Variable Switching Frequency PWM Research Articles

Variable switching frequency PWM for quasi‐Z‐Source inverter based on DC current ripple prediction

AbstractHerein, a variable switching frequency pulse width (VSFPWM) modulation strategy for quasi‐Z‐source inverter (qZSI) based on a recently proposed modulation method, named as ZSVM8, is proposed. The formulae of quasi‐Z‐source inverter inductor current ripple of ZSVM8 are deduced in detail, and a prediction model for the current ripple is obtained. Combining with the VSFPWM technique, an improved modulation method named ZSVM8 VSFPWM is proposed to further reduce the switching times without increasing the maximum inductor current ripple. As a result, the switching losses can be reduced compared with the conventional ZSVM8. Besides, ZSVM8 VSFPWM also suppresses electromagnetic interference noise, such as current EMI and common‐mode voltage. Simulations and hardware experimental results are implemented to verify the efficacies of the proposed modulation method.

VSFPWM Based on Circulating Current Ripple Prediction for ZVS in Two Paralleled Grid-Tied Inverters With Coupled Inductors

Zero voltage switching (ZVS) control is an effective and promising way to further improve the power density, efficiency and electromagnetic interference for the two paralleled silicon carbide inverters with coupled inductors. In this article, focusing on the popular 180 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> interleaved pulsewidth modulation (PWM), the circulating current ripple prediction model is first derived as a function of operating conditions in the time-domain. With the assistance of this model, the actual trajectory of phase-leg currents can be reconstructed by superposition of sampling fundamental current and predicted circulating current ripple, without adding any high-frequency current sensor or auxiliary circuit. By carefully considering the ZVS requirement of all switches, a variable switching frequency PWM (VSFPWM) for full range ZVS control is proposed in this article. The proposed VSFPWM shows a good performance of ZVS realization in various load situations, as well as a good dynamic response of the inverter during current step change. In addition, due to the real-time variation of switching frequency, the proposed VSFPWM demonstrates the obvious advantage in conductive EMI reduction. Both the simulation and experimental results are presented to verify the effectiveness of the analysis and proposed method.

Optimal Periodic Variable Switching PWM for Harmonic Performance Enhancement in Grid-Connected Voltage Source Converters

Variable switching frequency PWM (VSFPWM) modulation can be advantageously implemented in industrial applications, such as renewable energy, motor drives, and uninterrupted power supply (UPS) systems, to reduce the injected current harmonic amplitudes, to suppress audible noise, and to improve semiconductor power efficiency. In this article, the usage of periodic VSFPWM methods in a voltage source converter (VSC) is proposed, analyzed, and benchmarked in terms of harmonic spectrum spreading, following the IEEE-519 current harmonic standard for the connection to the distribution grid. Particular attention is paid to the influence of VSFPWM on the ac filter design. First, the analytical model of the voltage harmonic spectrum generated by a three-phase three-wire two-level VSC implementing several periodic VSFPWM methods is derived. Subsequently, a design guideline for the commonly used <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter in the grid-tied VSC application is proposed, which minimizes the size requirement of the necessary components. The voltage spectrum models of the proposed VSFPWM method and the optimal switching profiles are verified by MATLAB/Simulink simulations and a 5-kW three-phase two-level VSC hardware demonstrator. The study shows that the ac filter power density for the studied VSFPWM methods can be greatly increased when compared with the conventional and widely employed constant switching frequency continuous PWM strategies.

Novel Variable Switching Frequency PWM Strategy for a SiC-MOSFET-Based Electric Vehicle Inverter to Increase Battery Usage Time

In this study, a novel variable switching frequency pulse width modulation (VSFPWM) strategy is proposed to achieve improved electric vehicle inverter efficiency. The silicon carbide (SiC) MOSFET inverter has excellent switching characteristics, thus enabling pulse width modulation control with a high switching frequency. The high switching frequency can reduce the voltage ripples in DC-link capacitors, which enables their use at a reduced capacitance. The switching frequency is typically set to a level that is within the limits of the voltage ripple in the maximum output region. Given that the same switching frequency is applied to the entire operating region, there is a sufficient margin with respect to the limits of the voltage ripple in the low-to-medium output range. The proposed method is designed to consider the real-time minimum switching frequency by considering the voltage ripple of the capacitor during operation under loaded conditions, thereby minimizing the switching loss. In addition, the method is suitable for high-switching frequency control because the calculation time is short. Because it does not require additional hardware, it is easy to apply to the existing inverter. The validity of the proposed method was verified based on simulations and experiments.

