Abstract
In DC microgrids (MG), the fractional order (FO) model of DC/DC converter is more accurate than an integer order (IO) version because the capacitor and inductor orders have a great effect on the converter performance. On this basis, a FO DC/DC buck converter is constructed to deal with the instability issues associated with a constant power load (CPL), which has the possibility of destabilizing DC microgrids. In this context, Oustaloup recursive approximation method (ORA) is employed to establish the FO converter’s components, and the dynamic equations of the FO buck converter are developed by means of the average method. As the CPLs have nonlinear characteristics, a FO nonlinear backstepping controller (BSC) is presented to effectively avoid the instability problem of the DC bus voltage. Furthermore, the asymptotic stability is proved using the fractional Lyapunov function. Finally, numerical results demonstrate the superiority of the fractional order controller over the integer order version of the backstepping control when the system faces all possible perturbations or disturbances.