Complex behavior of parallel-connected DC/DC converters from nonlinear viewpoint

Power electronic converters are nonlinear dynamical systems. The complex behavior for stand-alone converters, such as Hopf bifurcation, period doubling, border colliding, etc., has been studied in the past decades. In parallel-connected converter systems, several converters are connected together and mandatory control is needed to ensure proper current sharing. In such kind of systems, the effect of nonlinearity becomes more significant due to the complex interaction of the coupled systems. In this chapter, we attempt to study the complex behavior for parallel-connected buck converters under proportional-integral (PI) control. Basically, we find that for parallel-connected DC/DC converters, the desired operating orbit is not always reached from all initial conditions, even though the orbit has been found locally stable (e.g., from a linearized model). Depending on the initial state, the system may converge to different attractors, which can be a stable period-one orbit, a limit cycle of a long period, quasi-periodic orbit or chaotic orbit. Basins of attraction of desired and undesired attractors will be identified for different parametric perspectives. Furthermore, two distinct types of bifurcations have been identified for parallel-connected converters under PI control, namely, slow-scale bifurcation [1, 2, 3] and fast-scale bifurcation [4, 5]. The determining parameters are the integral-control time constants τF1and τF2. We will study the effects of τF1and τF2and identify the boundaries between these two types of bifurcations. Finally, we will analyze the bifurcation scenarios using the discrete-time mapping approach.