### Abstract

Electrical networks, and physical systems in general, are known to satisfy a power balance equation which states that the rate of change of the energy in time equals the power at the port of the network minus the power dissipated. However, when complex power is considered, there does not seem to exist a similar statement for the imaginary power, either in the timedomain or in the frequency-domain. Recently, in the context of electromagnetic fields, it has been shown by complexifying the time to t+js and interpreting s as reactive time, that it is possible to set up an imaginary power balance in terms of the rate of change of reactive energy in reactive time. Here these ideas are specialized to linear and time-invariant RLC networks. For non-sinusoidal waveforms it is shown that the rate of change of reactive energy in reactive time contains all the essential properties and features of the commonly accepted definition of reactive power under sinusoidal conditions. We believe that this provides an unambiguous and physically motivated resolution to the longstanding debate on how to generalize reactive power to non-sinusoidal waveforms.

Original language | English |
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Title of host publication | Proceedings of the 2016 10th International Conference on Compatibility, Power Electronics and Power Engineering, CPE-POWERENG 2016 |

Place of Publication | Piscataway |

Publisher | IEEE |

Pages | 21-26 |

Number of pages | 6 |

ISBN (Electronic) | 978-1-4673-7293-0 |

ISBN (Print) | 978-1-4673-7294-7 |

DOIs | |

Publication status | Published - 2016 |

Event | 2016 10th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG) - Bydgoszcz, Poland Duration: 29 Jun 2016 → 1 Jul 2016 |

### Conference

Conference | 2016 10th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG) |
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Country | Poland |

City | Bydgoszcz |

Period | 29/06/16 → 1/07/16 |

### Keywords

- Mathematical model
- Reactive power
- Load modeling
- Transforms
- Ports (Computers)
- Frequency-domain analysis
- Power measurement

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## Cite this

*Proceedings of the 2016 10th International Conference on Compatibility, Power Electronics and Power Engineering, CPE-POWERENG 2016*(pp. 21-26). [7544032] IEEE. https://doi.org/10.1109/CPE.2016.7544032