The Effect of Conductor Sag on EMF Exposure Assessment for 400 kV Double-Bundle

Abstract

This study investigates the effect of seasonal conductor sag on electromagnetic field (EMF) exposure to near 400 kV double-bundle overhead transmission lines. The conductor sag study resulted in clearance values of 28.0 m for winter (−10 °C, sag ≈ 7.0 m) and 23.4 m for summer (+35 °C, sag ≈ 11.65 m). For both seasonal examples, the electric field strength and magnetic flux density were calculated at a pedestrian height of 1.5 m, and the image approach to account for ground effects. The winter setup resulted in maximum values of 1.35 kV/m (E) and 27.2 µT (B), while the summer configuration produced higher values of 1.96 kV/m and 38.5 µT, respectively. Autumn field measurements, representing intermediate seasonal circumstances, produced average values of 1.294 kV/m and 1.399 µT, with peaks of 8.39 kV/m and 6.85 µT for electric field and magnetic flux density, respectively. The electric field projections were nearly identical to measurements; however, the magnetic field predictions were significantly higher, most likely due to the model’s assumptions of balanced currents and ideal geometry. These findings suggest that seasonal conductor sag variation is a real and substantial factor in assessing EMF exposure, with the electric field being particularly sensitive to clearance changes. The findings emphasize the need to incorporate a large analysis into EMF compliance assessments, especially in cases where terrain relief between towers may further diminish clearance in mid-span regions.

1. Introduction

From a theoretical standpoint, the presence of electromagnetic fields (EMF) near overhead high-voltage transmission lines originates from the fundamental principles of classical electrodynamics, as expressed by Maxwell’s equations. Alternating current (AC) flowing between phase conductors produces time-varying magnetic fields that ring the conductors, according to Ampère’s Law and Maxwell’s Correction. At the same time, the conductors’ high electric potential relative to the ground causes electric fields to radiate out into the surrounding space. These fields’ magnitude and spatial distribution are determined by important parameters such as voltage amplitude, current magnitude, conductor construction, and height above ground [1]. Although power line EMF operates at extremely low frequencies (ELF) (50 Hz), the resulting field arrangement is far from basic. The interactions of the three-phase conductors result in non-uniform spatial distributions, with areas of constructive and destructive interference determined by phase alignment, current load, and spatial layout. In this context, the height of conductors above ground is essential since it directly affects field intensity at human exposure points, such as pedestrian level.

This conductor’s height, however, does not remain constant. It is impacted by a variety of environmental factors, the most notable of which is ambient temperature. During the summer, higher temperatures and increasing electrical load cause the conductors to thermally expand, resulting in more sagging and a drop in average clearance from the ground [2,3]. Winter circumstances, on the other hand, result in more clearance due to less conductor expansion and loading. As a result, the strength of electric and magnetic fields near ground level varies annually, making temperature an important environmental variable in EMF exposure research.

Understanding seasonal behavior is critical for accurate field predictions, exposure mapping, and safety assessments. While several studies have explored EMF distribution around high-voltage transmission lines, the majority assume a stable conductor shape, typically overlooking temperature-induced height fluctuations and their repercussions on EMF levels [4,5,6,7]. This absence can result in an underestimation of peak field values, especially during the summer when clearances are low and public exposure is more likely to exceed upper standards. Exposure to electromagnetic fields should be addressed, particularly in environments where exposure to these fields is most sensitive, such as near daycare facilities, hospitals, and schools [8,9].

In response to this gap, the current study provides a quantitative assessment of electric and magnetic fields in the vicinity of 400 kV overhead transmission lines, with a focus on the impact of temperature-induced variations in conductor height. Using specialist simulation tools, the study creates realistic models based on genuine transmission setups. Simulations are conducted for both summer and winter circumstances, capturing the complete range of climatic influences on conductor elevation and, as a result, EMF exposure.

To guarantee the results’ validity, field measurements were taken at selected sites near 400 kV lines with calibrated EMF monitoring equipment. Electric and magnetic field strengths were measured at different heights and distances from the conductor’s axis. The comparison of simulated and measured data demonstrated a high level of agreement, validating the modeling methodology’s legitimacy.

The purpose of this study is to look at how seasonal variations in conductor elevation, mostly caused by ambient temperature, affect the spatial distribution of electric and magnetic fields near high-voltage transmission lines. The findings provide practical insight into exposure variability under real-world settings, enhance risk assessment frameworks, and aid in the optimization of corridor design and safety requirements for transmission infrastructure.

