High Gradient Magnetic Fields Generated in Events on the 230 kV

Electric Power Transmission Infrastructure:

Human Exposure Analysis and Risk

FABIAN RICARDO ROJAS1, GERARDO GUERRA1, SERGIO RIVERA2

1Enlaza-GEB,

COLOMBIA

2Departamento de Ingeniería Eléctrica,

Universidad Nacional de Colombia SEDE Bogotá,

COLOMBIA

Abstract: - This work presents a process for analyzing human exposure to high-gradient magnetic fields based

on protection models for patients undergoing magnetic resonance examinations developed by the International

Commission on Non-Ionizing Radiation Protection (ICNIRP). A series of events presented in the electrical

energy transmission infrastructure is taken, with typical currents and front times, a case of extreme failure is

added, and results are presented. Subsequently, with a classic lightning signal, compliance with the exposure to

this type of field in the right-of-way strip of a transmission line is verified and validated in the event of a

hypothetical atmospheric discharge impact event. Finally, a simulation is implemented with space discretization

techniques, establishing the signal resulting from the magnetic field generated as a function of time. The

exposure is evaluated using the presented model. Only in one of the analysis cases was it found that the

perception threshold is exceeded at distances less than 0.6 cm, virtually a situation in which the worker has

contact with the down conductor. With the results obtained and the cases analyzed, it is concluded that failures

of this type do not generate significant exposure to high-gradient magnetic fields and do not exceed the

determined perception thresholds.

Key-Words: - Magnetic Field, Transmission Line, Fault Current, Lightning, High Voltage, Substation.

Received: April 28, 2024. Revised: September 9, 2024. Accepted: October 8, 2024. Published: November 13, 2024.

1 Introduction

The electric power transmission infrastructure

fulfills a strategic function for our society, carrying

electric power from generation centers to

consumption centers. This network is frequently

exposed to incidents in the operation of Substations

(SE) and Transmission Lines (LT) caused by

atmospheric discharges or transient voltage and/or

current events, which originate the emission of

electromagnetic fields of high amplitude and high

gradient. These phenomena have been the subject of

analysis and research that have allowed

theestablishment of strategies to characterize risk

exposure, generating a knowledge base on the

possible effects.

The exposure estimation methodologies that

have provided the best results are those established

within the recommendations and safety guidelines

for magnetic resonance examinations. The

characterization of the risk of being affected by this

type of field is an essential element for the safe

operation and maintenance of the transmission

infrastructure, but also for the general population in

their areas of influence. With the growing concern

and the evolution in the knowledge of the

communities concerning the typical interactions of

electromagnetic fields emitted by LT and SE with

human health, concern has been generated regarding

the exposure to high gradient fields in the vicinity of

the easement strips, especially due to observations

of atmospheric discharges that impact the

infrastructure and failure modes that generate

visually perceptible disruptions in isolation.

High gradient fields associated with industrial

frequency are generally very limited by the designs

and protection systems, so they do not present levels

that can be perceived as dangerous. On the other

hand, the fields that originated in atmospheric

discharges are the highest gradient fields and those

that have been the subject of the most in-depth

analysis. Some investigations have reported that

those phenomena that present characteristics of very

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short front and tail times apparently would not have

a harmful effect because they are much faster than

the Chronaxie of tissue excitation. However, some

research has also reported that slow atmospheric

discharges with longer times of up to 200 μs could

generate a nerve stimulation effect. In addition, the

electric and magnetic fields generated by

overvoltages/overcurrents caused by events have

front times that can be in the order of milliseconds,

so they could be in the spectrum of nerve

stimulation impulses and could have characteristics

comparable to the limit determined for muscle

stimulation. The possible effects associated with the

magnetic field are of particular interest, which

typically has no controls to mitigate the possible

risk; on the other hand, the electric field has a

specific control implemented through fixed or

temporary grounding.

