Alex Ruderman

Improved Natural Balancing With Modified Phase-Shifted PWM for Single-Leg Five-Level Flying-Capacitor Converters

Flying-capacitor converters (FCCs), like most multilevel converter topologies, require a balancing mechanism of the capacitor voltages. FCCs feature natural voltage balancing when a special modulation technique is used. The classic methods, such as phase-shifted pulse width modulation (PS-PWM), result in very slow balancing for some duty-ratio ranges. Previous work has shown that for a single-leg five-level FCC, one time constant is infinite for a zero desired output voltage. In this paper, a modified PS-PWM scheme for a single-leg five-level FCC is presented, which results in faster balancing over the total duty-ratio range. The modified PS-PWM scheme is studied, resulting in an averaged voltage-balancing model. This model is verified using simulations and experiments. The modified PS-PWM scheme solves the slow-balancing problems of the normal PS-PWM method for odd-level FCCs, while maintaining the passive control property, and it provides a self-precharge capability.

Five-level single-leg flying capacitor converter voltage balance dynamics analysis

The attractive feature of a flying capacitor converter is the natural voltage balance property. The reported voltage balance dynamics analytical research methods are based on heavy frequency domain transformations (Fourier transform, Bessel functions etc) and are rather algorithmic and difficult to use in an everyday engineering practice. Suggested time domain approach uses stitching of piece-wise analytical solutions for consecutive switching intervals. The small parameter analysis of a five-level single-leg converter yields physically meaningful, simple, and accurate expressions for average voltage balance dynamics giving an in-depth insight into parameters, carrier frequency, and modulation strategy impact for both DC and AC PWM.

Simple analysis of a flying capacitor converter voltage balance dynamics for DC modulation

Flying capacitor multilevel PWM converter with a natural voltage balance is an attractive multilevel converter choice because it requires no voltage balance control effort. Flying capacitor converter practically does not suffer from voltage balance imposed performance limitations as opposed to multiple point clamped converter. Voltage balance dynamics analytical research methods reported to date deal mostly with an AC modulation case and are essentially based on a frequency domain analysis using double Fourier transform. Therefore, these methods require high mathematical skills, are not truly analytical and rather difficult to use in an everyday practice by electrical engineer. In this paper, we consider a DC modulation case to demonstrate that a straightforward time domain approach based on switching intervals piece-wise analytical solutions makes it easy to obtain time-averaged discrete and continuous models for voltage balance dynamics simulation. A primitive single-phase single-leg three-level converter analytical investigation yields a surprisingly simple accurate expression for capacitor charge / discharge related time constant revealing its dependence on inductive load parameters, carrier frequency, and duty ratio.

Asymptotic Time Domain Evaluation of a Multilevel Multiphase PWM Converter Voltage Quality

Voltage total harmonic distortion and quadratic voltage ripple criteria are accepted figures of merit of a multilevel pulse width modulation (PWM) converter voltage quality. The dominating frequency domain approach does not deliver simple closed-form expressions and practically requires accounting up to 40-50 switching harmonics. Assuming infinitely high switching frequency, suggested time domain approach to a multilevel multiphase PWM voltage quality evaluation provides closed-form piece-wise analytical solutions. These simple formulas clearly reveal the dependence on modulation index for arbitrary voltage level and odd phase numbers. The results are applicable to any type of multilevel converters (including interleaved, open winding and other) operated with nearest level/nearest space vector modulation and relatively high switching frequency.

About Voltage Total Harmonic Distortion for Single- and Three-Phase Multilevel Inverters

Many recent multilevel inverter papers end up with voltage total harmonic distortion (THD) values obtained from numerical voltage spectrum calculations (measurements). Motivated by IEEE Standard 519, a part of the multilevel research community uses a limited harmonic count to evaluate the multilevel voltage quality. First, this causes significant voltage THD underestimation, particularly for relatively high frequency PWM. Second, for a three-phase star-connected balanced load with an isolated neutral and phase symmetric modulation strategy, the calculated load line and phase voltage THD become different. However, simple considerations show that line and phase voltage THDs are essentially the same in this case. It may be difficult to judge about the multilevel voltage quality given a numerically calculated (measured) voltage THD value that may be subject to computation errors. Presented are simple smooth hyperbolic voltage THD upper and lower bound approximations for single- and three-phase inverters with nearest synchronous switching. They are valid for arbitrary modulation indices and uniformly distributed level counts and may practically serve as good reference values.