On the estimation error of position sensorless control of PM synchronous motors

The influence of several key parameters of the electric drive system on the rotor position estimation error of the sensorless control is studied. Here a saliency based sensorless method using a zero-sequence carrier is considered. Based on the theoretical analysis, there exists a relationship between the current ripple on three phase currents and the estimation error of the rotor position. Through analysis of a simulation model with LRC load, the change of modulation ratio, neutral capacitance and switching frequency can seriously influence the estimation error. Afterwards, all the simulation analysis was validated on a practical electric drive system with a PM synchronous motor. Variable switching frequency PWM (VSFPWM) is also applied to further increase the accuracy of the rotor position estimation. It is proved that the current ripple surely affects the estimation significantly. This study also paves the way of a further theoretical research of the relationship between the current ripple and estimation error, and thus lays the foundation of an optimized parameter selection for the EDSs using the position sensorless control strategy.

Bipolar and unipolar schemes for confined band variable switching frequency PWM based inverter

The single phase inverter performance through the unipolar and bipolar strategies has been previously analyzed based on the constant switching frequency pulse width modulation (CSFPWM). However, the confined band variable switching frequency PWM (CB-VSFPWM) is currently proposed as a new variable switching frequency PWM technique through unipolar strategy to facilitate the design of high order filter, to reduce the switching losses, and to reduce the current total harmonics distortion (THD) as well. To evaluate the performance of a single phase inverter based on the CBVSFPWM through bipolar strategy, this paper presents a comparative study of the CB-VSFPWM based inverter performance using the unipolar PWM and the bipolar PWM strategies. The study adopts MATLAB/Simulink to simulate the inverter and to analyze the simulation results in terms of harmonics spectrum, total harmonic distortion (THD), and fundamental components. The analysis of the study results gives an indication about the appropriate type of CB-VSFPWM strategy (unipolar PWM or bipolar PWM) to guarantee the desired performance of the connected inverter in terms of the electrical grid standards like THD, and harmonics spectrum of the inverter current.

Analysis and Optimization of Torque Ripple Reduction Strategy of Surface-Mounted Permanent-Magnet Motors in Flux-Weakening Region Based on Genetic Algorithm

One of the parameters required for a high-performance drive of a surface-mounted permanent magnet synchronous motor (SPMSM) operating in the flux-weakening region is the torque ripple reduction. In general, the torque ripple results from many reasons, such as the machine structure, oscillations of measured speed, etc. Hence, this article proposes an optimized strategy that works in conjunction with a variable switching frequency pulsewidth modulation algorithm to reduce the torque ripple peak. For the modulating algorithm, the updated frequency changes linearly with the desired torque ripple and its predicted maximum peak. For the proposed strategy, the reflection of proportional-integral (PI) parameters is observed at the torque ripple caused by the current ripples. Therefore, a robust method for adjusting PI parameters is proposed that relies on the improved fitness function that can minimize the regulators' error and maximize the drive stability bandwidth in the flux-weakening region. This objective function is optimized offline using a genetic algorithm optimization technique. Meanwhile, a third-order generalized integral flux observer is applied in this article, providing evidence of torque ripple reduction. For driving in the flux-weakening region, the reference magnitude of the duty cycles can produce the required <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis reference current to prevent the saturation of current controllers. Finally, comprehensive simulations and experiments are presented to validate the proposed strategy effectively. In comparison with the conventional method, the proposed strategy can reduce the copper and switching losses simultaneously and control the current and speed in the flux-weakening region efficiently.