2 General Aspects of Exposure to

Electric (CM) and Magnetic (CM)

Field

The World Health Organization (WHO), in its role

as the guiding and coordinating authority for health

action in the United Nations system, plays a leading

role in world health matters. With this focus, it

commissioned the ICNIRP to prepare a set of

recommendations and guidelines for the protection

of people from non-ionizing radiation. As a result of

this Commission’s work, the conclusions on the

scientific evidence related to the effects of NIR on

health were published in 1998, which became a

reference document for governmental, public, and

private institutions responsible for the population’s

health, as well as for researchers in the field and the

general public. These recommendations have been

periodically updated and validated in documents

published by ICNIRP from 1998 to the present, [1],

[2]. Due to the diverse characteristics of the

exposure, the impossibility of fully determining the

causal effect, and the complexity associated with

calculating the induced parameters, two types of

values are considered for limiting EMF exposure.

The exposure values associated with the basic

restrictions are based on health effects that have

been precisely established, and their values are

given in induced physical quantities, making them

difficult to measure in practice. To ensure protection

against such effects, the corresponding values

should never be exceeded, [3], [4], [5], [6].

The exposure values associated with the

reference levels are obtained from the basic

restrictions, using mathematical models that relate

the induced variables to more easily measurable

physical parameters. In addition, they take into

account the factors that can modify the exposure, in

order to provide a direct comparison parameter.

They are calculated for the condition of maximum

coupling of the field with the exposed individual,

frequency dependence, and dosimetric uncertainties,

thus providing maximum protection, [4], [6]. If the

measured values are higher than the reference

levels, it does not necessarily imply that the basic

constraints are being exceeded, but further analysis

is essential to assess compliance with the basic

constraints, [4], [5], [6].

ICNIRP recommendations are widely known for

exposures to constant frequency fields or those

whose spectral content can be decomposed into a

reasonable number of components and specific

constraints applied to each frequency, and then total

weighting applied. High gradient fields with shapes

far from sinusoidal and frequencies not

characterizable with classical transforms must have

different considerations for compliance verification

in the framework of their exposure safety. Some

models of lightning signals that can give rise to

these fields can be found in [7].

Specifically for high gradient fields, ICNIRP

has recommended three models for the evaluation of

exposure to pulsed or complex signals, which can be

consulted in detail in [2], [5], [6].

The first consists of converting the signal,

generally rectangular, to an equivalent sinusoidal

signal by adjusting the frequency of the resulting

wave with the width of the original pulse. This

method has weaknesses in complex waveforms

since it ignores the signals superimposed on the

equivalent main frequency, [5].

A second method consists of the spectral

decomposition in frequency of the original signal

and the unitary comparison of each of the

amplitudes of the frequencies of the resulting

spectrum, in relation to the limits determined for

each frequency, weighting an overall exposure that

adds one by one each exposure component. This

method yields good results in periodic signals with

several coherent cycles, however, it presents

important weaknesses in non-periodic signals due to

the convergence problem associated with the signal

sampling and the low-frequency components

resulting from using time-frequency transforms in

truncated signals, [2], [5]. Filtering solutions have

been proposed, however, for high gradient pulsed

signals or narrow band sinusoidal bursts, they can

artificially hide or reduce the exposure associated

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with peak values that exceed the RMS values

typically present in this type of signal, [2], [5].

A third approach is based on evaluating the

exposure using dB/dt peak weighting of the signal

and then calculating the induced current density

using a constant of proportionality of the electrical

conductivity of the tissue and the effective radius of

the current loop, [8], [9]. This approach seeks to

better approximate the characteristics of the

waveforms and the nature of the biological

interactions, [5], [6]. This approach presents

weaknesses in the evaluation of high gradient fields

because the proportionality constants for the

calculation of induced current are theoretically

derived from calculations for induced currents in the

head originating in sinusoidal signals, which makes

them overly conservative for high gradient fields,

[2], [8].

The exposure and compliance estimation

models used in the present work have been reviewed

and published previously and present a good result

for the characterization of the magnetic field with

this type of characteristics, [2], [10], [11]. This one

has remarkable advantages in its accuracy because

they are derived from exposure thresholds in

Magnetic Resonance Imaging (MRI) examinations

[9], therefore, the way of development is based

much more extensively on clinical trials and real

exposure, measuring physical variables on cohorts

of patients and volunteers, with this approach the

biological constants are more accurate and the

thresholds much more adjusted to the real measured

exposure, without neglecting the precautionary

principle, [10]. Moreover, because of the type of

signal used in this type of examination, broader

similarities with pulsed high-gradient signals are

observed, [11].