Observer-Based Compensation of Additive Periodic Torque Disturbances in Permanent Magnet Motors

The impact of additive periodic torque disturbances on the controlled motion of permanent magnet motors can be significant. The paper shows how an observer-based drive control can efficiently reject the harmonic torque disturbances providing smooth angular velocity. The proposed control design is based on the state-space torque harmonics representation and Luenberger observer that proved to be adequate. The designed control algorithms are verified using an experimental setup with a permanent magnet synchronous motor with well-detectable torque harmonics. The rejection of additive position periodic torque disturbances is experimentally demonstrated for two first harmonics and that for different angular velocities.

Simple comparison of different PWM strategies for a three-level H-bridge flying capacitor converter

The paper presents a comparison of phase-shifted and modified level-shifted carrier-based PWM strategies for a three-level H-bridge flying capacitor converter. While the optimal voltage quality of the nearest level switching may be obtained using both of them, natural voltage balancing dynamics is different. Using elementary circuit theory and switched system time domain analysis, it is possible to obtain simple analytical averaged voltage balancing dynamics solutions. Modified level-shifted carrier-based PWM is shown to provide much faster voltage balancing dynamics, especially, for small DC PWM voltage commands and AC PWM modulation indices. The explanation of this fact is obtained by analysis of zero voltage state sequences for different modulation strategies. Relatively fast voltage balancing dynamics rate provided by modified level-shifted carrier-based PWM for zero voltage command makes it possible to implement simple flying capacitors self-precharge procedure at power-up.

Evaluation of motor PWM loss increase due to zero common-mode voltage modulation strategy of multilevel converter

Voltage source converter Pulse Width Modulation common-mode voltages have an adverse affect of inducing motor shaft voltages and bearing currents that result in premature bearings failure. Common-mode voltage cancellation PWM strategies significantly compromise the optimal voltage quality of the nearest three space vector modulation. The paper presents a quantitative estimation of associated motor PWM loss increase for a three-phase multilevel converter.

Simple time domain averaging methodology for flying capacitor converter voltage balancing dynamics analysis

Accepted voltage balancing dynamics research methods flying capacitor converters are based on frequency domain transformations that involve double Fourier series with Bessel function coefficients. Therefore, these methods require high mathematical skills, are not truly analytical and difficult to use in engineering practice. In this paper, a “physical” approach to switched systems analysis based on stitching analytical solutions for consecutive switching subintervals, is applied to flying capacitor average voltage balancing dynamics analysis. It is shown that time domain averaging methodology generates simple analytical solutions that reveal the dependences on load parameters, carrier frequency, and normalized DC voltage command (AC modulation index). The power of suggested approach is demonstrated using single-leg converter voltage balancing dynamics analysis examples.

Flying-capacitor multilevel converter voltage balance dynamics for pure resistive load

Multilevel converters need voltage balancing to be able to generate an output voltage with high quality. Flying capacitor converter topology has a natural voltage balancing property. Voltage balance dynamics analytical research methods reported to date are essentially based on a frequency domain analysis using double fourier transform. These complicated methods are not truly analytical, which makes an understanding of parameter influence on time constants difficult. In this paper, a straightforward time domain approach based on stitching of switch intervals piece-wise analytical solutions to a DC modulated H-bridge flying capacitor converter is discussed. This method allows to obtain time-averaged discrete and continuous voltage balance dynamics models. Using small-parameter approximation for pure resistive loads, simple and accurate expressions for voltage balance time constants are deduced, revealing their dependence on load parameters, carrier frequency and duty ratio.