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On the static and small signal analysis of DAB converter

Yuxin Yang, Hang Zhou, Hourong Song, Branislav Hredzak

TL;DR

The paper develops a compact discrete-time framework to compute the periodic operating point of a Dual-Active-Bridge (DAB) by deriving a recursive closed-form for the state and a periodic fixed-point equation using interval transition matrices. It exploits symmetry through a half-cycle mapping approach, showing that four fixed-frequency phase-modulation surfaces are equivalent in the $z$-domain under DAB symmetry, which reduces analysis complexity. A full small-signal model is then built for fixed-frequency phase modulation, including segment maps, endpoint timing sensitivities, and a SIMO transfer function, with a detailed treatment of two-interval half-cycle templates and surface equivalence. The work also analyzes the relation between constrained (same-cycle) and unconstrained modulation, showing that the constrained model approximates the exact model at low frequency with an $O(\omega T_h)$ error, thereby supporting practical controller design with reduced computation.

Abstract

This document develops a method to solve the periodic operating point of Dual-Active-Bridge (DAB).

On the static and small signal analysis of DAB converter

TL;DR

The paper develops a compact discrete-time framework to compute the periodic operating point of a Dual-Active-Bridge (DAB) by deriving a recursive closed-form for the state and a periodic fixed-point equation using interval transition matrices. It exploits symmetry through a half-cycle mapping approach, showing that four fixed-frequency phase-modulation surfaces are equivalent in the -domain under DAB symmetry, which reduces analysis complexity. A full small-signal model is then built for fixed-frequency phase modulation, including segment maps, endpoint timing sensitivities, and a SIMO transfer function, with a detailed treatment of two-interval half-cycle templates and surface equivalence. The work also analyzes the relation between constrained (same-cycle) and unconstrained modulation, showing that the constrained model approximates the exact model at low frequency with an error, thereby supporting practical controller design with reduced computation.

Abstract

This document develops a method to solve the periodic operating point of Dual-Active-Bridge (DAB).
Paper Structure (31 sections, 4 theorems, 71 equations, 3 figures)

This paper contains 31 sections, 4 theorems, 71 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Statement and Objectives
  3. Product Notation: Direction and Boundary
  4. Main Results: Recursive Closed‐Form and Fixed‐Point Equation
  5. Recursive Closed‐Form
  6. Periodic Fixed‐Point Equation
  7. System Matrices For Dual Active Bridge
  8. Notation
  9. Similarity / Sign Identities
  10. $H$–$G$ Operator Proof for the Four-Step Fixed Point
  11. Small-Signal Model of DAB Under Fixed-Frequency Phase Modulation
  12. Half-cycle rectified coordinate and SIMO physical output
  13. Segment maps, endpoint identity, and a two-interval half-cycle template
  14. A. Endpoint identity
  15. B. Large-signal half-cycle map
  16. ...and 16 more sections

Key Result

Lemma 1

Let with the structural and timing assumptions Then the following hold:

Figures (3)

  • Figure 1: Schematic of the DAB converter
  • Figure 2: Schematic of the piecewise intervals.
  • Figure 3: Four modulation edges in DAB control.

Theorems & Definitions (10)

  • Lemma 1: Similarity and Sign Relations
  • proof
  • Theorem 2: Half‐Cycle Fixed‐Point Characterization
  • proof
  • Lemma 3: Similarity invariance
  • proof
  • Theorem 4: Equivalence of fixed-frequency surfaces
  • proof
  • Remark 1
  • Remark 2