Frequency Modulation Ratio Research Articles

Mechanism and Suppression of Frequency-Decrease Effect Related to the Low Modulation Frequency Ratio in a High-Ratio MMC-Based DC Transformer

The high-ratio MMC-based DC transformer is the crucial device for the interconnection between different DC distribution networks. Compared to the typical MMC, the transformer has a similar structure and low modulation frequency ratios (FR). Thus, it also has the severe frequency-decrease effect and similar operating performance deterioration. However, because of the extremely lower FRs that are close to 1, the feature of the frequency-decrease effect in the transformer has different manifestations. And because of the two-stage structure which combines the MMC and rectifiers, more factors emerged in the transformer to determine the frequency-decrease effect. Therefore, this study further develops the theory and elaborates the frequency effect's mechanism that is originally from the MMC to adapt to the more complex structure of the transformer. A quantitative analysis of the frequency-decrease effect is then provided, demonstrating that because of the transformer's two-stage structures, two types of FRs and concomitant factors exist in the transformer, thus having a combined effect on the harmonic distributions of capacitor voltages and causing more proportional voltages' harmonics distorting into the slope harmonics. Based on the analysis, the study entirely redesigns the FRs and regulates the modulation strategy of the transformer to fundamentally eliminate the frequency-decrease effect. The study also confirms that the FRs in the two sides cannot be set to the same, and their decimal part cannot cause extra low-frequency harmonics. The frequency-decrease effect, the deteriorations, and the efficiency and comparisons of the proposed methods are finally demonstrated via simulations and experiments.

The splitting mechanism of the second-order rogue wave—Interaction between two component first-order Akhmediev breathers

Based on the nonlinear Schrödinger equation, it's illustrated that the peak intensity of Akhmediev breather is negatively correlated with the modulation frequency firstly. Then, two splitting modes of the second-order rogue wave have been studied in detail through the second-order rogue wave train formed by the nonlinear superposition of two first-order Akhmediev breathers whose modulation frequency ratio is 1:2. It is revealed that the process of the mode B splitting can be divided into three stages: the restructuring stage where the intensity of the latter sub-peaks of the main peak decreases first and then increases, the competition stage where the fine structure forms and the relaxation stage. The process of the mode A splitting can be divided into two stages: the restructuring stage and the relaxation stage. And both are due to the interaction between the two first-order component Akhmediev breathers. The results can be used to explain the different characteristics of the two splitting modes of the second-order rogue wave. In addition, the inevitability of the fine structure appearance in the process of the mode B splitting of the second-order rogue wave, which causes the transformation point on the peak intensity curve of the second order rogue wave, is also revealed. We anticipate that it will be a meaningful and novel way to study the characteristics of the high-order rogue wave through interaction between breathers with certain modulation frequency ratio.

Stator Current Spectral Content of Inverter-Fed Cage Rotor Induction Motor

The paper analyzes the influence of the number of rotor bars on the stator current spectral content in a three-phase cage induction motor fed by a pulse-width modulated (PWM) inverter. It is shown that each of the higher-order time harmonics in the supply voltage produces space harmonics in a rotating magnetic flux density wave, which results in induced rotor slot harmonics (RSHs) in the stator current spectrum. The conditions for the existence of these space harmonics are identical to those applying to a mains-fed motor. In other words, the number of rotor bars of a mains-fed motor yielding an RSH-free stator current spectrum produces the same stator current spectrum even in case the motor is inverter-fed. Additionally, to minimize the adverse effects of RSHs in the stator current spectrum, one must consider not only the number of rotor bars, but also its relationship with the frequency modulation ratio of the PWM inverter. Analytical predictions are presented to illustrate these results supported both by numerical simulations of the induction motor modelled through the winding function theory and experimentally taking the case a two-pole cage induction machine as a case study.

Minimization of DC-Link Capacitance and Improved Operational Performance of a 5-Level Hybrid Multilevel DC-Link Inverter

This study analyzes a single-phase hybrid multilevel dc-link (MLDCL) inverter, in which a dc-link with two capacitors is integrated into a single dc source. When controlled under the conventional modulation scheme, the MLDCL inverter synthesizes a five-level output voltage. As the capacitor-voltage balancing depends on the fundamental period, the output voltage may contain unsolicited low-order harmonics. Moreover, in the conventional scheme, this inverter requires large dc-link capacitors. To avoid these problems, the present paper develops a simple phase-shifted pulse-width modulation scheme based on redundant switching states, which controls the MLDCL inverter and balances the capacitor voltage within each carrier period. The proposed modulation scheme also minimizes the dc-link capacitance by a factor of the frequency modulation ratio while reducing the total harmonic distortion of the output voltage and current. Unlike the conventional method, the proposed scheme considerably reduces the capacitor-voltage ripples and can be regulated by increasing the carrier frequency, thereby reducing the voltage stress on the switches and improving the reliability of the inverter. The feasibility of the proposed scheme over the conventional scheme is confirmed in a comparative study. Finally, the steady-state and dynamic performances of the proposed strategy are demonstrated in simulations and validated in experiments.

