Arbitrary order generalized state space average modeling of switching converters

Javaid, Uzair; Dujić, Dražen

doi:10.1109/ecce.2015.7310556

Cited by 13 publications

(7 citation statements)

References 10 publications

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“…Mostly, only the first harmonic at fundamental frequency is incorporated [18], [19], or some known harmonics of the system are selected to write the state-space and design a controller [6]. However, it could have been developed for an arbitrary large number of harmonics [9]. What is not clearly stated in the literature is that EHD and DHD approaches are equivalent and that they are a systematical writing of the LTI state space model that one can get by applying GSSA equations to analyze a LTP system with an arbitrary, possibly infinite number of harmonics.…”

Section: Discussionmentioning

confidence: 99%

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A comparison of harmonic modeling methods with application to control of switched systems with active filtering

Blin

Riedinger

Daafouz

et al. 2019

2019 18th European Control Conference (ECC)

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Many harmonic modeling approaches have been introduced in the literature, such as generalized state-space averaging, dynamic phasors, extended harmonic domain, and harmonic state-space. They are capable of capturing both the transient evolution and the steady-state of harmonics. They model the frequency coupling nature of a system and can expose the frequency couplings within interconnected components. By these modeling techniques, a linear time-periodic system can be converted into a linear time-invariant system, which allows the use of traditional analysis and control methods. This paper presents a state of the art of harmonic modeling approaches. Its contribution is to clearly establish the links between the different approaches, in particular through the specification of the decomposition of non-periodic signals in generalized Fourier series with time-varying coefficients. This paper also shows the advantages of harmonic modeling to analyse the frequency couplings within associated systems and to the control with active filtering.

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Section: Discussionmentioning

confidence: 99%

“…They employ Fourier series of timevarying coefficients and have been widely used in power system modeling and control, e.g. [9], [12], [19]. Extended Harmonic Domain (EHD) [11] and Dynamic Harmonic Domain (DHD) [3] have been introduced to analyse Linear Time-Periodic (LTP) systems.…”

Section: Introductionmentioning

confidence: 99%

A comparison of harmonic modeling methods with application to control of switched systems with active filtering

Blin

Riedinger

Daafouz

et al. 2019

2019 18th European Control Conference (ECC)

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“…The current flowing through the inductance does not contain DC level, only AC current. The model presented in this paper is based in the generalized state space model, explained in [18] and [19], where higher order harmonics are considered. In this paper, another control variable f sw , high order harmonics of the output voltage and half-bridge adaptation signal are also taken into account.…”

Section: Generalized State-space and Small-signal Modeling Of An Dual Active Bridgementioning

confidence: 99%

Small Signal Modelling for Variable Frequency Control With Maximum Efficiency Point Tracking of DAB Converter

et al. 2021

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Dual active bridge (DAB) converters have experienced a boom thanks to the demands of new applications where bidirectional energy transfer, galvanic isolation and high efficiency are essential. In order to improve the efficiency of the stage without losing sight of the converter advantages, previous works have proposed complex forms of control that are not always applicable. This paper proposes the use of a variable frequency control strategy plus an additional control loop to find the point of maximum efficiency. Therefore, in this paper, the generalized state space average model is developed in depth to obtain in an analytical way a new small-signal model between the switching frequency and the output voltage, which is used to design the digital variable frequency control. In addition, to increase efficiency, reduce losses and ensure zero voltage switching, a second loop based on perturb and observe methodology is presented. The results obtained in the analysis of this control are validated and contrasted by simulation and experimentally with a 1kW prototype. INDEX TERMSDual active bridge, digital control, GSSAM VOLUME 4, 2016This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2021.3084630, IEEE Access Ivan Ruiz Erni et al.: Variable frequency digital control with maximum efficiency point tracking of DAB converter

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“…Concerning the uniqueness part, if ( 16) admits an unique solution for a given x 0 , then the unicity of the trajectory x leads to the unicity of the initial condition for (17). If (17) admits several solutions in H, then for two distinct solutions…”

Section: Harmonic Modeling a General Case: Carathéodory Systemsmentioning

confidence: 99%

“…The models introduced in these papers capture both the transient evolution and the steady-state of harmonics and are widely used for power systems analysis and control, e.g. [23], [17], [21], [29], [31], [2], [8], [18], [26], [11]. We also mention [34], [35], [6] where control design methods based on harmonic Lyapunov or Riccati equations are proposed.…”

Section: Introductionmentioning

confidence: 99%

Necessary and Sufficient Conditions for Harmonic Control in Continuous Time

Blin¹,

Riedinger²,

Daafouzi³

et al. 2021

Preprint

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In this paper, we revisit the concepts and tools of harmonic analysis and control and provide a rigorous mathematical answer to the following question: when does an harmonic control has a representative in the time domain ? By representative we mean a control in the time domain that leads by sliding Fourier decomposition to exactly the same harmonic control. Harmonic controls that do not have such representatives lead to erroneous results in practice. The main results of this paper are: a one-to-one correspondence between ad hoc functional spaces guaranteeing the existence of a representative, a strict equivalence between the Carathéorody solutions of a differential system and the solutions of the associated harmonic differential model, and as a consequence, a general harmonic framework for Linear Time Periodic (LTP) systems and bilinear affine systems. The proposed framework allows to design globally stabilizing harmonic control laws. We illustrate the proposed approach on a single-phase rectifier bridge. Through this example, we show how one can design stabilizing control laws that guarantee periodic disturbance rejection and low harmonic content.

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Arbitrary order generalized state space average modeling of switching converters

Cited by 13 publications

References 10 publications

A comparison of harmonic modeling methods with application to control of switched systems with active filtering

A comparison of harmonic modeling methods with application to control of switched systems with active filtering

Small Signal Modelling for Variable Frequency Control With Maximum Efficiency Point Tracking of DAB Converter

Necessary and Sufficient Conditions for Harmonic Control in Continuous Time

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