## EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity

## Abstract

A simple model for coupling of an electromagnetic plane wave incident on a conductor above ground has been developed using reciprocity theory, providing some advantages as compared to the conventional transmission line approach. The model is developed using a semi-infinitely long single conductor above a lossy ground plane and connected by an arbitrary load impedance to a vertical grounding conductor. This configuration corresponds to the worst-case wave coupling, because it leads to a line induced current larger than in the cases of finite and multiconductor lines. A frequency-domain Thévenin equivalent model is developed to relate the incident wave amplitude to the voltage across a generic load, connected at any point on the vertical conductor. The application to the threat analysis of a high-altitude electromagnetic pulse impact on a power transmission line is discussed by considering the time-domain solution (via inverse Fourier transform) for an incident EMP fast-rise transient (E1) waveshape, following the standard IEC specifications. For typical high-voltage power line load impedances, it is shown that voltage magnitudes in the MV range can be induced across the line termination, in the case of a wave with a near-grazing incidence angle and with wave vector aligned along the horizontal conductor.

- Authors:

- Washington State Univ., Pullman, WA (United States). School of Electrical Engineering and Computer Science
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Electricity Delivery and Energy Reliability (OE)

- OSTI Identifier:
- 1462874

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Electromagnetic Compatibility

- Additional Journal Information:
- Journal Name: IEEE Transactions on Electromagnetic Compatibility; Journal ID: ISSN 0018-9375

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Electromagnetic pulse (EMP); high-voltage transmission lines; transmission line analysis

### Citation Formats

```
Olsen, Robert G., and Tarditi, Alfonso G. EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity. United States: N. p., 2018.
Web. doi:10.1109/TEMC.2018.2838080.
```

```
Olsen, Robert G., & Tarditi, Alfonso G. EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity. United States. doi:10.1109/TEMC.2018.2838080.
```

```
Olsen, Robert G., and Tarditi, Alfonso G. Thu .
"EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity". United States. doi:10.1109/TEMC.2018.2838080. https://www.osti.gov/servlets/purl/1462874.
```

```
@article{osti_1462874,
```

title = {EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity},

author = {Olsen, Robert G. and Tarditi, Alfonso G.},

abstractNote = {A simple model for coupling of an electromagnetic plane wave incident on a conductor above ground has been developed using reciprocity theory, providing some advantages as compared to the conventional transmission line approach. The model is developed using a semi-infinitely long single conductor above a lossy ground plane and connected by an arbitrary load impedance to a vertical grounding conductor. This configuration corresponds to the worst-case wave coupling, because it leads to a line induced current larger than in the cases of finite and multiconductor lines. A frequency-domain Thévenin equivalent model is developed to relate the incident wave amplitude to the voltage across a generic load, connected at any point on the vertical conductor. The application to the threat analysis of a high-altitude electromagnetic pulse impact on a power transmission line is discussed by considering the time-domain solution (via inverse Fourier transform) for an incident EMP fast-rise transient (E1) waveshape, following the standard IEC specifications. For typical high-voltage power line load impedances, it is shown that voltage magnitudes in the MV range can be induced across the line termination, in the case of a wave with a near-grazing incidence angle and with wave vector aligned along the horizontal conductor.},

doi = {10.1109/TEMC.2018.2838080},

journal = {IEEE Transactions on Electromagnetic Compatibility},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {6}

}