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It is well known that switching dc-dc converters show a wide range of nonlinear behaviours including bifurcation, sub-haraionics and chaos when they operate outside their design specifications. These nonlinear patterns force the converter to change its normal periodic behaviour to a random-like behaviour; a situation that must be avoided. In this thesis, the nonlinear dynamics of switching dc-dc converters are investigated. It is shown for the first time that the concept of the monodromy matrix (i.e. the state transition matrix for one switching cycle, including the state transition matrices during the switching slants) can be successfully applied to determine the stability of switching dc-dc power converters.

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Photovoltaic pumping systems have become a favourable solution for water supply particularly for sunny regions that have no access to an electric grid. The maximization of energy utilization of these systems via maximum power point tracking (MPPT) has not been sufficiently exploited in the literature. As a result, most commercial photovoltaic pumping systems either utilize inefficient MPPT control or do not utilize MPPT control at all thus wasting up to 50% of the available solar power depending on component matching and weather conditions. It is therefore important that the operating behaviour of these systems under MPPT control must be better understood and their reliability proven under practical operating conditions. This thesis details an investigation of the performance characteristics of directly connected photovoltaic pumping systems, systems operated at a constant array voltage, and those utilizing MPPT control. Two hill-climbing MPPT algorithms namely perturb and observe algorithm and incremental conductance algorithm were chosen because of their simplicity and ease of implementation with a low cost microcontroller/DSP. Particular focus is given to the evaluation of the practical implementation of these two MPPT algorithms and the choice of their parameters. A simple and accurate empirical model is derived for each individual component of the system and the system is simulated numerically using the MATLAB/Simulink environment. A comprehensive analysis of the stability and the performance characteristics of the system in different operation modes is presented. The various advantages and drawbacks of each MPPT control technique are identified and energy utilization efficiency is calculated for different weather conditions. Experimental operation of the system was tested using a 1080Wp photovoltaic array connected to a lkW permanent magnet de motor-centrifugal pump set. A power converter was constructed and used as a pump controller to match the motor-pump set with the PV array. A Texas Instruments TMS320F2812 DSP based eZdsp kit was used for real-time control and data acquisition. Data acquisition is accomplished utilizing the real-time data exchange feature of the DSP kit. Practical results show very good agreement with the numerical simulation of the systems.

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