Occurrence and Suppression of Limit Cycle Oscillations in Coupled DC-DC Converters with Constant Power Loads

Abstract

In recent times, DC distribution power systems (DPSs) consisting of a network interconnection of controlled switching power converters are becoming increasingly common in various practical applications; such as, in VLSI mainframe computers' power supplies, telecommunication systems, electric cars, aircraft, DC power generation and distribution systems, and so on. Advantages of these DC DPSs are the power interfacing flexibility due to reduced size and weight, highly efficient energy conversion, simpler implementation of power source paralleling, easy incorporation of DC-type renewable resources, and the ability to satisfy a variety of control objectives. However, major problems for such DC distribution is the potential stability degradation that can occur when switching converters are connected to a common DC bus. This destabilizing effect can happen because of the negative impedance property of the load-side converter and hence leads to the undesirable large-scale oscillations (called as limit cycle oscillation) in the systems. This thesis explores the cause of occurrence of such limit cycle oscillations and their suppression in couple cascaded DC-DC converters systems using the concepts of nonlinear dynamics and bifurcation theory, in particular, the amplitude death (AD) phenomena. The AD is a well-known mathematical phenomenon characterizing the coupling induced stabilization of several interconnected nonlinear oscillatory systems. It has been discussed that AD-based solutions can be used for the stabilization of DC DPSs under various coupling schemes. These have been demonstrated here through numerical simulations and experimental validations. Numerical results reveal that if heterogeneity ( e.g., the system parameters are mismatched) is introduced in coupled oscillatory systems, the AD can happen. However, in some situations, when internal parameters of the systems are not accessible to the user, AD can only happen if an instantaneous delay is introduced. It has been found that adding a dynamical coupling - where coupling link has its dynamical properties - is a replacement of delay circuits, and that can lead the coupled identical and nonidentical oscillating systems to steady-state equilibrium point through AD phenomena.To do so, the stability of the equilibrium solution is analyzed for coupled converters systems using the averaged differential equations near a supercritical Hopf bifurcation. Death regions are identified for asymptotic stability under different coupling conditions. It is shown that the largest eigenvalue obtained from XPPAUTO completely characterizes the effect of connection configuration on the stability of diffusively coupled identical and nonidentical systems. In particular, all identical systems have no death regions regardless of the type of couplings. Furthermore, identical converters systems with delay, dynamical or relay coupling, or nonidentical systems with any types coupling provide, respectively, upper and lower bounds for the parametric stability regions. The results further characterize the different coupling configurations as the mechanism for the death of coupled oscillators near Hopf bifurcation. Also, some generalizations are given for converters networks with LRC-type coupling.