Decomposed Discrete-Time Model and Multiscale Oscillations Analysis of the DAB Converter

Full‐state discrete‐time model‐based stability analysis and parameter design of dual active bridge converter in energy storage system

“…The correlation factors between the state variables and Floquet multipliers of the DAB converter are shown in Table 2 and Figure 15. In addition, the modulus of the correlation factor in Table 2 represents the relevant degree between the state variable and the Floquet multiplier [14]. Obviously, each state variable corresponds to a closely related Floquet multiplier.…”

“…Thus, the sensitivity analysis of Floquet multipliers to the system parameters of DAB converter is proposed in this part. According to [14], the sensitivity of the Floquet multiplier λ i to the system parameter K j is expressed as (34), where U and V are the matrices of the right and left eigenvectors of the Jacobian matrix J , respectively. $$\begin{equation}S_{{K_j}}^{{\lambda _i}} = \frac{{\partial {\lambda _i}}}{{\partial {K_j}}}{K_j} = \frac{{{{\bf V}}_i^T\left( {\frac{{\partial {{\bf J}}}}{{\partial {K_j}}}} \right){{{\bf U}}_i}}}{{{{\bf V}}_i^T{{{\bf U}}_i}}}{K_j}\end{equation}$$…”

“…Conventional state‐space averaging method [16] is widely used to model the converters. However, because the inductor current of DAB converter is pure AC, the small ripple hypothesis no longer holds [14]. Therefore, the generalized averaging method [17] is proposed to investigate the small‐signal characteristics of DAB converter [18].…”

“…In order to extend the lifetime of a battery, it is necessary for the DAB converter to provide accurate charge current and voltage through stable operations [13]. If there are unstable phenomena, the corresponding fast-scale subharmonic oscillation and the slow-scale low-frequency oscillation will lead to the undesired current and voltage levels, which can increase the devices stress, decrease their reliability and even damage the DAB converter and its interconnected equipment [14]. To investigate the stability of the system, it is essential to apply proper modelling methods and analysis tools to reveal the complex dynamic behaviours of the system and facilitate the design of high-performance controllers [15].…”

Application of dual active bridge DC-DC converter in solid state transformer

“…However, the absence of the inductor current dynamics in the commonly used reduced-type continuous-time model in the literature [21,38,53,55,56,83] limits its study for the stability analysis. But the conventional discrete-time model [48,49,117,[152][153][154] including bilinear models [50][51][52] contains the complicated terms like exponential matrix in the state variable expression as discussed in the previous chapters. Moreover, the simplest first-order approximation of the matrix exponential used in the PWM dc-dc converter like a buck, boost, or buck-boost [99] shows significant error for the DAB converter [48].…”