### Abstract

This paper describes the waveform analysis of impulse voltage or impulse current. The analysis is accomplished by solving the biquadratic equation for the lightning impulse test circuit. Three discriminants classify the solutions into nine categories. Some calculations using the roots of biquadratic equation demonstrate the effectiveness of the analysis. For example, the overshoot or oscillating impulse superposed on standard lightning impulse voltage is calculated as the magnitude of relative overshoot. The polarity reversal waveform together with the double frequency oscillation or without oscillation is analyzed, which is not expressed by the third-order differential equation. The analyses also clarify the relationship between the waveform and the circuit parameters. This means that the definition of relative overshoot magnitude based on the base curve for oscillating impulse or overshoot is supported by the theory.

Original language | English |
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Pages (from-to) | 553-560 |

Number of pages | 8 |

Journal | IEEJ Transactions on Electrical and Electronic Engineering |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Jul |

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### Keywords

- Biquadratic equation
- High-voltage testing
- Lightning impulse test
- Oscillating impulse
- Overshoot
- Waveform parameter

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**Analysis of oscillating and non-oscillating impulse waveform for high-voltage impulse test using the roots of biquadratic equation.** / Matsumoto, Satoshi; Nishimura, Nobuaki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Analysis of oscillating and non-oscillating impulse waveform for high-voltage impulse test using the roots of biquadratic equation

AU - Matsumoto, Satoshi

AU - Nishimura, Nobuaki

PY - 2009/7

Y1 - 2009/7

N2 - This paper describes the waveform analysis of impulse voltage or impulse current. The analysis is accomplished by solving the biquadratic equation for the lightning impulse test circuit. Three discriminants classify the solutions into nine categories. Some calculations using the roots of biquadratic equation demonstrate the effectiveness of the analysis. For example, the overshoot or oscillating impulse superposed on standard lightning impulse voltage is calculated as the magnitude of relative overshoot. The polarity reversal waveform together with the double frequency oscillation or without oscillation is analyzed, which is not expressed by the third-order differential equation. The analyses also clarify the relationship between the waveform and the circuit parameters. This means that the definition of relative overshoot magnitude based on the base curve for oscillating impulse or overshoot is supported by the theory.

AB - This paper describes the waveform analysis of impulse voltage or impulse current. The analysis is accomplished by solving the biquadratic equation for the lightning impulse test circuit. Three discriminants classify the solutions into nine categories. Some calculations using the roots of biquadratic equation demonstrate the effectiveness of the analysis. For example, the overshoot or oscillating impulse superposed on standard lightning impulse voltage is calculated as the magnitude of relative overshoot. The polarity reversal waveform together with the double frequency oscillation or without oscillation is analyzed, which is not expressed by the third-order differential equation. The analyses also clarify the relationship between the waveform and the circuit parameters. This means that the definition of relative overshoot magnitude based on the base curve for oscillating impulse or overshoot is supported by the theory.

KW - Biquadratic equation

KW - High-voltage testing

KW - Lightning impulse test

KW - Oscillating impulse

KW - Overshoot

KW - Waveform parameter

UR - http://www.scopus.com/inward/record.url?scp=77749326698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77749326698&partnerID=8YFLogxK

U2 - 10.1002/tee.20443

DO - 10.1002/tee.20443

M3 - Article

AN - SCOPUS:77749326698

VL - 4

SP - 553

EP - 560

JO - IEEJ Transactions on Electrical and Electronic Engineering

JF - IEEJ Transactions on Electrical and Electronic Engineering

SN - 1931-4973

IS - 4

ER -