Nonlinear modeling and analysis of a practical controllable rectifier

The complicated nonlinear behaviors of a triacbased controllable rectifier are investigated in this paper. The triac is modeled as a nonlinear equivalent resistor. Considering the triggering and conducting conditions of the triac and the conducting condition of the rectifier, a piecewise state space model is set up. Based on that, a discrete iteration mapping model is further developed to analyze the transient behavior of the system. The typical characteristics of various period-doubling bifurcation phenomena are described by phase portraits. Using the symbolic sequence analysis method, both the border collision and standard period-doubling bifurcations are identified in the system. It has been found that the border collision bifurcation is caused by the missing conduction of the triac. A set of bifurcation diagrams showing the period doubling bifurcation behaviors of the system with relation to the circuit variables and parameters have been plotted. The results obtained can be used to guide the analysis and design of thyristor type controllable rectifier circuits. The analysis method is useful for investigating nonlinear bifurcation behaviors in similar switch-mode circuits.