An autonomous Ć uk converter controlled by a hysteresis current controller is studied in this paper. Filippov's method is employed for the first time to investigate the stability of an autonomous power converter. The Neimark bifurcation, via which the converter loses its stabile period one operation, was stabilized by applying two alternative control strategies based on the analysis of the behaviour of the complex eigenvalues of the monodromy matrix of the system.

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Grid connected inverters play a crucial role in generating energy to be fed to the grid. A filter is commonly used to suppress the switching frequency harmonics produced by the inverter, this being passive, and either an L- or LCL-filter. The latter is smaller in size compared to the L-filter. But choosing the optimal values of the LCL-filter is challenging due to resonance, which can affect stability. This paper presents a simple inverter controller design with an L-filter. The control topology is simple and applied easily using traditional control theory. Fast Fourier Transform analysis is used to compare different grid connected inverter control topologies. The modelled grid connected inverter with the proposed controller complies with the IEEE-1547 standard, and total harmonic distortion of the output current of the modelled inverter has been just 0.25% with an improved output waveform. Experimental work on a commercial PV inverter is then presented, including the effect of strong and weak grid connection. Inverter effects on the resistive load connected at the point of common coupling are presented. Results show that the voltage and current of resistive load, when the grid is interrupted, are increased, which may cause failure or damage for connecting appliances.

Higher order converters, without an external voltage control loop, have been known not to exhibit a fast-slow scale bifurcation interaction, as the slow-scale bifurcation has generally been believed to be caused by parameter changes in the outer loop. In this paper, it is shown that a current-mode controlled Ćuk converter can exhibit an interaction between fast-scale and slow-scale bifurcations even in the absence of this closed outer voltage control loop. The phenomenon is probed using an approach based on the system's monodromy matrix that does not only predict this instability but also provides a systematic method for the development of new control strategies to avoid the onset of this bifurcation. Analytical and numerical results prove that the new controller greatly extends the stable region of operation of the converter.

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