3 High Gradient Magnetic Field

Assessment Exposure Model

Initial evaluation models can be found in [2] and

[8], but in the search for a complementary

methodology, it is found that the lightning current

signal and its associated magnetic field gradient

have some similarities with the signals used

medically for MRI. Taking advantage of this

similarity, it is proposed to use the methodology to

assess the safety of patients against the magnetic

field emissions used in this type of examination and

associate it to the signal of interest. Accordingly, we

take as a reference what is proposed in [9], where an

evaluation of the average perception threshold is

proposed from the following expression:



 󰇡

󰇢󰇟󰇠 (1)

Where  is the effective stimulus duration in

[ms]. The effective stimulus duration is the duration

of the monotonically increasing or decreasing

gradient period [9].

It is been established in [9] that the cardiac

stimulation threshold is well above the intolerable

stimulation threshold for high gradient signals.

Furthermore, the lowest percentile for intolerable

stimulation is 20% above the average threshold for

peripheral nerve stimulation. In that sense, the

interest now is to establish whether the nervous

stimulation threshold and the intolerable stimulation

threshold are exceeded with an exposure such as the

one studied.

For this objective, we analyze the academic and

scientific references taken by ICNIRP [9] for the

issuance of its recommendations within the

framework of patient protection during MRI

examinations. The basic equation of magnetic field

gradient stimulation is presented in [10] and is

defined as: 

  󰇡  

󰇢󰇟󰇠 (2)

Where b is the Rheobase, the asymptotic dB/dt

for long-duration pulses, c is the Chronaxie, the

pulse duration at which the dB/dt is twice the

Rheobase and d is the pulse duration [10].

The population average has a perception

threshold with values of b=14.91 [T/s] and c=365

[µs] [10]. Significant contractions in the thoracic

skeletal muscles were observed for magnetic field

gradients approximately 50% higher than those

associated with the perception threshold [10]. A

dB/dt intensity of approximately twice the

perception threshold was found to be intolerable

[10]. Using these factors, the graphs of gradient

intensity and effective stimulus duration are

constructed, for the three thresholds of interest:

perception threshold, muscular stimulation

threshold, and intolerable stimulation threshold.

4 Failure and Exposure Analysis for

Substations

As stated in previous sections, this work is

motivated by analyzing two events that occurred in

the electrical power transmission infrastructure in

Colombia and Brazil, respectively. Both events

occurred during asset operation and maintenance

activities. In the first case, power equipment

maintenance activities were performed on a 230 kV

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line bay (BL). The associated transmission line (LT)

has a double circuit, so BL1 was being worked on

while BL2 remained in service. Physically, both line

bays are arranged next to each other within the

physical topology of a substation with a double

busbar configuration with an interconnector. The

conditions of the work to be performed required the

opening and grounding of the LT at both ends of the

line. During the execution of the activities, a ground

current discharge occurred through the temporary

grounding arrangements provided to protect the

work area of the intervened BL. This condition

forced the temporary suspension of the activity and

the taking of additional actions to preserve the

safety of the work teams participating in the

maintenance. Following the Root Cause Analysis

(RCA), it was established that a contact occurred

between one of the phases of the in-service circuit

and one of the phases of the maintenance circuit at a

specific point on the LT. This situation gave rise to

the incident and originated in atypical wind

conditions in a geographical area within the LT

corridor.

The second case also occurred during the

maintenance of electrical equipment for substations

on a 230 kV BL. The LT has a double circuit, so

BL1 was disconnected while BL2 remained in

service. Physically, both line bays are arranged side

by side within the physical topology of a substation

with a double bus configuration. The conditions of

the work to be carried out required the opening and

grounding of the LT at both ends of the line. During

the execution of the activities, tests had to be carried

out on the grounding switch. Due to loss of

situational awareness and deviations in the

execution of the maintenance procedure, the

grounding switch of the energized bay (BL2) was

closed, which generated a free ground fault that was

evacuated by the solid ground connection of the

disconnector. After the event, the activity was

temporarily suspended, and actions were taken

according to the security incident procedure,

evaluating the contingency and taking action to

regain situational awareness and ensure operating

conditions. A Root Cause Analysis (RCA) was

subsequently developed.