Comprehensive Analysis of Hexagonal Sigma-Delta Modulations for Three-Phase High-Frequency VSC Based on Wide-Bandgap Semiconductors

The efficiency of wide-bandgap (WBG) power converters can be greatly improved using high-frequency modulation techniques. This article proposes using single-loop and doubleloop hexagonal sigma-delta (H-ΣΔ and DH-ΣΔ, respectively) modulations for voltage source converters (VSC) that use silicon carbide (SiC) semiconductors. These allow high switching frequencies to operate more efficiently than silicon devices. Thus, ΣΔ modulations are excellent candidates for taking advantage of WBG devices. The proposed modulation techniques allow working with a variable switching frequency, thus producing an extreme reduction in switching losses and mitigating the low-order harmonics in comparison with the classical space vector pulsewidth modulation (SVPWM) technique, and with the innovative variable switching frequency pulse-width modulation (VSFPWM). The performance and losses of both ΣΔ techniques are analyzed here using MATLAB/Simulink and PLECS, and then compared with SVPWM and VSFPWM. Furthermore, the frequency spectrum and the total harmonic distortion are evaluated. Experimental results performed on a VSC converter that uses SiC MOSFETs show how H-ΣΔ and DH-ΣΔ greatly improve efficiency and generate fewer low-order harmonics than the SVPWM and VSFPWM strategies do.

Investigation of current-ripple for three-phase four-wire inverter-fed motors

The three-phase four-wire drive system (4wEL) has been proved to be available of realizing fault-tolerant operation. However, this type of electric drive system (EDS) still has problems of higher current ripple than traditional three-wire EDSs. For a better understanding of the current ripple, a theoretical methodology of predicting the current-ripple in 4wEL is proposed for the first time. Based on the former study on traditional three-wire EDSs, the novel ripple prediction expression for the 4wEL is obtained by the study of corresponding voltage vectors and switching sectors. It is found that the prediction of current-ripple peak in 4wEL requires less calculation effort than in traditional three-phase EDSs. Besides, the difference of the current ripple peak between 4wEL and three-wire EDSs tend to be smaller for a lower modulation rate, while the variable duty cycle of the neutral phase of 4wEL can also influence the peak of current ripple. The theoretical prediction was also validated experimentally in a practical EDS and shows a proper accuracy of the current ripple prediction for both 4wEL and three-wire EDSs, which paves the path for the application of variable-switching-frequency PWM (VSFPWM) in 4wEL.

Periodic variation in the effect of switching frequency on the harmonics of power electronic converters

Switching frequency is an important factor in the performance control of power electronic converters. It can help optimize switching losses, switching ripples and electromagnetic interference, especially for newly developed high-switching-frequency silicon carbide converters. Periodic variation in the switching-frequency methods has been developed for this purpose, especially the model-predictive variable switching-frequency pulse width modulation (VSFPWM) method. The effect of periodic switching-frequency variation on the harmonics of a converter using double Fourier analysis and simulations are investigated. This work verifies that the switching harmonics can be reduced by periodic variation in the switching frequency, and the low-frequency (baseband) harmonics only incur a slight change. The analysis provides a theoretical foundation for the application of VSFPWM in power electronic converters.

The Impact of VSFPWM on DQ Current Control and a Compensation Method

The variable switching frequency pulsewidth modulation (VSFPWM) is varying the carrier frequency of pulsewidth modulation (PWM) based on the prediction model to reduce the switching losses and lower the electromagnetic interference (EMI). However, it may cause some deterioration in digital dq current control of voltage source converters. This article takes the L -type grid-connected converter as the research object, and first presents the generation mechanism of the varying time delay caused by VSFPWM. In the case of proportional-integral current regulator implemented with VSFPWM, the varying time delay is accompanied by the frame rotation, which causes a varying phase lag in output voltages, degrading the system performance. Subsequently, an analytical method based on complex coefficient transfer functions is developed to provide an accurate explanation of the relation between the VSFPWM and the corresponding impacts. A compensation method is then proposed to eliminate the varying phase lag of output voltages when the VSFPWM is employed, improving the steady state and dynamic performance of dq current control. Finally, the simulation and experimental results are presented to verify the analysis and the effectiveness of the proposed compensation method.

