### Abstract

The classical complex phasor representation of sinusoidal voltages and currents is generalized to arbitrary waveforms. The method relies on the so-called analytic signal using the Hilbert transform.This naturally leads to the notion of a timevarying power triangle and its associated instantaneous power factor. Additionally, it is shown for linear systems that Budeanu’s reactive power can be related to energy oscillations, but only in an average sense. Furthermore, Budeanu’s distortion power is decomposed into a part representing a measure of the fluctuation of power around the active power and a part that represents the fluctuation of power around Budeanu’s reactive power. The results are presented for single-phase systems.

Original language | English |
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Title of host publication | Mathematical Control Theory I |

Subtitle of host publication | Nonlinear and Hybrid Control Systems |

Publisher | Springer |

Pages | 51-72 |

Number of pages | 22 |

ISBN (Electronic) | 978-3-319-20988-3 |

ISBN (Print) | 978-3-319-20987-6 |

DOIs | |

Publication status | Published - 14 Jul 2015 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Publisher | Springer |

Volume | 461 |

ISSN (Print) | 0170-8643 |

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## Cite this

Stramigioli, S. (2015). Time-Varying phasors and their application to power analysis. In

*Mathematical Control Theory I: Nonlinear and Hybrid Control Systems*(pp. 51-72). (Lecture Notes in Control and Information Sciences; Vol. 461). Springer. https://doi.org/10.1007/978-3-319-20988-3_4