The new approach minimizes harmonics in a single-phase three-level NPC 400 Hz converter for airplanes

<span lang="EN-US">This paper provides a new approach to reducing high-order harmonics in 400 Hz inverter using a three-level neutral-point clamped (NPC) converter. A voltage control loop using the harmonic compensation combined with NPC clamping diode control technology. The capacitor voltage imbalance also causes harmonics in the output voltage. For 400 Hz inverter, maintain a balanced voltage between the two input (direct current) (DC) capacitors is difficult because the pulse width modulation (PWM) modulation frequency ratio is low compared to the frequency of the output voltage. A method of determining the current flowing into the capacitor to control the voltage on the two balanced capacitors to ensure fast response reversal is also given in this paper. The combination of a high-harmonic resonator controller and a neutral-point voltage controller working together on the 400 Hz NPC inverter structure is given in this paper.</span>

Multi-Objective Hierarchical Optimization: A Design Framework for Grid-Connected Interleaved H-Bridges

The paralleling of power converters connected to the grid for power-sharing is a widely used technique. In this context, the design framework for a low-cost, lightweight, compact and high-performance optimum configuration is an open problem. This paper proposes an innovative Multi-Objective Hierarchical Optimization Design Framework (MO-HO-DF) for an AC grid interface with $N$ interleaved H-bridges, each with $M$ parallel “to-be-determined” switches, connected through coupling inductances ( $L_f$ ). A total of eight figures of merit (FOMs) were identified for the design framework optimization. A rigorous model of the power electronic system is presented. Next, a highly computationally efficient algorithm for the estimation of the required frequency modulation ratio ( $m_f$ ) to meet current harmonic performance requirements for any given configuration is proposed. Then, the concept and implementation of the algorithm are presented for the MO-HO-DF. The effectiveness of the design optimization framework is demonstrated by comparing it to a base case solution. Finally, the design calculations are validated via PLECS simulation with manufacturer-provided 3D power semiconductor models that include thermal modelling.

Randomized Pulse Pattern Strategy of Synchronized SVPWM for Low-Frequency-Ratio Applications

Low switching frequency operation is preferred in machine drives of high-power applications for controlling the switching loss of power-electronic devices to a tolerable level. Hence, the modulation frequency ratio is usually low. Synchronized space vector pulsewidth modulation (synchronized SVPWM) is a method designed to reduce current harmonic distortion in low-frequency-ratio occasions. However, the switching frequency apparently varies when the pulse pattern of synchronized SVPWM changes, which makes it impossible to fully use the available switching frequency. In this article, the alternative pulse patterns of synchronized SVPWM are extended by the proposed randomized pulse pattern strategy. The proposed strategy divides pulse patterns in a line cycle of the synchronized SVPWM into six pulse pattern units according to the symmetry conditions, and randomly combines these pulse pattern units according to the probability theory. The pulse pattern units from different pulse patterns are analyzed and modified to concatenate together smoothly. The proposed strategy keeps the advantages of synchronized SVPWM that low-order harmonics are suppressed. Meanwhile, lower harmonic distortion and torque ripples are achieved compared with the conventional strategy. The proposed strategy is verified through simulations and experiments.

Analysis and Suppression of the Frequency-Decrease Effect in the Capacitor Voltage Related to the Low Modulation Frequency Ratio in an MMC System

The carrier phase-shift pulsewidth modulation (PWM) strategy is widely used in modular multilevel converters (MMCs), where the modulation frequency ratio of switching and fundamental frequency is a major parameter. However, a low modulation frequency ratio, which is often implemented to decrease the power loss in a high-power MMC system, can greatly decrease the harmonic frequencies of the submodules' capacitor voltages. Such effect is defined as the frequency-decrease effect in the capacitor voltage, which can cause several severe deteriorations, such as the low-frequency fluctuations, the unstable charge-discharge state of submodules' capacitors, and unbalance phenomenon of the capacitor voltages, thus significantly deteriorating the system working performance. This study first proposes the mechanism of the frequency-decrease effect. A quantitative analysis of the relations between the frequency-decrease effect, the modulation frequency ratio, and corresponding deteriorations is then provided, indicating the root cause of the frequency-decrease effect. Based on the analysis, an appropriate enhanced balance strategy is introduced into the system. An optimal design method is used to determine an appropriate modulation frequency ratio and to mitigate the frequency-decrease effect; and an improved balancing method, which combines the direct-bias injection and condition selection to determine the modulation wave, is used to further improve the system performance. The frequency-decrease effect, the corresponding deteriorations, and the efficiency of the enhanced balance strategy to suppress the frequency-decrease effect are finally demonstrated via simulations and experiments.

