Firstly, this thesis investigates the electrical power harmonics in an attempt to utilize harmonic current and its distortion power in a novel idea to reconvert the distortion power into useful power. This is done, in order to feed different DC or AC loads in single and three-phase power system by using passive or active filters and accordingly, develop a new topology of hybrid active power filter (HAPF). In addition, this circuit can be considered as a power factor corrector (PFC) because it reduces the total harmonic distortion (THD) and improves the power factor (PF). Secondly, this thesis works on a new design of active power factor correction (APFC) circuit presenting two circuits with the same design principle: the first design consists of two active switches without an external complex control circuit, while the second design contains a single active switch with an additional control circuit. The main contribution of this circuit is 98% reduction of the inductor's value used in the newly proposed PFC circuit in comparison with the conventional boost converter which may lead to a huge reduction in size, weight and the cost of the new PFC circuit. Also, the active switches depend on a carefully designed switching pattern that results in an elimination of the third order harmonic from the input source current which decreases the value of total current harmonic distortion (THDI) to (14%) and improves the input PF to (0.99). Consequently, the simplicity of the design without requiring a complex control circuit and without a snubber circuit plus the minimum size of inductor, gives the newly proposed circuit the superiority on other PFC circuits. Thirdly, this research aims to describe the distortion power through submitting two novel power terms called effective active power (Pef ) & reactive power (Qef ) terms with a new power diagram called Right-Angled Power Triangle (RAPT) Diagram. In addition, a novel de nition of total apparent power (St) has been submitted in order to illustrate the physical meaning of (St) in non-sinusoidal systems. The new RAPT Diagram is based on the orthogonality law and depends on geometrical summation to describe the relationship between different aspects (apparent-active-reactive) of power, and different components (total-fundamental distortion), drawing a bridge to connect the time domain with the frequency domain in a two-dimensional diagram.

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