# Attenuation of Lightning-Induced Effects on Overhead Distribution Systems in Urban Areas

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## Abstract

**:**

## 1. Introduction

## 2. Lightning Details, FEM Model, and LIGHT-PESTO Code

- Lightning current evaluation
- EM fields’ computation
- Induced voltages’ computation.

#### 2.1. Lightning Details

- v is the return stroke speed (assumed to be the half of the light speed)
- $P\left({z}^{\prime}\right)$ is the attenuation function (assumed to be exponential, as dictated by the Modified Transmission Line Exponential (MTLE) model [17],
- u is the Heaviside function.

#### 2.2. EM Fields’ Computation

#### 2.3. Induced Voltage Computation

## 3. Results

- Set $D=200$ m
- Set $h=10$ m
- Set $w=10$ m
- Consider a single-conductor line
- Terminate the conductor with its matching impedances.
- Set the line length = 2000 m
- Vary H from 5 m to 50 m
- Vary d from 5 to 200 m.

#### 3.1. EM Fields

- Calculation of the ratio (${k}_{E}$) between the maximum value of the electric field amplitude in the presence of buildings (${E}_{max,Building}$) with respect to the case without (${E}_{max,noBuilding}$), shown in Figure 3, Figure 4 and Figure 5. The electric field was measured at the point corresponding to the middle of the line.$${k}_{E}=\frac{|{E}_{max,Building}|}{|{E}_{max,noBuilding}|}$$

#### 3.2. Induced Voltages

- An overhead line characterized by three conductors placed at 10 m, 1 m from each other
- A finite ground conductivity of 1 mS/m instead of a PEC ground.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Ratio between the maximum value of the electric field with and without the building. (A) H = 20 m, and d varies from 5 to 200 m.

**Figure 4.**Ratio between the maximum value of the electric field with and without the building. (B) H = 5 m, and d varies from 5 to 200 m.

**Figure 5.**Ratio between the maximum value of the electric field with and without the building. (C) d = 10 m, and H varies from 5 to 50 m.

**Figure 6.**Comparison between the electric field measured along the whole line. (A) H = 20 m, and d varies from 5 to 200 m.

**Figure 7.**Comparison between the electric field measured along the whole line. (B) H = 5 m, and d varies from 5 to 200 m.

**Figure 8.**Comparison between the electric field measured along the whole line. (C) d = 10 m, and H varies from 5 to 50 m.

**Figure 9.**Ratio between the maximum voltage induced on the line considering or not considering the presence of a building. (A) H = 20 m, and d varies from 5 to 200 m.

**Figure 10.**Ratio between the maximum voltage induced on the line considering or not considering the presence of a building. (B) H = 5 m, and d varies from 5 to 200 m.

**Figure 11.**Ratio between the maximum voltage induced on the line considering or not considering the presence of a building. (C) d = 10 m, and H varies from 5 to 50 m.

**Figure 15.**Ratio between the maximum voltage induced on the line considering or not considering the presence of a building. (A) H = 20 m, and d varies from 5 to 200 m. A multiconductor line is considered.

**Figure 16.**Ratio between the maximum voltage induced on the line considering or not considering the presence of a building. (A) H = 20 m, and d varies from 5 to 200 m. A finite ground conductivity of 1 mS/m is considered.

Case | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\gamma}$ | $\mathit{\delta}$ |
---|---|---|---|---|

A | 0.88 | 0.0006 | −0.86 | −0.085 |

B | 1.45 | −0.39 | 0.97 | 0.0001 |

C | 1.71 | −0.05 | −0.75 | −0.17 |

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**MDPI and ACS Style**

Mestriner, D.; Marchesoni, F.; Procopio, R.; Brignone, M.
Attenuation of Lightning-Induced Effects on Overhead Distribution Systems in Urban Areas. *Appl. Sci.* **2022**, *12*, 7632.
https://doi.org/10.3390/app12157632

**AMA Style**

Mestriner D, Marchesoni F, Procopio R, Brignone M.
Attenuation of Lightning-Induced Effects on Overhead Distribution Systems in Urban Areas. *Applied Sciences*. 2022; 12(15):7632.
https://doi.org/10.3390/app12157632

**Chicago/Turabian Style**

Mestriner, Daniele, Flavia Marchesoni, Renato Procopio, and Massimo Brignone.
2022. "Attenuation of Lightning-Induced Effects on Overhead Distribution Systems in Urban Areas" *Applied Sciences* 12, no. 15: 7632.
https://doi.org/10.3390/app12157632