2. Materials and Methods

2.1. Theoretical Basis of Electromagnetic Fields

The simulation of electromagnetic fields (EMF) near high-voltage power lines is based on classical electrodynamics and controlled by Maxwell’s equations. In the quasi-static approximation at ELF (50 Hz), the electric and magnetic fields can be decoupled and examined individually using electrostatic and magnetoquasistatic formulations. The electric field $\overrightarrow{E}$ is obtained as the negative gradient of the electric potential Φ, according to the relation:

$$\overrightarrow{E}=-\nabla \mathsf{\Phi }$$

(1)

This formula implies that the electric field points in the direction of the largest decrease in the electric potential, with the magnitude corresponding to the rate of change.

On the other hand, the electromagnetic field $\overrightarrow{\mathrm{B}}$ is generated by time-varying or steady-state current density $\overrightarrow{J}$, and is governed by Ampère’s Law as:

$$\nabla \times \overrightarrow{\mathrm{B}}={\mu }_0\overrightarrow{J}$$

(2)

The curl operator ∇× depicts the rotation of magnetic fields around current-carrying conductors, while μ₀ represents the permeability of free space.

Numerical solutions were achieved using COMSOL Multiphysics, version 6.2, simulation software, which allowed for combined frequency-domain evaluations of both the electric and magnetic field components. Two separate physical interfaces were used: one for electrostatics (to solve for potential distribution owing to high voltage) and one for magnetic and electric fields (to assess flux density due to AC).

2.2. Geometrical Configuration and Material Properties

In this study, a two-dimensional cross-sectional model of a 400 kV three-phase overhead transmission line is created using COMSOL (version 6.2) Multiphysics. The electric and magnetic field distributions are evaluated under actual operating conditions [10]. The transmission system consists of three symmetrically ordered phases (A, B, and C), each implemented with a double-conductor bundle, reflecting the usual engineering practice of using Aluminum Conductor Steel Reinforced (ACSR) lines in high-voltage power transmission [11].

The conductors are horizontally positioned across the X-axis, with phase centers at −9 m (Phase A), 0 m (Phase B), and +9 m (Phase C) from the system’s central axis. Within each phase, two conductors are aligned parallel to each other with a horizo8ntal separation of 0.45 m, resulting in a compact bundled structure. All conductors are mounted at a vertical height of 35 m above the ground, which corresponds to a typical clearance height under normal mechanical and electrical loading circumstances [12].

Each conductor is represented as a solid circle with a radius of 1.5 cm, based on the physical specifications of common ACSR cables. All geometrical configurations are set up in software as presented in Figure 1. The ACSR material is a composite construction made of high-conductivity aluminum strands wrapped around a steel-reinforced core. This combination gives both outstanding electrical performance and mechanical durability, with significant attributes including high electrical conductivity, heightened thermal conductivity, moderate density, and increased magnetic permeability due to the steel core.

To account for the influence of the Earth’s surface on the simulation without explicitly simulating the soil, the image approach is used. This technique uses a mirrored counterpart of each overhead conductor, reflected at an equivalent distance below ground level. The presence of these virtual conductors enables precise depiction of the electromagnetic boundary conditions imposed by a perfectly conducting ground plane. As a result, the system consists of six actual conductors and six mirrored duplicates, totaling twelve current-carrying elements.

The surrounding environment is modeled as air, which is viewed as a uniform and lossless dielectric medium. The air domain is the propagation medium for both electric and magnetic fields, and it has normal ambient qualities such as one-to-one relative permittivity and permeability, as well as near-zero electrical conductivity, which is consistent with its behavior as an insulator.

This geometric and material design provides a realistic and consistent foundation for numerically simulating electromagnetic field interactions near high-voltage transmission lines. It guarantees that the evaluated field results are consistent with usual installation characteristics and environmental conditions, allowing for valid comparisons to regulatory exposure limits and field measurements.

2.3. Modeling Conditions and Boundary Treatments

This study uses external current density assignments, frequency-domain simulation, and mirror-image modeling techniques to accurately depict the electromagnetic field behavior near high-voltage overhead power lines. Each of these components is crucial in ensuring that the simulation’s physical and mathematical realism coincides with real-world transmission systems.

COMSOL’s Magnetic and Electric Fields (mef) interface uses the External Current Density function to define the current flowing through the conductors. Each physical conductor is assigned a uniform current density along the z-axis, which corresponds to the typical direction of current propagation in overhead lines. The current density vector is given in complex exponential form to indicate the sinusoidal nature of AC. The three-phase system is specifically represented, with each phase having identical magnitude but being phase-shifted by 120 degrees relative to the others. This is a common depiction of an ideal three-phase system, which is used in power transmission and electromagnetic field modeling due to its inherent symmetry and efficiency.

