the attention is directed to the instantaneous oscillating real power component at twice the line frequency, rather than to other power components. The noncharacteristic current components analyzed in this paper, such as the fundamental negative sequence and third-order harmonic components of positive and negative sequences are calculated using the proposed model in time-domain simulations. A simple model to calculate the dc-side capacitor to mitigate these noncharacteristic harmonic problems is presented.

DC voltage control strategy of chain star STATCOM with second‐order harmonic suppression

Chain static synchronous compensators (STATCOMs) with star structure produce second-order harmonic fluctuations on the DC side. This effect is often ignored and only the average voltage value is taken into consideration when describing this system for control purpose. In this study, the unbalance of per-phase DC voltages caused by active power absorbed and consumed by the chain is analysed. The steady-state expressions regarding the average capacitor voltage balancing between phase clusters as well as the suppression of second-order harmonic fluctuation are obtained, respectively, based on the injection of fundamental and third-order harmonic zero-sequence voltages. Although the expressions are helpful to understand the essence of DC capacitor voltage control, this method has complicated calculation process and the calculation results may be beyond the modulation limit. Therefore, it is not conducive in real-time control. For this reason, a new control strategy based on the instantaneous zero-sequence voltage injection is proposed. The evaluation function with the transient variables is established to get the instantaneous value of the zero-sequence voltage including fundamental and third-order harmonic components. The fundamental and third-order harmonic zero-sequence voltages are automatically allocated to fully use the remaining modulation capacity. Finally, simulation and experimental results are provided, which verifies the correctness of the theoretical analysis and the high performance of the proposed method.

Phase diagram of the chiral magnetCr1/3NbS2in a magnetic field

We construct the phase diagram of the chiral magnet ${\mathrm{Cr}}_{1/3}{\mathrm{NbS}}_{2}$ in a dc magnetic field $({H}_{\mathrm{dc}})$ using ac magnetic susceptibility measurements. At ${H}_{\mathrm{dc}}=0$, the ac response at the transition from the helical magnetic (HM) state to the paramagnetic (PM) state consists of a giant third-order harmonic component $({M}_{3\ensuremath{\omega}})$ and a first-order harmonic component $({M}_{1\ensuremath{\omega}})$. By applying ${H}_{\mathrm{dc}}$ perpendicular to the $c$ axis, the HM state is transformed to the chiral soliton lattice (CSL) state, which is a superlattice tuned by ${H}_{\mathrm{dc}}$. The above giant ${M}_{3\ensuremath{\omega}}$ is markedly suppressed at small ${H}_{\mathrm{dc}}$. The CSL state is found to consist of CSL-1, with dominant helical texture and a poor ferromagnetic array, and CSL-2, with a large ferromagnetic array. The transition between CSL-1 and the PM state causes a linear magnetic response, the dominant component of which is the in-phase ${M}_{1\ensuremath{\omega}}$. With increasing temperature, CSL-2 is transformed into the forced ferromagnetic (FFM) state, and ultimately the PM state is reached. The transition between CSL-2 and the FFM state consists of a large ${M}_{3\ensuremath{\omega}}$ and large out-of-phase ${M}_{1\ensuremath{\omega}}$ as well as in-phase ${M}_{1\ensuremath{\omega}}$. The transition between the FMM and PM states also yields a linear magnetic response, like the CSL-1--PM-state transition. Five typical magnetic dynamics in the transitions among the HM state, CSL-1, CSL-2, FFM state, and PM state were identified according to the equivalent dynamical motion equation of a nonlinear spring model.

A Virtual Space Vector Modulation Technique for the Reduction of Common-Mode Voltages in Both Magnitude and Third-Order Component

A virtual space vector modulation technique reducing both magnitude and third-order harmonic component of the common-mode voltage (CMV) in a two-level voltage-source inverter (VSI) is proposed in this paper. The presented method employs a set of virtual space vectors constructed from original stationary space vectors to conduct modulation. Since the created virtual vectors have the lowest instantaneous and zero average CMVs, both the magnitude and third-order harmonic component of the generated CMV are reduced, contributing to better overall CMV performance and common-mode filter design in VSI applications. Three variants of the proposed modulation method using different virtual space vector combinations are presented. The concept of the virtual space vector modulation technique demonstrated with two-level inverter in this paper can also be extended to multilevel inverters. Simulation and experimental results, as well as comparisons with existing methods are provided to verify the proposed technique.

Dynamic correlation length scales under isochronal conditions.

The origin of the dramatic changes in the behavior of liquids as they approach their vitreous state-increases of many orders of magnitude in dynamic time scales and transport properties-is a major unsolved problem in condensed matter. These changes are accompanied by greater dynamic heterogeneity, which refers to both spatial variation and spatial correlation of molecular mobilities. The question is whether the changing dynamics are coupled to this heterogeneity; that is, does the latter cause the former? To address this, we carried out the first nonlinear dielectric experiments at elevated hydrostatic pressures on two liquids, to measure the third-order harmonic component of their susceptibilities. We extract from this the number of dynamically correlated molecules for various state points and find that the dynamic correlation volume for non-associated liquids depends primarily on the relaxation time, sensibly independent of temperature and pressure. We support this result by molecular dynamic simulations showing that the maximum in the four-point dynamic susceptibility of density fluctuations is essentially invariant along isochrones for molecules that do not form hydrogen bonds. Our findings are consistent with dynamic cooperativity serving as the principal control parameter for the slowing down of molecular motions in supercooled materials.