Model Orders and Numerical Issues in LLC Resonant DC-DC Converters

Abstract

The condition number of a Sylvester matrix composed of the denominator and numerator polynomial of a model is investigated numerically for an LLC resonant dc-dc converter. The order of the model is changed from six to one in a certain manner and they are discretized using the step-invariant and matched-pole-zero methods expressed in the delta and shift operators. Their condition numbers show that in both operator forms, the higher the order is, the larger the condition number becomes, implying poorer numerical conditioning. It was also found that the stepinvariant model is more ill-conditioned than the matchedpole-zero models in general. While the number becomes constant as the sampling frequency increases for the delta cases, it keeps increasing for the shift cases, which is well known. However, in the range of sampling frequencies expected in recent practices, the models expressed in shiftform have smaller condition numbers and are betterconditioned than those in delta-form of respective orders.