The current density for each phase is specified in complex exponential form, allowing both magnitude and phase information to be conveyed concisely. Each phase has the magnitude of $2.689\times {10}^6{\displaystyle \frac{\mathrm{A}}{{\mathrm{m}}^2}}$, correlates to the peak or effective current density commonly found in high-voltage power lines, such as those operating at 400 kV. The respected values are used for modeling as they are presented in

Table 1. The current density specification for each phase in exponential complex form.

Phase	Current Density Expression [A/m2]	Phase Angle
		Radians	Degrees
A	${\overrightarrow{J}}_A=2.689\times {10}^6$	0	0°
B	${\overrightarrow{J}}_B=2.689\times {10}^6{e}^{{\displaystyle \frac{-2\pi i}{3}}}$	$-{\displaystyle \frac{2\pi }{3}}$	−120°
C	${\overrightarrow{J}}_C=2.689\times {10}^6{e}^{{\displaystyle \frac{2\pi i}{3}}}$	${\displaystyle \frac{2\pi }{3}}$	+120°

.

In the equations of Table 1, the i is the imaginary unit ($i=\sqrt{-1}$), used to express phase shifts in exponential form through Euler’s identity. This approach is especially useful in time-harmonic simulations and frequency-domain analysis of electromagnetic fields because it simplifies the handling of sinusoidal quantities. Using this symmetrical, balanced arrangement produces predictable electromagnetic fields with reduced harmonic content and diminished neutral current benefits, which are critical for both efficient power transmission and accurate computational modeling.

To approximate the effect of a ground plane conducting without explicitly modeling soil conductivity, the image approach is used. In this technology, virtual mirror conductors are implanted at the same depth below ground level as actual conductors above it. These mirrored conductors carry current densities of similar magnitude but opposite direction (negative sign in the z-component), resulting in a Dirichlet-like boundary condition for the magnetic vector potential near the ground. The P point in Figure 2 represents the point of interest when the calculation and measurements of EMF were performed. This approach provides for an accurate estimate of field distortion and attenuation due to ground reflection, which is especially important for analyzing public and occupational exposure levels [13]. In this technology, each conductor is mirrored beneath the ground surface, with the matching current density reversed in sign. These virtual (picture) conductors are arranged at the same vertical distance below the ground plane, replicating the electromagnetic boundary condition that cancels the tangential electric field at the ground surface.

2.4. Frequency-Domain Simulation Configuration

In Study Step 2, the simulation is carried out in the frequency domain utilizing a harmonic steady-state analysis. This approach presupposes a sinusoidal temporal dependency of the type. e^jωt, where ω = 2fπ represents the angular frequency, and f is the grid frequency, typically 50 Hz in European transmission systems. Frequency-domain analysis allows for the direct computation of phasor quantities such as electric and magnetic fields under steady-state AC circumstances, removing the requirement for time-stepping and considerably increasing computing efficiency.

2.5. Mesh Grid Resolution Strategy

To balance computational expense and solution accuracy, a non-uniform mesh is used. The meshing approach assures higher resolution near crucial locations, such as conductor surfaces with the largest field gradients, and coarser resolution in the simulation domains outside regions, where field changes are smoother. This adaptive technique promotes numerical stability while maintaining the fidelity of estimated parameters such as electric field strength at low altitudes (e.g., 1.5 m above ground) and magnetic flux density near current-carrying items [14].

2.6. Impact of Ambient Temperature on Electrical Conductor Sag Behavior

The conductor sag of a high-voltage overhead conductor was evaluated for an ACSR Drake arrangement put between two support towers 350 m apart, each with a 35-m attachment height. The calculations were performed for two extreme environmental temperatures: −10 °C was chosen as the average minimal temperature during the winter, and +35 °C was chosen as the average maximum temperature during the summer. These reflect the average winter and summer temperatures. These temperatures were selected as representative extremes in order to highlight the variations that may occur in the intensity of electromagnetic fields across different seasonal conditions. Other conductor sag-influencing elements such as wind and ice were not taken into consideration by this model.

From Figure 3, the letter “s” represents the conductor sag length. The physical properties of ACSR Drake were approximately 15.97 N/m (1.63 kg/m) with a rated tensile strength (RTS) of around 140 kN.

