Boris Reznikov

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.

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.

Five-level H-bridge flying capacitor converter voltage balance dynamics analysis

Flying Capacitor (FC) multilevel Pulse Width Modulated (PWM) converters are an attractive choice due to the natural balancing property of the capacitor voltages. A single-leg flying capacitor converter voltage balance dynamics analytical solution may be obtained using switched systems time domain approach based on stitching of switching intervals piece-wise analytical solutions in combination, for inductance dominated load, with a small parameter technique. In this paper, a symmetric five-level H-bridge flying capacitor converter common mode voltage balance dynamics solution is obtained from its single-leg prototype using “mirror hypothesis” formalism. Simple analytical expressions clearly reveal the dependences on load parameters, carrier frequency, and DC PWM normalized voltage command. For AC modulation, the solution obtained by averaging on a fundamental AC period does not depend on a fundamental frequency. The results of the theoretical analysis are confirmed by extensive switched simulations.

PWM power converter voltage quality bounds and their applicability to non-PWM control schemes

The paper presents simple closed-form analytical expressions for PWM power converter ripple voltage Normalized Mean Square lower and upper bounds. These estimates obtained in time domain are asymptotic in the sense that switching-to-fundamental frequencies ratio is supposed infinitely large. Ripple voltage Normalized Mean Square in the first approximation represents normalized additional eddy current iron core loss in electric motor, transformer, or coupling inductor caused by converter switching that is a dominant switching loss mechanism. Non-PWM voltage control schemes like sliding mode, hysteresis, direct torque and power control, and predictive control may deliver better tracking, and disturbance rejection performance at the expense of compromising voltage quality thus increasing converter switching caused iron core loss. Comparison with PWM voltage quality asymptotic lower and upper bounds may be useful for making a fair assessment of different non-PWM strategies from additional switching caused iron core loss perspective.

Simple Time Averaging Current Quality Evaluation of a Single-Phase Multilevel PWM Inverter

This paper addresses theoretical calculation of a single-phase multilevel pulsewidth modulation (PWM) inverter current total harmonic distortion (THD). Analytical approach introduced in late 1980s for a two-level inverter is generalized for an arbitrary level count for a single-phase inverter. Although the obtained closed-form piecewise analytical solutions assume (infinitely) large ratio of switching and fundamental frequencies and pure inductive load, they are practically very accurate for the ratios of (apparent) switching and fundamental frequencies larger than 25-30 and inductance-dominated loads. Along with strict mathematical solutions, simple accurate Bessel function approximation and hyperbolic average trend one are suggested. The formulas clearly reveal a single-phase PWM inverter current THD dependence on modulation index for an arbitrary voltage level count and are easily modified to cover grid-connected cases.