# Software Program for the Evaluation of Human Exposure to Electric and Magnetic Fields

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Calculation Module of the Electric and Magnetic Field Generated by a Transmission and Distribution Electric Line

^{−6}%), in comparison to the real situation, if this theory is applied to determine the fields at distances up to 100 m from an OHTL [27,28,29].

#### 2.1.1. Calculation Module of the Electric Field Generated by OHTL

_{0}[29]:

- r
_{1}is the distance from the real conductor to the calculation point; - r
_{2}is the distance from the image conductor to the calculation point; - h is the distance from the ground to the real conductor;
- r
_{0}is the conductor radius.

- r
_{1k}is the distance from each real conductor to the calculation point; - r
_{2k}is the distance from each image conductor to the calculation point; - h
_{k}is the distance from the ground to each real conductor; - r
_{0k}is the radius of each conductor.

#### 2.1.2. Calculation Module of the Magnetic Field Generated by OHTL

- r is the distance from the conductor to the calculation point;
- ${\overline{\mathrm{r}}}_{1}$ is a vector of the module equal to r, but rotated from the position vector $\overline{\mathrm{r}}$ with π/2 in a trigonometric reverse direction.

#### 2.2. The EMF Software Program

- Distance between the OHTL conductors;
- The height of the conductors from the ground;
- The height at which the calculations are made;
- The conductor’s radius;
- The distance from the outside of the conductors up to that at which the analyses are made;
- The supply voltage of the conductors;
- The intensity of the electric current passing through the three conductors.

#### 2.2.1. The Calculation Algorithm for the Electric Field Generated by the OHTL

- The height of the conductors from the ground (to the lines’ sag), h = 11.2 m;
- The distance between conductors, d_cond = 10.2 m;
- The height of the calculation point P, y = 1.8 m;
- The nominal voltage on the phase V
_{0}= 419 kV; - The nominal current on the phase is I
_{n}= 151 A.

#### 2.2.2. The Calculation Algorithm of the Magnetic Field Generated by the OHTL

## 3. Results

#### 3.1. Case Study—400 kV OHTL, Cluj-Napoca, Romania

#### 3.2. Determination of the Electric Field and the Magnetic Field Using the EMF Program

^{5}calculation points, for the determination of both the electric and magnetic field distributions.

#### 3.3. Determination of the Electric and Magnetic Fields Using ANSYS Maxwell 3D Software Program

## 4. Discussion

_{r}is chosen as the assessment metric, being computed between the (i) measurement and EMF program, and the (ii) Ansys results and EMF program, respectively, for all three paths.

_{r}decreases with the OHTL height; thus, on the 3rd path, minimum ε

_{r}values are obtained. The maximum ε

_{r}is around 0.2 for both the measured and Ansys results. On the one hand, for the case of the measurements ε

_{r}, important deviations can emerge due to physical influences (e.g., vegetation, terrain, OHTL steel structure). On the other hand, for the case of the Ansys ε

_{r}, important deviations can emerge due to meshing and a domain region around the studied model.

_{r}decreases with the OHTL height; thus, on the 3rd path, minimum ε

_{r}values are obtained. In this case, the maximum ε

_{r}is around 0.2 for both the measured and Ansys results, as in the previous case. The measurement ε

_{r}values are smaller compared to the E measurement ε

_{r}, with the maximum value being under 0.1 (10%).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Electric field distribution obtained for the project taken from [30], f = 50 Hz.

**Figure 4.**Comparison between the electric field distribution E on the width of the OHT corridor taken from [30] and the electric field distribution E calculated using the EMF program, f = 50 Hz.

**Figure 5.**Magnetic field distribution obtained for the project taken from [30], f = 50 Hz.

**Figure 6.**Comparison between the magnetic induction B on the width of the OHTL corridor taken from [30] and the magnetic induction calculated with the developed EMF program, f = 50 Hz.

**Figure 8.**(

**a**) Electric- and magnetic-field-measuring device, Maschek ESM—100; (

**b**) explanation of experimental measurements.

**Figure 9.**Experimental results: (

**a**) electric field distribution in the tested area; (

**b**) magnetic field distribution in the tested area, f = 50 Hz.

**Figure 10.**The electric field intensity distribution along the three paths experimentally determined: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 11.**The magnetic induction distribution along the three paths experimentally determined: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 12.**The electric potential distribution along the three paths, determined using the EMF program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 13.**The electric field intensity distribution along the three paths, determined using the EMF program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 14.**The magnetic induction distribution along the three paths, determined using the EMF program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 15.**The electric field values in the three points of interest found using the EMF software program.

**Figure 16.**The magnetic field values in the three points of interest found using the EMF software program.

**Figure 17.**The field distribution in the area between two pillars (poles) of the 400 kV OHTL in Cluj-Napoca using the EMF program: (

**a**) electric field; (

**b**) magnetic field, f = 50 Hz.

**Figure 19.**Electric field intensity distribution along the three paths found using the ANSYS Maxwell 3D software program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 20.**The magnetic induction distributions along the three paths found using the ANSYS Maxwell 3D software program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 21.**The electric field intensity distribution along the three paths was found experimentally, using the ANSYS Maxwell 3D program, and using the EMF program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

**Figure 22.**The magnetic field intensity distribution along the three paths found experimentally, using the ANSYS Maxwell 3D program, and using the EMF program: (

**a**) 1st path, h = 27 m; (

**b**) 2nd path, h = 14 m; (

**c**) 3rd path, h = 11 m, f = 50 Hz.

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**MDPI and ACS Style**

Giurgiuman, A.; Gliga, M.; Bojita, A.; Andreica, S.; Munteanu, C.; Topa, V.; Constantinescu, C.; Pacurar, C.
Software Program for the Evaluation of Human Exposure to Electric and Magnetic Fields. *Technologies* **2023**, *11*, 159.
https://doi.org/10.3390/technologies11060159

**AMA Style**

Giurgiuman A, Gliga M, Bojita A, Andreica S, Munteanu C, Topa V, Constantinescu C, Pacurar C.
Software Program for the Evaluation of Human Exposure to Electric and Magnetic Fields. *Technologies*. 2023; 11(6):159.
https://doi.org/10.3390/technologies11060159

**Chicago/Turabian Style**

Giurgiuman, Adina, Marian Gliga, Adrian Bojita, Sergiu Andreica, Calin Munteanu, Vasile Topa, Claudia Constantinescu, and Claudia Pacurar.
2023. "Software Program for the Evaluation of Human Exposure to Electric and Magnetic Fields" *Technologies* 11, no. 6: 159.
https://doi.org/10.3390/technologies11060159