Taking the described incidents as a reference,

and in the search for more and more exhaustive

analyses to guarantee the safety of the electrical

industry personnel, and in general of any person

close to high voltage infrastructures, the evaluation

of the exposure to high gradient magnetic fields

originated by the fault currents of different fault

events is proposed. This evaluation is relevant and

totally necessary to complement the widely

documented analyses (in the electrical industry

literature) on exposure to industrial frequency

electric fields or faults, which have specific control

measures, such as the adequate design of grounding

systems with the respective control and monitoring

of step and contact voltages, and which are required

in the technical regulations and standards applicable

to the power transmission sector in Colombia and

the world. On the other hand, exposure to high-

gradient magnetic fields is an aspect that has not

been extensively characterized and documented. In

the framework of the precautionary principle, it is

necessary to carry out analyses such as those

proposed.

Figure 1 presents a schematic context of

exposure to a high gradient magnetic field caused by

a fault current flowing through the conductor of a

temporary grounding equipment (TGE) while a

worker performs activities on adjacent equipment at

a short distance. This model assimilates to the

operating condition of the first event described. The

fault current, generated by the contact between the

phases of circuit 1 and circuit 2 in the LT trace,

flows through the conductor of the de-energized

circuit to the SE. Due to the working conditions, the

surge arresters are disconnected from their down

conductors, and a (TGE) is connected between the

temple and the grounding system connection of the

SE, in the lattice at the base of the equipment. Under

this operating scenario, the fault current flows

directly to the ground through the (TGE) causing a

high-gradient magnetic field in the area near the

conductor. This current generates a magnetic field

of similar waveform, which materializes the

exposure of workers in the vicinity of the down

conductor. This context is the one chosen for the

following calculations and estimations, since it

presents a higher exposure than the one generated in

event two, due to the fact that in the latter the

distance to the energized bay is wider because no

work was being carried out there.

Thus, as indicated in the previous paragraphs

and taking into account what was established in [8],

[9] and [11], a high-gradient magnetic field could

result in an induced current with acute harmful

effects on the human body. Therefore, it would be

plausible that a gradient of a fault current in the

Transmission System can generate a field gradient

that generates some interaction. Then, the fault

current gradient will be calculated to analyze

whether any overshot of perception thresholds,

muscle stimulation, or intolerable stimulation is

possible.

To calculate the current gradient, an

approximation of the upward ramp of the signal is

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made, taking into account the condition of its

monotonic increase to an almost linear

characteristic. This approximation represents an

error of less than 10% in signals up to twice as fast

as a lightning current, in accordance with what is

established in [2], so this approximation will not

generate a marked uncertainty in the results.

With the current gradient, we now turn to

Ampère's law, which allows us to calculate the

magnetic field (B) caused by a time-varying current

(I). It is necessary to take into account that this

approach has some limitations associated with the

finite length of the conductor that clears the fault

current, the effect of field reflections generated by

the equipment and supports adjacent to the

grounding conductor, and the contributions of the

fault currents that circulate through the earth.

Assuming these conditions, the typical expression is

used to calculate the magnetic field generated by an

infinite streamline, and expressing it in terms of its

time derivative, we obtain:

  

 

 





(3)

With d representing the distance in meters to the

infinite current line, B is the magnetic field, I am the

current, and μ_0 It is the vacuum permeability.

Once the expression that relates the derivative

of current with the derivative of the magnetic field

is established, four fault events of the 230 kV

transmission system cleared by the relay-switch

assembly are selected to calculate the exposure they

could generate under conditions like those

described.

Figure 2 presents the oscillographs of the

currents of the three phases of four selected events.

From left to right the faults are presented in phase

C, phase A, phase B, and phase B, respectively.

With a descending order of the signals for the

phases, top A, middle B, and bottom C.

Schematically two vertical lines and two vertical

arrows in blue and yellow are used to highlight the

beginning of the smoothed current ramp and the end

of the smoothed current ramp. Which are used to

calculate the amplitude and the monotonic rise time,

in the faulted phase that has the highest current

amplitude, and which is where the sharpest gradient

occurs.