Harmonic Suppression Strategy in Single-phase SPWM Based on Mixed Integer Nonlinear Programming

In single-phase bipolar SPWM inverter circuit, the output voltage contains high content of harmonic components. To solve this problem, we build a model of output voltage in single-phase SPWM bipolar inverter based on SPWM theory and Fourier series theory. Through theoretical analysis, calculation and plotting, we work out the distribution of harmonic in output voltage, investigate the relationship between amplitude modulation (AM) depth and harmonic components and finally determine a proper amplitude modulation depth to efficiently reduce harmonic components. To further reduce harmonic components of output voltage, we use LC low-pass filter. Then, based on the mathematical model of the filter and the distribution law of harmonics, we establish a mixed integer nonlinear programming to fully suppress harmonics and reduce switching losses. After searching for two times based on genetic algorithm, we work out the best frequency-modulation ratio and LC low-pass filter parameter. Finally in simulation, total harmonic distortion is reduced from 213.47 percent to 0.16 percent after harmonic suppression strategy implemented. The result has proved the effectiveness of the harmonic suppression strategy we applied, which can be used as a reference for output voltage harmonic elimination in single-phase SPWM inverter.

Analysis of the Unbalance Phenomenon Caused by the PWM Delay and Modulation Frequency Ratio Related to the CPS-PWM Strategy in an MMC System

The carrier phase-shift pulsewidth modulation (CPS-PWM) strategy is widely used in modular multilevel converters. However, the PWM delay and modulation frequency ratio, which are typically neglected in the design of the CPS-PWM strategy, are the primary factors that can cause an unbalance phenomenon in the submodules’ capacitor voltages and thus deteriorate the system working performance. This study first proposed mechanism of the balance of the capacitor voltage related to the CPS-PWM strategy. A quantitative analysis of the relations between the PWM delay, modulation frequency ratio, and unbalance phenomenon is then provided based on the balance mechanism, indicating the root cause of the unbalance phenomenon related to the CPS-PWM strategy. Based on this analysis, the appropriate compensation methods are introduced into the system: an optimal design of the system parameters is used to mitigate the effect of the PWM delay. And an improved balance strategy, which combines the rotations of the carrier waves, the method regulating the phase-shift angle, and a state switcher with a balance-time calculator, is used to suppress the effect of a low modulation frequency ratio. The unbalance phenomenon caused by the PWM delay and low modulation frequency ratio, and the efficiency of the compensation methods to balance the capacitor voltage, are finally demonstrated via experiments.

A Dual-Carrier Modulation Technique for Half-Bridge Resonant Converter With Wide Soft-Switching Range

A dual-carrier modulation technique is proposed to improve the performance of the half-bridge resonant converter in this paper. By alternately using two different sawtooth waveforms as a carrier, the dual-carrier modulation combines the characteristics of both variable frequency modulation and fixed-frequency modulation. According to the structure of modulator, there are two kinds of dual-carrier modulation: type A and type B. Type A dual-carrier modulation is suitable for resonant converters operating in inductive region to achieve a wide zero voltage switching (ZVS) range, while type B dual-carrier modulation is preferred for resonant converters operating in capacitive region to obtain a wide zero current switching range. By utilizing both switching frequency modulation and duty ratio modulation, the proposed dual-carrier modulation not only extends soft-switching range of the resonant converter, but also reduces switching frequency variation range. In order to verify the benefits of the proposed modulation, a 500-W dual-carrier modulated LCC resonant converter operating in inductive region is designed and built. Simulation and experimental results show the prototype achieves ZVS soft-switching operation for 200–400 V input voltage and 100–500 W output power, with only about 10 kHz switching frequency variation.

Model of parafoveal chromatic and luminance temporal contrast sensitivity of humans and monkeys.

