Generalized averaging method for power conversion circuits

Abstract

Abstractapplied to a wide range of power circuits that includes the resonant type converters. The basic limitation in resonant The method of state-space averaging has been successfully converters is that these circuits have state variables that exapplied to pulse-width modulated power converters, but has hibit predominantly oscillatory behavior. This paper investiits limitations with switched circuits that do not satisfy a gates a more general averaging scheme that can, in principle, accomodate arbitrary types of waveforms. The method is small ripple" condition. This work considers a more general accomodate arbitrary types of waveforms The method is small ripple" condition. This work considers a more general based on a time-dependent Fourier series representation for a averaging procedure that encompasses state-space averaging "sliding window" of a given waveform. For example, for an and is potentially applicable to a much broader class of cir-arbitrary time-domain waveform x(o), the method considers cuits and systems. In particular, the technique is shown to the Fourier coefficients of x(s) for s E (t -T, t] at the time be effective on a number of examples including resonant type instant t. Simplifying approximations can be made by omitconverters.ting insignificant terms in this series. For instance, to recover the traditional state-space averaged model, one would retain only the DC coefficient in this averaging scheme.

High Performance Control of a Single-Phase Shunt Active Filter

“…This value can be obtained from the analysis of the load current as (22) Remark 7: Note that (20) in Proposition 5 describes the desired averaged behavior of the capacitor energy dynamics in (6). Alternatively, these results can be obtained by applying averaging theory [24] as in [25] and [26].…”

“…Proof: Equation (7) is a first-order linear differential equation with an exogenous input ; therefore, it can be written in input-output form as (25) Note that ; therefore, the system is stable. As, in steady state, the input is a periodic signal, the output will also be a periodic signal.…”

Modeling and Analysis of Induction Heating Converters

“…These are generally formulated as the small ripple condition and the linear ripple approximation (Erickson & Maksimović, 2004), (Sanders et al, 1991). Small ripple means that the DC component of the signal for which this condition is applied is much larger than the other terms of its Fourier expansion.…”

“…There are also questions, whether the averaged model is valid for large variations of the signals and whether stability properties of the system are preserved by the transformation, or not. Periodically driven systems, like the power-electronic converters can be modelled using the generalized averaging method, presented in (Sanders et al, 1991). The generalized averaging concept is based on the calculation of the time-dependent complex Fourier coefficients of the circuit variables, using a sliding frame equal with a switching period.…”

“…the second term) is of interest. For a circuit variable x , the coefficients of the series (4) are defined by (5) (Sanders et al, 1991). ( )…”