The horizontal tension H in the conductor was calculated as a percentage of the RTS, a standard measure for defining the mechanical capability of overhead power line conductors. Because temperature changes have a considerable influence on conductor tension, the percentage of RTS used varies with environmental circumstances to provide both mechanical safety and proper ground clearance. Lower ambient temperatures, such as −10 °C, cause the conductor to contract, leading to higher tension values. In this situation, the horizontal tension was calculated as 25% of RTS. At higher ambient temperatures (+35 °C), the conductor swells, and the strain is lowered by 15% of RTS. This variation guarantees that in cold conditions, the conductor remains within safe mechanical limits without exceeding stress thresholds, but under hot conditions, conductor sag develops, but the reduced tension prevents excessive mechanical load on towers and insulators.

More detailed information on conductor sag can be found elsewhere [16,17]. Here is used the simplified equation to find the conductor sag, approximated using the parabolic formula:

$$S\approx {\displaystyle \frac{\omega L^2}{8H}}$$

(3)

S represents conductor sag (m), ω is weight per unit length (N/m), L is span length (m), and H is horizontal tension (N). The mid-span clearance was then established by the difference between the attachment height and the predicted conductor sag.

2.7. On-Site EMF Measurements

Throughout the autumn season, 87 electric and magnetic field measurements were taken. The measurements were collected with an NFA1000 (Gigahertz Solutions, Im Kessel 2, 90579 Langenzenn, Germany) instrument, which was positioned in the middle of two transmission towers (x = 0 m) directly beneath 400 kV overhead wires. This position is presented in Figure 3, identified as the Hc point. To minimize any impact from neighboring items in the measuring space, the device was set on a tripod 1.5 m above ground level. Each measurement was recorded for a minimum of five minutes to guarantee consistent and representative results.

The NFA1000 equipment operates in the frequency range of 5 Hz to 1 MHz for both electric and magnetic fields, covering the exposure from a power frequency of 50 Hz. The NFA1000 is equipped with a 3D isotropic probe that can detect electric and magnetic field components along all three spatial axes. This allows for precise vector summing of field strengths without requiring the sensor to be manually oriented. The integrated probe enables frequency-selective analysis, with measurement data filtered into distinct channels.

The built-in multi-channel data logger records all signals, allowing for long-term monitoring and analysis using the NFAsoft program, version 176. Users can use the software to apply frequency filters, visualize time-domain fluctuations, and assess exposure in accordance with international criteria. The instrument provides both RMS (True Root Mean Square) and Peak/Peak-Hold modes, allowing you to describe both continuous background fields and transient or pulsed phenomena.

3. Results and Discussion

The conductor sag analysis for the ACSR Drake double-bundle 400 kV line revealed a seasonal clearance difference of around 4.6 m between winter and summer operating circumstances. At −10 °C, a horizontal tension of 35 kN (25% RTS) produced a conductor sag of approximately 7.0 m and a mid-span clearance of 28.0 m. At +35 °C, when the horizontal tension was dropped to 21 kN (15% RTS), the conductor sag increased to 11.65 m, reducing the clearance to 23.4 m. This seasonal variation has a direct impact on electromagnetic field (EMF) levels at ground level, particularly at pedestrian height, due to changes in conductor shape.

Electromagnetic field calculations were carried out in COMSOL Multiphysics utilizing the image approach to describe the conductive ground plane, a three-phase balanced setup, and double-bundle ACSR Drake conductors conveying 50 Hz currents. Two reference locations were chosen at a height of 1.5 m above ground. However, the mid-span projections were employed at y = 26.5 m for winter and y = 21.85 m for summer, which corresponded to the clearances obtained via conductor sag analysis.

The winter configuration resulted in a maximum electric field intensity of 1.35 kV/m and magnetic flux density of 27.2 µT. The summer setup resulted in higher values of 1.96 kV/m and 38.5 µT. Both field components increased by around 43%, which reflects the shorter distance to electrified conductors. The electric field was more proportionally sensitive to clearance change, consistent with its electrostatic dependency on vertical separation, but the magnetic field variation followed the quasi-static 1/r decay of current-carrying elements.

In Figure 4a, the profile has two peaks and a central minimum. The minimum at x = 0 m is due to symmetry: the horizontal components of E from the outer phases cancel, while the vertical components from all phases (including their image charges in the ground) combine to provide a lower resultant than at off-center locations. The peaks are not directly under the outer conductors (±9 m), as the electric field at ground is a vector superposition of contributions from all six sub-conductors and their images. Near the projection of an outer phase, the field from that phase is partially offset by the central and opposite outer phases (and their images), causing the local maximum to be displaced outward to the point where the constructive vertical contribution from the nearest phase dominates and cancellation from the others is reduced.

