On the Coexistence of Multiple Limit Cycles in H-Bridge Wireless Power Transfer Systems With Zero Current Switching Control

Abstract

This paper deals with the analysis of limit cycle oscillations in H-bridge wireless power transfer resonant inverters under primary-side Zero Current Switching (ZCS) control. The limit cycles are computed by solving their initial value problem. If this problem is not dealt with properly, erroneous results may be derived and ghost or physically inadmissible limit cycles may be obtained. A complementary condition must be added to obtain only real limit cycles that can take place in the system. The stability analysis of these real cycles is performed using Floquet theory. For the case of the series-series compensated topology, the resulting monodromy matrix reveals that these cycles are stable whenever they exist and the load resistance is larger than a critical value. On the contrary, for load resistance smaller than this critical value, coexistence of different real stable limit cycles is also possible. While one of the limit cycles always exists for the whole range of load resistance values, two of them are created/destroyed through a cyclic fold bifurcation. The boundary of this bifurcation is determined. Numerical simulations corroborate the theoretical predictions and some experimental measurements are presented to validate some of the theoretical and simulation results.