Singular Perturbation Theory for DC—DC Converters and Application to PFC Converters

Many control schemes for dc–dc converters begin with the assertion that inductor currents are “fast” states and capacitor voltages are “slow” states. This assertion must be true for power factor correction (PFC) converters to allow independent control of current and voltage, and is important for many other applications. In the present study, singular perturbation theory is applied to two-state switching-power converters to provide rigorous justification of the timescale separation. Krylov-Bogoliubov-Mitropolsky averaging is used to include switching ripple effects. A relationship between inductance, capacitance, load resistance, and loss resistances derives from an analysis of the off-manifold dynamics of an approximate model. Similar results hold for boost, buck, and buck–boost converters. Experimental boost converters validate the results. Discrete-time analysis is also shown. Simulated PFC converters demonstrate a simple, sensorless control technique that requires timescale separation.