The increased penetration of power electronics interfaced resources in modern power systems is unlocking new opportunities and challenges. New concepts like multiport converters can further enhance the efficiency and power density of power electronics-based solutions. The triple active bridge is an isolated multiport converter with soft switching and high voltage gain that can integrate different sources, storage, and loads, or act as a building block for modular systems. However, the triple active bridge suffers from power flow cross-coupling, which affects its dynamic performance if it is not removed or mitigated. Unlike the extensive literature on two-port power converters, studies on modeling and control comparison for multiport converters are still lacking. Therefore, this paper presents and compares different modeling and decoupling control approaches applied to the triple active bridge converter, highlighting their benefits and limitations. The converter operation and modulation are introduced, and modeling and control strategies based on the single phase shift power flow control are detailed. The switching model, generalized full-order average model, and the reduced-order model derivations are presented thoroughly, and a comparison reveals that first harmonic approximations can be detrimental when modeling the triple active bridge. Furthermore, the model accuracy is highly sensitive to the operating point, showing that the generalized average model better represents some dynamics than the lossless reduced-order model. Furthermore, three decoupling control strategies are derived aiming to mitigate cross-coupling effects to ensure decoupled power flow and improve system stability. To assess their performance, the TAB converter is subjected to power and voltage disturbances and parameter uncertainty. A comprehensive comparison reveals that linear PI controllers with an inverse decoupling matrix can effectively control the TAB but exhibit large settling time and voltage deviations due to persistent cross-coupling. Furthermore, the decoupling matrix is highly sensitive to inaccuracies in the converter’s model parameters. In contrast, linear active disturbance rejection control and sliding mode control based on a linear extended state observer achieve rapid stabilization, demonstrating strong decoupling capability under disturbances. Furthermore, both control strategies demonstrate robust performance under parameter uncertainty.

Numerical simulations reveal that a single-stage differential boost AC module supplied from a PV module under an Maximum Power Point Tracking (MPPT) control at the input DC port and with current synchronization at the AC grid port might exhibit bifurcation phenomena under some weather conditions leading to subharmonic oscillation at the fast-switching scale. This paper will use discrete-time approach to characterize such behavior and to identify the onset of fast-scale instability. Slope compensation is used in the inner current loop to improve the stability of the system. The compensation slope values needed to guarantee stability for the full range of operating duty cycle and leading to an optimal deadbeat response are determined. The validity of the followed procedures is finally validated by a numerical simulations performed on a detailed circuit-level switched model of the AC module.

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

This article proposes an adaptive control method for a class of second-order fractional-order dynamic systems characterized by distinct eigenvalues in the state space. The control scheme developed is a generalization of the MRAC (Model Reference Adaptive Control) framework to scalar systems with fractional derivatives. To ensure accurate tracking of a reference model that is also fractional, an adaptive state feedback controller is designed. This is based on the tracking error between the outputs of the system and the model, incorporating a fractional-order adaptation law to ensure parameter convergence. Numerical simulations validate the effectiveness of the proposed approach and, through comparison with conventional MRAC control, highlight its superior performance in terms of tracking accuracy and robustness in the presence of uncertainties.

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