Equitably coloured balanced incomplete block designs

In this thesis we determine necessary and sufficient conditions for the existence of an equitably ℓ-colourable balanced incomplete block design for any positive integer ℓ > 2. In particular, we present a method for constructing non-trivial equitably ℓ-colourable BIBDs and prove that these designs are the only non-trivial equitably ℓ-colourable BIBDs that exist. We also observe that every equitable ℓ-colouring of a BIBD yields both an equalised ℓ-colouring and a proper 2-colouring of the same BIBD. We also discuss generalisations of these concepts including open questions for further research. The main results presented in this thesis also appear in [7].

Use of active power filter to reduce the effects of harmonics in solid oxide fuel cells

The Solid Oxide Fuel Cell (SOFC) is a class of fuel cells that is capable of generating very high levels of power at high temperatures. SOFCs are used for stationary power generation and as Combined Heat and Power (CHP) systems. In spite of all the beneficial features of the SOFC, the propagation of ripple currents, due to nonlinear loads, is a challenging problem, as it interferes with the physical operation of the fuel cell. The purpose of this thesis is to identify the cause of ripples and attempt to eliminate or reduce the ripple propagation through the use of Active Power Filters (APF). To this end, a systematic approach to modeling the fuel cell to account for its nonlinear behavior in the presence of current ripples is presented. A model of a small fuel cell power system which consists of a fuel cell, a DC-DC converter, a single-phase inverter and a nonlinear load is developed in MATLAB/Simulink environment. The extent of ripple propagation, due to variations in load magnitude and frequency, are identified using frequency spectrum analysis. In order to reduce the effects of ripple propagation, an APF is modeled to remove ripples from the DC fuel cell current. The emphasis of this thesis is based on the idea that small fuel cell systems cannot implement large passive filters to cancel the effects of ripple propagation and hence, the compact APF topology effectively protects the fuel cell from propagating ripples and improves its electrical performance.