| Abstract |
The performance of a pulse-width modulated (PWM) converter is analyzed as a result of switching
time uncertainties. In the absence of control actions, random noises will force a system to leave its
stability region in a finite time, even if the system is initially at its stable equilibrium point. From this
aspect, the deterministic model of stability will no longer apply and the cumulative effect of small
random perturbations on a dynamical system may be considerably different. The cumulative effect of
small random fluctuations on a system parameter can push the system operating point beyond a
predefined boundary. A stochastic model of an inverter with practical uncertainties, which has not
been addressed before, is pointed out. This stochastic model is based on the introduction of
perturbations in the duty ratio of switching converters as random noise processes, which has been
developed by the use of the theory of stochastic differential calculus. In this paper, random
characteristics of the system parameters are modeled by a zero mean gaussian white noise, which is
inherently associated with power electronic converters and represents the behavior of the system in a
fluctuating environment. The singular perturbation technique is employed to transform the
differential algebraic system into system differential equations with the help of a singular parameter.
Commutation rise and fall times are quantified through the singularly perturbed parameter. A
performance index, known as the mean first passage time (MFPT) is also determined. The MFPT of
the stable state of the process is defined as the passage time of the process in a certain domain of
attraction, averaged over all possible initial states. Effects of switching time uncertainties on the
inverter system are compared between the MFPT and its deterministic counterpart, critical energy (E'c). |