Rhesus monkeys are a valuable model for studies of primate visual contrast sensitivity. Their visual systems are similar to that of humans, and they can be trained to perform detection tasks at threshold during neurophysiological recording. However, the stimulus dependence of rhesus monkey contrast sensitivity has not been well characterized. Temporal frequency, color, and retinal eccentricity affect the contrast sensitivity of humans in reasonably well-understood ways. To ask whether these factors affect monkey sensitivity similarly, we measured detection thresholds of two monkeys using a two-alternative, forced-choice task and compared them to thresholds of two human subjects who performed the same task. Stimuli were drifting Gabor patterns that varied in temporal frequency (1–60 Hz), L- and M-cone modulation ratio, and retinal eccentricity (2°–14° from the fovea). Thresholds were fit by a model that assumed a pair of linear detection mechanisms: a luminance contrast detector and a red-green contrast detector. Analysis of model fits indicated that the sensitivity of these mechanisms varied across the visual field, but their temporal and spectral tuning did not. Human and monkey temporal contrast sensitivity was similar across the conditions tested, but monkeys were twofold less sensitive to low-frequency, luminance modulations.

Total Harmonic Distortion Comparison between Sinusoidal PWM Inverter and Multilevel Inverter in Solar Panel

This research compared the performance of PWM (Pulse Width Modulation) inverter and multilevel inverter in terms of their output voltage and current total harmonic distortion (THD). The inverters were designed to have the output voltage of 220 V at 50 Hz. The input voltage for both inverters are 400 VDC. For PWM inverter, the PWM technique utilized was sinusoidal PWM (SPWM) and for multilevel converter, the number of voltage level is five with diode-clamped topology. The study included circuit implementation, analysis, and THD calculation, all of which were carried out through simulation using PSpice software. In controlling the SPWM inverter output, the adjusted parameters included amplitude modulation ratio, frequency modulation ratio, and filter components’ parameters. On the other hand, the firing angles of the switching components were designated as controlling parameters in multilevel inverter. From the study, it was found that the best THD values of the designed SPWM inverter are 4.2% (voltage) and 1.7% (current), while those of multilevel inverter are 27% and 11%, for voltage and current, respectively. Thus, it can be concluded that SPWM inverter is better than 5-level inverter for the application in solar panel due to its lower THD. In our study, 5-level inverter did not satisfy the THD requirement specified in IEEE 512-1992, i.e. 5%.

Elimination of cross‐terms in the Wigner–Ville distribution of multi‐component LFM signals

A novel method is put forward to remove cross-terms in the Wigner–Ville distribution (WVD) of multicomponent linear frequency modulation (LFM) signals. For the difference of the amplitude of auto-terms and cross-terms, the WVD matrix is filtered using low-pass filter in the direction of frequency modulation ratio. Furthermore, a novel technique called energy weight is proposed for the cross-terms with low-oscillation frequency which cannot be eliminated because of the limitation of filters. The gain of signal to noise ratio (SNR) after filtering is derived while the resolution and computational cost are also analysed. The simulation and experimental results prove that this method improves the SNR along with the removal of cross-terms with maintaining high resolution.

Impact of Switching Harmonics on Capacitor Cells Balancing in Phase-Shifted PWM-Based Cascaded H-Bridge STATCOM

The purpose of this paper is to investigate the impact of switching harmonics on the instantaneous power distribution in the cells of a cascaded H-bridge-based STATCOM when using phase-shifted pulse width modulation. The case of high- and low-switching frequency for the converter cells is investigated and the interaction between voltage and current harmonics is analyzed. It is shown that in both cases, this interaction results in an uneven power distribution among the cells in the same phase leg, leading to drifting of the dc-capacitor voltages and thereby the need for proper stabilization control loops. It is also shown that the selected frequency modulation ratio affects the active power distribution among the cells. In particular, the selection of a noninteger frequency modulation ratio helps in providing a more uniform power distribution among cells of the same phase leg, thus contributing to the capacitors balancing. A methodology for optimal selection of the frequency modulation ratio is given. Theoretical conclusions are validated through simulation and experimental results.

Analysis of Triangular Periodic Carrier Frequency Modulation on Reducing Electromagnetic Noise of Permanent Magnet Synchronous Motor

This paper introduces a simple approach to reduce the electromagnetic noise of permanent magnet synchronous motor (PMSM) driven by pulse width modulation (PWM) supply. Alleviating the PMSM electromagnetic noise has become an important demand due to demanding requirement on human life environment. The PMSM electromagnetic noise concentrated at multiples of switching frequency results from the concentrative current harmonic. Triangular periodic carrier frequency modulation (PCFM) is introduced to alleviate the PMSM current harmonic and electromagnetic noise in this paper. The principle of triangular PCFM in reducing PMSM current harmonic and electromagnetic noise is analyzed. The impact of modulation frequency ratio on reducing PMSM electromagnetic noise is investigated. Simulations and experiments of PMSM driven by standard PWM and triangular PCFM are implemented. The simulated and experimental results verify the disciplinarian of triangular PCFM in alleviating PMSM current harmonic and electromagnetic noise.

