Bifurcation analysis with applications to power electronics

The problem of sudden loss of stability (more precisely, sudden change of operating behaviour) is frequently encountered in power electronics. A classic example is the current-mode controlled dc/dc converter which suffers from unwanted subharmonic operations when some parameters are not properly chosen. For this problem, power electronics engineers have derived an effective solution approach, known as ramp compensation, which has become the industry standard for current-mode control of dc/dc converters. In this chapter, the problem is reexamined in the light of bifurcation analysis. It is shown that such an analysis allows convenient prediction of stability boundaries and facilitates the selection of parameter values to guarantee stable operation. It also permits new phenomena to be discovered. An example is given at the end of the chapter to illustrate how some bizarre operation in a power-factor-correction (PFC) converter can be systematically explained.