Daniel Juan Pagano

This work addresses the nonlinear dynamics of a reduced model for islanded DC microgrids with bus voltage droop control, whose loads are active and nonlinear, e.g., constant power loads (CPLs). Two CPL models are considered: (i) an ideal CPL and (ii) a piecewise-smooth CPL with Buck converter characteristics; and the analysis is performed separately for each of them. Case (ii) is the main focus of study in this work, being described as a planar continuous piecewise-smooth system with two zones separated by a straight line. The main objective is to characterize local and global nonlinear phenomena based on multiparametric analysis of bifurcations and asymptotic stability. Among the original results obtained, the following stand out: proof of the occurrence of Hopf-like bifurcations and the description of explicit conditions on the system parameters that ensure global asymptotic stability of the desired operating point.

This work analyzes the stability and bifurcation behavior of a bidirectional DC–DC converter operating in Buck mode and regulated by a Proportional–Integral (PI) controller subject to saturation. The dynamic behavior is modeled by a three-dimensional continuous piecewise-linear system with three zones and a unique equilibrium point. Explicit conditions on the control parameters are derived to ensure local stability of the equilibrium and to characterize the emergence of a stable limit cycle via the Focus-Center-Limit Cycle bifurcation. These results provide practical guidelines for tuning PI controllers, helping designers avoid unwanted oscillations and improve robustness against load disturbances. Numerical simulations and experimental results support the theoretical analysis.

Chaos in a DC–DC boost converter operating in discontinuous conduction mode when controlled by sliding mode control is detected. A route to chaos through sliding bifurcations is shown along with the coexistence of the chaotic regime with a stable operating point. A bifurcation analysis in the sliding vector field is carried out with the objective of defining a range of values for which control parameters guarantee the robustness of the system, at least locally. The analysis is based on the study of possible sliding bifurcations, that is, bifurcations inherent to the sliding dynamics. It is rigorously shown that there is an unstable limit cycle in the sliding dynamics due to a subcritical Hopf bifurcation. The existence of this limit cycle and its evolution with parameters turn out to be of great importance for the stability and robust control of this type of power converter.

Currently, high-performance power conversion requirements are of increasing interest in microgrid applications. In fact, isolated bidirectional dc-dc converters are widely used in modern dc distribution systems. The dual active bridge (DAB) dc-dc converter is identified as one of the most promising converter topology for the mentioned applications, due to its benefits of high power density, electrical isolation, bidirectional power flow, zero-voltage switching, and symmetrical structure. This study presents a power management control scheme in order to ensure the power balance of a dc microgrid in stand-alone operation, where the renewable energy source (RES) and the battery energy storage (BES) unit are interfaced by DAB converters. The power management algorithm, as introduced in this work, selects the proper operation of the RES system and BES system, based on load/generation power and state-of-charge of the battery conditions. Moreover, a nonlinear robust control strategy is proposed when the DAB converters are in voltage-mode-control in order to enhance the dynamic performance and robustness of the common dc-bus voltage, in addition to overcoming the instability problems that are caused by constant power loads and the dynamic interactions of power electronic converters. The simulation platform is developed in MATLAB/Simulink, where a photovoltaic system and battery system are selected as the typical RES and BES, respectively. Assessments on the performance of the proposed control scheme are conducted. Comparisons with the other control method are also provided.

This study presents the design and evaluation of robust controllers, based on linear programming, Kharitonov's theorem and Chebyshev's theorem, in order to enhance the performance of a typical structure of multi-stage converters present in direct current (dc) systems. In such electric power distribution systems, point-of-load converters act as a constant power load (CPL), which introduces a destabilizing nonlinear effects to their supply bus voltage. The multi-stage converter system uses a simplified scheme based on cascaded converter, which is comprised of two dc-dc buck converter in series connection. The robust controllers evaluated overcome the negative incremental impedance instability problem due to CPL, which causes a high risk of instability in interconnected converters. Thereby, the robust controllers evaluated ensure robust control performance and stability with a minor performance degradation compared to a conventional controller when the cascaded converter system is subjected to parametric uncertainties. The control methodologies evaluated are applied in both dc-dc buck converters. Assessments on the performance of the control methodologies evaluated are conducted. Experimental validations on a 150-W dc-dc cascaded converter system test board are carried out to verify the theoretical claims.

The present research work aims to study the large signal stability of two parallel-connected voltage-source inverters operating with resistive droop control through bifurcation analysis. This minimal setup can be considered as a prototype of a small islanded ac microgrid studying where droop control acts as a synchronization scheme between inverters. Since switching power converters are strong nonlinear circuits, bifurcation analysis helps to understand nonlinear phenomena more deeply than the standard linear approach. Plenty of complicated nonlinear phenomena have been observed through bifurcation analysis, such as multi-equilibria, period-doubling bifurcation, Hopf bifurcation, quasi-periodicity, border collision, bi-stability and chaos. Thereby, a set of parameters under certain conditions can influence the equilibrium point and its stability, leading to some of the aforementioned nonlinear phenomena. In this sense, the main contribution of this work is to detect the nonlinear phenomena in the considering islanded ac microgrid in order to determine a safe droop parameter region for a more robust microgrid operation. This information can be summarized in bifurcation diagrams leading to practical rules for choosing the control and droop parameters. Experimental results are performed to validate the main instabilities predicted by the theoretical models.