Currents' Physical Components (CPC) in systems with semi-periodic voltages and currents

There are situations in electrical distribution systems where voltages and currents cannot be regarded as periodic quantities. They could be non-periodic. Nonetheless, properties of electrical systems confine this non-periodicity of voltages and currents to a particular sub-set of non-periodic quantities, referred to as semi-periodic quantities in this paper. The paper presents the concept of semi-periodic quantities and defines major functionals, such as the running active power, the running rms value, the scalar product and the running complex rms (crms) value of quasi-harmonics, needed for describing electrical systems with such voltages and currents in power terms. A recursive approach to calculation of these functionals was presented as well. The paper presents fundamentals of the Currents' Physical Components (CPC) - based power theory of systems with semi-periodic voltages and currents. An application of the semi-periodic concept to a load current decomposition in single-phase circuits with linear loads and with harmonics generating loads is presented as well. The paper presents also a concept of extrapolation of CPC into the closest future, which enables quasi-instantaneous generation of control signals for switching compensators..