Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations

Abstract

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.

The Phasor Diagram of a Superconducting Synchronous Electrical Machine

“…Analytical methods were algorithmized with the development of computer technologies, and as a result, computer software for automated calculation was developed. As an example of a perspective technique, one can consider a recently developed approach to power analysis [6,7] which is exploiting cyclostationary properties [8,9] of voltage and current signals. Such an approach can mitigate the arbitrary periodic excitation which may be chosen as a possible way to further improve the tool presented in this paper.…”

Estimation of a Spectral Correlation Function Using a Time-Smoothing Cyclic Periodogram and FFT Interpolation—2N-FFT Algorithm

“…Second-order cyclostationarity, or wide-sense cyclostationarity, appears to be the intrinsic property exhibited by processes generating signals belonging to different classes. Thus, there are plenty of examples where it was reasonably taken into account in many research fields and engineering applications, including communication signals with various modulation schemes [ 6 ], radio signals used in passive radars [ 7 , 8 ], electromagnetic measurements with near-field probes [ 9 , 10 ], spectral sensing in cognitive radio [ 11 ], mechanical vibration of rotary machines [ 12 , 13 ], radio astronomy [ 14 , 15 ], power analysis of electric circuits [ 16 ], generalized detection [ 17 , 18 ] under conditions of the least certainty, electromagnetic compatibility [ 19 , 20 ], detection of vital signs in radar response [ 21 , 22 ], drone navigation signals [ 23 ] and others.…”