Swept area theory: An approach in nonlinear and switched network analysis

In this work, according to the concept of area' on the v-i plane, a new approach called swept area theory, under both nonlinear continuous and discontinuous conditions, is developed. Novel conservative functions, such as area velocity and closed area over time (CAT), involved in this theory, are proposed. An analysis is carried out, by means of these functions, over nonlinear R, L, and C elements and over the ideal switch. In addition, jump discontinuities are discussed in detail. The CAT is related to the harmonic reactive powers and under sinusoidal steady state becomes proportional to the classical reactive power. A balance rule concerning harmonic reactive powers over nonlinear resistor under continuous conditions is obtained and discussed as a novel interesting result. This aspect impacts on a possible expanded definition of reactive power under distorted conditions. Thanks to the switching power, a novel quantitative relation between hard-switching commutations and CAT is obtained, with both theoretical and applicative relevance. More explanation is presented through a demonstration that shows how an ideal switch and power converters can become sources of reactive power. Issues of principle regarding the ideal switch model with respect to the real one are another important result of this work.