Switching frequency variation based on current ripple analysis of a 3‐L PMSM drive system considering neutral point balance

The output current ripple of the three-level (3-L) inverter is important to the performance of the 3-L permanent magnetic synchronous motor (PMSM) drive system, but the neutral point (NP) balance for the 3-L T-type inverter is not considered in the analysis of current ripple up to this point. The NP balance algorithms change the current ripple distribution and it is necessary to develop novel methods for current ripple analysis. In this study, the sinusoidal pulse width modulation with zero-order voltage injection and virtual space vector PWM (VSV-PWM) are utilised to balance the NP potential of the 3-L inverter in the PMSM drive system. The analytical methods of current ripple under these two modulation methods are proposed and the effects of these two NP balance methods on the output current ripple are investigated, respectively. Based on the analysis of current ripple, two variable switching frequency PWM (VSF-PWM) methods considering the NP balance are proposed. The proposed VSF-PWM methods can not only reduce the switching loss but also suppress the electro-magnetic interference noise while keeping the NP potential balanced. Especially, the proposed variable switching frequency VSV-PWM (VSF-VSV-PWM) can effectively alleviate the intrinsic problem of high switching loss of VSV-PWM.

Analysis and Calculation of Current Ripple Considering Inductance Saturation and Its Application to Variable Switching Frequency PWM

The inductance is an important parameter impacting current ripple calculation, usually with the assumption that the designed inductance performs ideally in most of voltage source inverters (VSIs) applications. However, the initial permeability of magnetic material usually descends when the winding current reaches or goes beyond the saturation limit. In such region of saturation, the implemented inductor does not perform as expected in design stages and its value varies with the bias current. In this paper, analysis and calculation of the current ripple are presented for a three-phase VSI with powder cores-based inductors, which reveals the calculation error of current ripple caused by the soft saturation nature of powder cores. Based on the equivalent single-phase model, the influence of inductance saturation on current ripple can be quantitatively evaluated. Then, a comparison of the current ripple calculation between considering and ignoring inductance saturation of implemented inductors is drawn in detail. Furthermore, under the condition of inductance saturation, the output current ripple peak-to-peak value of three phases is used as the constraint for variable switching frequency pulsewidth modulation (VSFPWM) design. A comprehensive method is developed to compensate the effect of inductance saturation in VSFPWM. At last, the effectiveness of the proposed strategy is verified by the detailed simulation and experiment.

Variable Switching Frequency PWM Strategy for High-Frequency Circulating Current Control in Paralleled Inverters With Coupled Inductors

Determination of high-frequency circulating current is important for coupled inductor design of paralleled voltage source inverters (VSIs). A time-domain model describing the circulating current of coupled inductor within a switching period is presented in this article. Using this model, the peak or rms values of circulating current can be calculated for different pulsewidth modulation (PWM) methods. Both the conventional 180° interleaved PWM and zero-common-mode voltage PWM algorithms are studied here. Considering the saturation nature of the magnetic cores in determining the effective inductance of coupled inductors, the variable switching frequency PWM (VSFPWM) is proposed to better utilize the coupled inductor's saturation limit, which is determined by high-frequency circulating current peak value. With the proposed strategy, both switching losses and electromagnetic interference are improved with respect to the constant switching frequency PWM. Moreover, the detailed power losses analysis of paralleled VSIs has been presented and the dynamic performance of the proposed VSFPWM has been well investigated. Finally, the proposed method has been extended to the system with 2N paralleled inverters. Detailed simulation and experimental results are provided to validate the proposed method.

Uniform Distribution Pulsewidth Modulation Strategy for Three-Phase Converters to Reduce Conducted EMI and Switching Loss

It is necessary to suppress the emission level of conducted electromagnetic interference (EMI) for the power electronics converters, and the variable switching frequency pulsewidth modulation (VSFPWM) is an alternative approach to reduce conducted EMI without adding bulky passive components. However, the experimental results indicate that many obvious EMI spikes in spectrum remain so that the conducted EMI reduction for VSFPWM is limited. In order to eliminate the EMI spikes in spectrum, this article first investigates the cause of the EMI spikes for VSFPWM, and the analysis results show that the nonuniform distribution of switching frequency is the primary reason. Then, a novel PWM strategy called uniform distribution PWM (UDPWM) is proposed to eliminate the EMI spikes and to further reduce conducted EMI. The design of a UDPWM is based on the uniform distribution of switching frequency and the principle of less switching loss. Moreover, the analytical formula of switching frequency is also deduced in detail, which adopts fixed variation range of switching frequency whatever the modulation index is. Finally, the experiments are carried out to validate the effectiveness of the UDPWM in reducing conducted EMI and switching loss. The UDPWM can approximately reduce conducted EMI by 20 dB compared with the conventional constant switching frequency PWM, and all obvious spikes in the spectrum are eliminated compared with VSFPWM.