Table 1 record the current and monotonic time

parameters of each fault for the calculation of

current derivatives. To have an even more

conservative evaluation, the inclusion of an assumed

critical event with the most drastic fault conditions

is determined, a current of 40 kA with a time of 8.3

ms (valley-peak time of the industrial frequency),

this event seeks a calculation under the worst fault

conditions. It is at the limit of supportability of some

of the equipment installed in the 230 kV substations.

Figure 3 (Appendix) presents the results of

calculating the magnetic field derivatives in a

homogeneous monotonic time for all the faults, in

contrast to the thresholds of perception, muscular

stimulation, and intolerable stimulation. The

distance scale on the x-axis is in cm and allows

observation that from 0.75 cm, none of the faults

would generate an overshoot of any of the

thresholds. The 40 kA critical fault can exceed the

perception threshold only at distances of less than

0.6 cm from the source; an overrun of the muscle

stimulation threshold occurs at a distance of 1 mm,

i.e., virtually when the worker is in contact with the

conductive element through which the fault current

flows. This situation is extremely remote, and if it

were to materialize, the risks associated with the

electric field or its thermal effects would be of

greater concern.

Fig. 1: Schematic model of fault current flow

through grounding equipment while working on

adjacent equipment

The analysis is performed with the ramp of the

highest current gradient; the analysis with

successive ramps in the framework of the signal

damping yields lower results than those presented.

According to the results obtained in events where

the exposed worker is more than 0.75 cm from the

current source, no effect would be expected.

5 Proposed Analysis: Lightning

Signal Model

Works such as the one presented in [8] and [11]

have shown possible acute effects at distances less

than 30 cm from cables carrying lightning fault

currents. Based on these analyses, a calculation of

possible exposures to high gradient fields in the

Fault Current

Temporary grounding

Surge arrester

disconnected

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easement strips in certain cases of lightning strikes

on TL infrastructure is proposed.

Table 1. Fault currents and times for calculating

current gradients

Event Class

Fault

current

[kA]

Monotonic

Time [ms]

Substation

voltage

Event 1

1.89

8.3

230 kV

Event 2

2.65

8.3

230 kV

Event 3

4.38

8.1

230 kV

Event 4

10.7

8.5

230 kV

Assumed

critical event

8.3

230

For this purpose, a typical lightning signal is

selected, and an analysis similar to the one

presented for SE is performed.

A typical time domain lightning signal is

proposed for the analysis, as suggested in [7], and is

presented in equation 4.

  





󰇡

󰇢󰇛

󰇜 (4)

Where i is the current signal, I am the peak

current in [kA], k is the correction factor for the

peak current, t time in [µs],  the front time

constant, and  decay time constant

The peak current parameters and characteristic

times of the lightning signal are established as a

reference to what was stated in [7] to determine

probabilistic magnitudes of the parameters 95%,

50%, 5%, and <1%—the Table 2 presents the

parameters of the selected signals, and

Fig. 4 (Appendix) shows the resulting signals in

the time domain.

Table 2. Lightning signal parameters

[kA]

Probabilistic

magnitude

0.981

0.324

70.45

95%

0.981

0.324

70.45

50%

0.981

0.324

70.45

200

0.981

0.324

70.45

<1%

5.1 Event Analysis for a Lightning Strike on

an LT

The analysis for TL is based on the assumption of a

lightning strike on the power cable or guard with

peak current values between 24 and 200 kA,

assuming that at that exact moment, there is a

worker in the easement strip. Under typical

conditions the current flows in both directions away

from the point of impact, with amplitudes and

wavefronts determined by the impedances of the

cable, towers, grounding, and their interactions.

These reduce the gradients and maximum

amplitudes of each of the wavefronts. To perform

conservative calculations, the assumption is made

that all the lightning current flows in a single

direction, and attenuations of the medium and

impedances are discarded. Thus, the maximum

amplitude and maximum gradient scenario is

obtained, which is desirable in this type of exposure

calculation. The Fig. shows the impact scenario and

the signals used for the proposed calculation.

Fig. (Appendix) shows the results for a fast

front time with different amplitudes, in contrast to

the thresholds for perception, muscle stimulation,

and intolerable stimulation for that gradient time. It

can be seen that only with the 200-kA signal at a

distance of 50 cm the perception threshold is

exceeded, which demonstrates that even in a

scenario of very high and remotely probable current,

any worker in the easement strip would not have

effects associated with exposure to high gradient

magnetic fields.

