Dynamic Phasor and Nonstationary Power Theory as an Extension of Classical Phasor Theory

Representation of nonstationary sinusoidal signals as complex time-varying functions, known as Dynamic Phasors (DPs), has been a long-standing problem in the circuit theory and power system stability literatures. The desired features of a theoretical framework for DPs are heavily inspired on classical phasor theory: the ability to transform time differential equations into equivalent algebraic complex equations, while maintaining the familiar notions of phasors, magnitudes and phases, and describing instantaneous power by two components, active and reactive power. Current frameworks rely on integral transforms which need approximations and truncations to allow for practical computation and application and do not offer a theory of nonstationary power. Further, the integral transforms are difficult to operate with and are not suitable to transform any generic nonstationary signal due to convergence requirements and frequency resolution challenges. This paper presents a new theoretical framework for DPs, based on differential operators, that offers a natural and efficient framework to transform nonstationary sinusoidal signals into Dynamic Phasors, while also offering a solid theory on nonstationary power extending the conventional well defined active and reactive power definitions.