Variable Switching Frequency PWM Strategy of Two-Level Rectifier for DC-Link Voltage Ripple Control

The switching frequency is an important control parameter of pulse-width-modulation (PWM) rectifier to reduce switching losses and electromagnetic interference noise. This paper proposed a variable switching frequency PWM (VSFPWM) strategy for dc-link voltage ripple control in two-level rectifier. DC-link voltage ripple is determined by the dc-link current directly, and can be predicted synchronously with PWM signals. A real-time prediction model of dc-link voltage ripple is derived for a common voltage-oriented control PWM rectifier. Then, VSFPWM control is introduced, which changes the switching frequency cycle to cycle with a restriction of dc-link voltage ripple peak value. Furthermore, the dynamic behavior is also observed when the proposed VSFPWM control scheme is adopted. Detail simulation and experimental comparisons are carried out between VSFPWM and normal constant switching frequency PWM, which demonstrate the advantages of the proposed method.

Attenuation of Conducted EMI for Three-Level Inverters Through PWM

This paper presents two typical modulations to reduce conducted electromagnetic interference (EMI) for three-level voltage-source inverters. The first modulation called variable switching frequency pulse-width modulation (VSFPWM) based on real-time current ripple prediction is used to reduce differential-mode (DM) EMI noise. This technique can make conducted EMI between kHz and MHz achieve great attenuation. The other method named zero common-mode (CM) PWM is used to decrease CM voltage and current. A comprehensive analysis and comparison between normal SVPWM and zero-CM PWM state that zero-CM PWM pays the prices of higher Total Harmowic Distortion (THD), serious neutral voltage unbalance, more switching loss and lower modulation index to achieve theoretical elimination of CM voltage. Then, combination of VSFPWM and zero-CM modulation is designed to avoid the disadvantages such as large switching loss produced by zero-CM PWM, and the new method has obvious predominance of reducing conducted EMI noise. Relevant experimental results validate the advantages of these modulations.

Discussion of "A Variable Switching Frequency PWM Technique for Induction Motor Drive to Spread Acoustic Noise Spectrum With Reduced Current Ripple"

Discussion of "A Variable Switching Frequency PWM Technique for Induction Motor Drive to Spread Acoustic Noise Spectrum With Reduced Current Ripple"

Response to Discussion on “A Variable Switching Frequency PWM Technique for Induction Motor Drive to Spread Acoustic Noise Spectrum With Reduced Current Ripple”

In random pulse width modulation (RPWM) category, a wide variety of schemes is seen as described in the paper. The discussion part is mainly focused on the randomized carrier frequency approach, where the switching periods are selected randomly, irrespective of the ripple voltage. For prediction of rms current ripple over a switching cycle as well as rms current ripple over the line cycle, precise knowledge of the switching period is required; this is not possible with random PWM techniques, though these methods are following a probability distribution function. However, accurate prediction of current total harmonic distortion (THD) is possible with the variable frequency PWM (VFPWM) method, as the switching period is a function of the fundamental angle. The procedure followed for current THD prediction is explained in [1].

Using d–q Transformation to Vary the Switching Frequency for Interior Permanent Magnet Synchronous Motor Drive Systems

The switching frequency is one of the most important control parameters of the dc/ac inverter. In most motor drives for transportation, it is set as a constant value at some specific torque or speed. The variable switching frequency pulse width modulation (VSFPWM), which changes the switching frequency cycle to cycle based on a current ripple prediction method, has been proposed in previous literatures and realized in resistance—inductance (RL) loads and induction motors (IMs). It proves effective to increase the overall system efficiency and improve electromagnetic interference (EMI) performance. However, the previous current ripple prediction method encounters difficulty in dealing with more complex motors, e.g., interior permanent magnet (IPM) motors, which is widely used in electric vehicles. As a result, the benefits of VSFPWM cannot be fully utilized for IPM drive systems. This paper proposed a new current ripple prediction method using the d–q transformation instead of the conventional Thevenin equivalent circuit method and successfully implemented VSFPWM to IPM drives. Simulation and experiments on a 400-V IPM test bench validated the effectiveness of the method, which will vary the switching frequency from cycle to cycle in order to 1) restrain the three-phase current ripples; 2) increase the overall system efficiency; and 3) enhance the system electromagnetic capability (EMC).