Exact Numerical Method for Predicting Instabilities of Switching Converters with Constant Power Load

Switching converters are nonlinear dynamical systems irrespective of the load and can exhibit different types of instabilities with the variation of the parameters. Due to the on/off nature of the periodically controlled switches, this kind of system is modeled by a set of differential equations (i.e., subsystem) after satisfying different switching conditions within a switching period. Therefore, their steady-state behavior shows periodic waveforms in the time domain and periodic orbit in the state space. For resistive load, the stability analysis of the periodic orbit can be done by calculating the fundamental solution matrix or monodromy matrix using exponential matrices for evolution within the linear subsystems, and the saltation matrices for transition across subsystems through switching conditions. However, with Constant Power Load (CPL), the subsystems are nonlinear and the state matrices are state dependent. Therefore, the state transition matrices in each subsystem are not analytically available and have to be calculated numerically by solving the system differential equations and variational equations simultaneously. The presented numerical method for stability analysis is applicable to different operating conditions with no limitation in problem size i.e., dimensions and number of subsystems. A higher number of subsystems in a period only increases the number of matrices to be multiplied for the calculation of the monodromy matrix, and not the dimension of it. Apart from switching converters, this method can be used in general for any hybrid systems including mechanical impacting systems, robotic systems, power systems, and neuron models.