Recently, LLC resonant converters have attracted significant research from industry and academia for AC-DC and DC-DC power conversion with high efficiency and remarkable power density. They are appealing candidates for numerous vehicular and renewable energy applications including battery chargers for electric vehicles and drivers of LED lights. This study introduces a mathematical model of LLC resonant half-bridge DC-DC converter, which captures its steady-state behaviours for both continuous conduction mode and discontinuous conduction mode operations. One major advantage of the proposed model lies in accurate estimation of the switching frequency of power switches under a wide range of parametric variations. This benefit is, however, not offered by the prevailing method based on the first harmonic approximation (FHA). The analytical derivations of the system's state-space model, as well as equations for calculating the switching frequency by FHA, are discussed in details. For illustration, a 340 W digitally controlled LLC resonant converter is targeted in this study. The simulation analyses of current and voltage waveforms for light and heavy load conditions are presented. Moreover, the experimental results, along with the comparison of switching frequency estimation for both methods, are demonstrated and discussed, which confirms the validity and effectiveness of the proposed model.

Adjustable speed motor drives are among the most representative types of non-linear systems which can exhibit rich varieties of complex dynamic behaviours. This study presents the investigation of chaotic phenomena in the switched reluctance (SR) motor drive employing digital speed regulator and hysteresis current controller. For conducting stability analysis, a small signal discrete-time model of the SR drive has been derived and analysed for a range of control parameters. The simulation results of time-domain and frequency-domain analysis and phase portraits of the SR drive system are also demonstrated and discussed. Two influencing factors for chaotic behaviour in the SR drive system are identified and examined in detail: the feedback delay of the speed regulator and measurement imperfection from a rotary incremental encoder. For verification, an 8/6 pole 2.3 kW SR drive is employed in experimental tests. The bifurcation diagrams of the reference signal, waveforms of phase current, and the corresponding frequency spectra are recorded and illustrated for both normal and chaotic operations, which reveal the pattern of chaos exhibited from this type of electric drive system.