Nonlinear Stability Analysis of DC-DC Power Electronic Systems by Means of Switching Equivalent Models

The proliferation of renewable energy sources is promoting the use of dc-dc power electronic converters in power distribution systems. It is well-known that the interconnection of power electronic converters can be a source of instabilities. Traditionally, impedance-based stability analyses are performed using either the analytical description or the identification of the output impedance of the source converter and the input admittance of the load converter. However, this methodology is restricted by the small-signal conditions, which are usually violated in this kind of systems due to the high variability imposed by the renewable energy sources. In nonlinear systems, the stability analysis usually consists on the definition of the region of attraction around a stable equilibrium point. In the literature, the analysis of nonlinear systems is almost exclusively applied to analytical systems, where all the details are known. This paper proposes a black-box methodology to obtain the region of attraction of the equilibrium point of commercial off-the-shelf dc-dc converters working in power distribution systems. First, optimization algorithms are used to identify the parameters of a predefined structure, such that it is able to reproduce the dynamic behavior of the system. The parameters identified can be used to create a switching equivalent model that accounts for the nonlinearities produced by the switching process of the converters. Second, the bisection method is implemented to minimize the number of simulations needed to determine the region of stability accurately. The proposed methodology has been validated both with simulations and with an experimental setup.