### Abstract

A general solution is presented for the probability density function of the amplitude of the sum of a number of harmonics from different sources. In the solution, the phase angles and amplitudes of component vectors may vary randomly in any given range. If these variation ranges are the same for all the component vectors, then ‐ in addition to them ‐ only arithmetic and geometric sums of the maximum amplitudes need to be known in order to calculate the parameters of the probability density function.

Original language | English |
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Pages (from-to) | 293 - 297 |

Number of pages | 5 |

Journal | European Transactions on Electrical Power |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1993 |

MoE publication type | A1 Journal article-refereed |

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### Cite this

*European Transactions on Electrical Power*,

*3*(4), 293 - 297. https://doi.org/10.1002/etep.4450030407

}

*European Transactions on Electrical Power*, vol. 3, no. 4, pp. 293 - 297. https://doi.org/10.1002/etep.4450030407

**A general solution to the harmonics summation problem.** / Lehtonen, Matti.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - A general solution to the harmonics summation problem

AU - Lehtonen, Matti

N1 - Project code: SÄH 1340

PY - 1993

Y1 - 1993

N2 - A general solution is presented for the probability density function of the amplitude of the sum of a number of harmonics from different sources. In the solution, the phase angles and amplitudes of component vectors may vary randomly in any given range. If these variation ranges are the same for all the component vectors, then ‐ in addition to them ‐ only arithmetic and geometric sums of the maximum amplitudes need to be known in order to calculate the parameters of the probability density function.

AB - A general solution is presented for the probability density function of the amplitude of the sum of a number of harmonics from different sources. In the solution, the phase angles and amplitudes of component vectors may vary randomly in any given range. If these variation ranges are the same for all the component vectors, then ‐ in addition to them ‐ only arithmetic and geometric sums of the maximum amplitudes need to be known in order to calculate the parameters of the probability density function.

U2 - 10.1002/etep.4450030407

DO - 10.1002/etep.4450030407

M3 - Article

VL - 3

SP - 293

EP - 297

JO - International Transactions on Electrical Energy Systems

JF - International Transactions on Electrical Energy Systems

SN - 2050-7038

IS - 4

ER -