When image charges are present, a horizontal three-phase line at low height exhibits a two-lobe pattern with off-center maxima. This pattern is compatible with the electrostatic solution’s balanced-phase superposition. Figure 4b depicts the horizontal profile of magnetic flux density at a height of 1.5 m above ground in both winter and summer conditions. Despite the presence of three phases, the profile shows a single prominent peak around the centerline beneath the middle phase.

At the central point (x = 0 m), the contributions of the outside phases (A and C) are symmetric; their horizontal field components cancel, while their vertical components contribute to the vertical component of the core phase (B). Because all three phases contain equal currents displaced by 120° in phase, the time-averaged RMS magnetic field is greatest at this central position.

Positions precisely beneath the outer phases, on the other hand, yield no independent peaks because the phasor combination of all three currents at such sites results in partial cancellation. When observed from pedestrian height, the geometric symmetry, current balance, and 1/r decay of the magnetic field with distance from each conductor all point to a single-peak pattern centered beneath the middle phase. This is not a numerical artifact but rather a physical consequence of the electromagnetic field structure in balanced three-phase systems, which is enhanced by the inclusion of the earth’s image currents.

In all simulated scenarios, exposure levels at 1.5 m above ground remained considerably below International Commission on Non-Ionizing Radiation Protection (ICNIRP) public reference limits for 50 Hz fields (5 kV/m for electric field and 200 µT for magnetic flux density) [18] and Institute of Electrical and Electronics Engineers (IEEE) guidelines [19].

Nonetheless, the summer instance neared the upper limit of usual environmental measurements for high-voltage corridors, emphasizing the need to factor in conductor sag-induced clearance changes in EMF compliance assessments.

Overall, the findings show that seasonal conductor sag fluctuation is both a mechanical reliability element and a predictor of EMF exposure levels. For correct evaluation and regulatory compliance in 400 kV transmission lines, both mechanical and electromagnetic assessments should be integrated, with seasonal effects clearly recognized in route planning, public access control, and maintenance scheduling.

A comparison was made between the experimentally measured EMF values in autumn and the theoretically calculated values for summer and winter settings. Autumn’s environmental temperatures are typically between those of spring and winter. At the time of measurement, the ambient temperature was around 12 °C. Therefore, the conductor sag was calculated to be 9.8 m, resulting in a clearance of 25.2 m. The measurements showed an average electric field intensity of 1.294 kV/m and magnetic flux density of 1.399 µT. Measurements were taken at several positions between transmission towers, resulting in maximum values of 8.39 kV/m for the electric field and 6.85 µT for the magnetic flux density. The maxima differed significantly from the mean, with standard deviations of 1.34 kV/m and 1.21 µT. The elevated readings were observed at locations where the ground surface was locally higher, lowering the clearance between the detector and the overhead conductors. Although the conductor sag and detector height above ground remained constant throughout the trials, the higher topography resulted in a much shorter detector-to-conductor distance. As a result, the given data show the average exposure values and associated standard deviations, as well as localized differences caused by topographic factors.

In contrast, the theoretical modeling, which was done independently for the winter and summer conductor sag configurations, anticipated slightly greater magnetic field peaks and moderately higher electric field values. The winter scenario resulted in maximum intensities of 1.35 kV/m (E) and 27.2 µT (B), while the summer scenario yielded 1.96 kV/m and 38.5 µT. The tight match between measured and simulated electric field maxima for winter suggests that the autumn data show a clearance like the winter situation. However, the large difference in magnetic field magnitudes (measured values are an order of magnitude lower) suggests that the model’s assumptions—such as balanced phase currents, ideal conductor geometry, and the absence of load variations—may overestimate B-field levels under real-world operating conditions.

Overall, the agreement in electric field results supports the validity of the clearance-based modeling approach, whereas magnetic field differences highlight the importance of incorporating real-time load data and potential current imbalances into future simulations to better align theoretical predictions with measured conditions.

4. Conclusions

This study shows that seasonal temperature changes, via their effect on conductor sag, have a noticeable and significant impact on electric and magnetic field intensities at pedestrian height along 400 kV double-bundle transmission lines. The 4.6 m conductor sag difference between winter and summer configurations resulted in clearance reductions that increased both electric and magnetic field strengths, with the electric field being the most proportionally sensitive to clearance changes.

The modeling framework, which included precise geometric representation, balanced-phase current assumptions, and the image method to simulate ground effects, yielded electric field findings that were nearly identical to actual field measurements, indicating that it is valid for clearance-based EMF assessments. However, the model’s anticipated magnetic field magnitudes were significantly higher than actual values, implying that real-world issues such as unbalanced currents, load variability, and non-ideal conductor shape must be included to enhance forecast accuracy.