Effects of Low Frequencies on Three Phase Induction Motor Performance Operating in Close Proximity to Rated Speed

Variable speed drives (VSD) are adhered to induction motors in most of the present industrial applications. And since the world has become more conscientious to energy saving, inverters established them selves in domestic buildings and industry. Square wave inverters generate dominant harmonics of the 5th, 7th, 11th and 13th order. Inverters based on PWM strategy produce much higher harmonic order depending on the frequency modulation ratio. The presence of any sub-synchronous harmonics (sub-harmonics) is usually unheeded probably to their ineffective magnitude. The work in this paper is to investigate the effects of low frequencies on the performance of induction motors running near rated peed. Low frequencies are superimposed on the motor by a second inverter cascaded with the main inverter. The results shown in this paper manifest the significant effects of sub-harmonics on the speed stability of induction motors. The results obtained also show that sub-harmonics can adversely affect the motor performance even if they are present with small amplitudes. This work is expected to lead to the notion of using low frequency injection in speed control of induction motors.

Frequency encoding in renal blood flow regulation

With a model of renal blood flow regulation, we examined consequences of tubuloglomerular feedback (TGF) coupling to the myogenic mechanism via voltage-gated Ca channels. The model reproduces the characteristic oscillations of the two mechanisms and predicts frequency and amplitude modulation of the myogenic oscillation by TGF. Analysis by wavelet transforms of single-nephron blood flow confirms that both amplitude and frequency of the myogenic oscillation are modulated by TGF. We developed a double-wavelet transform technique to estimate modulation frequency. Median value of the ratio of modulation frequency to TGF frequency in measurements from 10 rats was 0.95 for amplitude modulation and 0.97 for frequency modulation, a result consistent with TGF as the modulating signal. The simulation predicted that the modulation was regular, while the experimental data showed much greater variability from one TGF cycle to the next. We used a blood pressure signal recorded by telemetry from a conscious rat as the input to the model. Blood pressure fluctuations induced variability in the modulation records similar to those found in the nephron blood flow results. Frequency and amplitude modulation can provide robust communication between TGF and the myogenic mechanism.

Two-tone optical heterodyne spectroscopy with diode lasers: theory of line shapes and experimental results

This paper presents a theoretical analysis of the line shapes and signal-to-noise ratios obtained in two-tone optical heterodyne spectroscopy with tunable lead-salt diode lasers. The theory is described in terms of the frequency-modulation (FM) index β, the amplitude-modulation (AM) index M, their relative phase shift ψ, and the ratio of modulation frequency to the absorption-line half-width ν¯m. Synthetic spectra are presented for both Gaussian and Lorentzian line shapes and show considerable structural variation with the theoretical parameters. Experimental two-tone optical heterodyne spectra were obtained by modulating a specially modified lead-salt diode laser in the radio-frequency region. The experimental spectra obtained from NH3 absorption lines confirm the theoretical results.

Speech synthesis using AM/FM sinusoids and band-pass noise

In the speech synthesis model presented in this paper, voiced speech is synthesized as the sum of sinusoidally modulated two FM sinusoids corresponding to the first and second formants. Each FM signal is generated such that its amplitude is equal to the formant amplitude, its carrier frequency to the formant frequency or its linear combination, its modulation frequency to the pitch, and its modulation index to one fifth of the carrier to modulation frequency ratio. Unvoiced speech is generated by shifting the center frequency of a low-pass noise with a bandwidth of 1 KHz, to the frequency where the energy of the unvoiced speech is concentrated. The drawbacks of this scheme are that the pitch and the formant frequencies of the FM signals may deviate up to 40% and 9%, respectively, and spurious formants may occur. A hardware implementation can be accomplished by driving a linear analog circuitry which can simply be integrated on a single chip, by a digital computer which supplies voltages at every T = 5 ms corresponding to seven parameter values. Examples of the signals and spectrograms of synthesized speech obtained by both synthesis by analysis and synthesis by rule are given along with a set of rules for text-to-speech synthesis of Turkish. It is observed that the speech synthesized by analysis loses the speaker's identity but it is highly intelligible, while understanding the speech synthesized by rules requires a training period.