5.2 Discretization Space Simulation

Although the analytical results clearly show that

there is no evident effect on the exposure of the

analyzed cases, to finalize this study, a simulation is

implemented using spatial discretization techniques

software with a lightning-type signal, which was the

one that showed higher derivatives and higher

exposure incidence in the previous calculations.

The software used is CST Studio Suite, which

implements the Finite Integration Technique (FIT)

and the Transmission Line Method (TLM), which

allows properly simulating of the return channel and

its associated fields, as well as the coupling effects.

This software has a presence of several decades in

the market of physical and electromagnetic

simulations, is widely validated, and is used by

multiple engineering companies worldwide. This

software allows simulation directly in the time

domain, improving some of the results of other

software that uses frequency domain techniques and

use back transforms to adjust the results in time,

[12].

The spatial domain is 20m x 20m x 20m, with

PML (Perfectly Matched Layer) boundaries that

generate a boundary condition with no absorptions

or reflections in the signals. A concrete block of

10m x 10m x 5m is included, and a downspout of

radius 0.02m and 5.2m high penetrates the block 0.2

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m, as shown in Fig. (Appendix), left side. The

excitation signal is a classical double ramp signal

with an amplitude of 200 kA, as shown in Figure 7

(Appendix) on the right side. The simulation occurs

in the time domain between 0 and 100 µs.

Fig. and Figure 8 (Appendix) presents the

simulation results; on the left, the magnetic field

distribution around the down conductor, a field

concentration is observed in the vicinity of the

excitation source. On the right, the magnetic field

signal is in [A/m]. The results show that for the

maximum gradient interval, the thresholds of

perception, muscle stimulation, or intolerable

stimulation are not exceeded. There is a significant

deviation in the simulation results Vs. the analytical

calculation because the exposure calculated in

previous sections has maximum coupling factors

and is markedly conservative; in addition, they are

made with an infinitely long conductor

approximation, [13]. On the other hand, the

simulations are theoretically more accurate and

consider the presence of the concrete block.

Additional simulations with the presence of a

support structure or additional equipment to show

the field distortion would be desirable. However, the

software used is in a student test license and has

extensive restrictions for meshing, which prevented

the realization of more complex simulations. The

student version allows a maximum of 100,000 mesh

cells. According to the determined simulation space

the maximum simulation accuracy is for a

discretization of  m³.

Nevertheless, the results obtained clearly show

that the levels of exposure to high gradient magnetic

field are marginal for the models analyzed.

6 Conclusion

Verification and validation of the exposure of high

gradient magnetic fields originating from fault

currents are necessary because, under certain

conditions, it has the possibility of exceeding the

perception, muscle stimulation, or intolerable

stimulation thresholds. One of the best methods that

has been documented is the use of assessment

methodologies for patient safety during MRI

examinations.

Results obtained from theoretical analysis and

computational simulations show mismatches due to

the approximate characteristics of the theoretical

equations since their models do not take into

account environmental elements, such as the ground

or adjacent elements. However, analytical models

are a valuable tool for initial verifications, with

great ease of application and usable results.

Analysis developed for power system failures

with peak currents of up to 40 kA and front times of

8.3 ms show that the perception threshold is only

exceeded at distances less than 0.6 cm from the

source. The stimulation threshold is only exceeded

in very remote conditions in which the worker is

virtually touching the downspout conductor; in this

scenario, risks associated with the electric field or

thermal stress may be more acute.

Results obtained from the analysis with a rapid

atmospheric discharge of 200 kA amplitude show

that none of the thresholds of interest are exceeded

in the easement strip. Exceeding the perception

threshold only occurs 50 cm from the conductor, a

scenario only possible for a worker who is passing

by the transmission line conductor just at the

moment when the lightning strike occurs.

In this way, this paper stood out for its analysis

of human exposure to high-gradient magnetic fields

originating from events on the 230 kV electric

power transmission infrastructure. It presents a

range of scenarios, including typical events and

extreme failures, and verifies compliance with

exposure thresholds. Additionally, the inclusion of a

lightning signal model added depth to the analysis,

showing the potential impact of atmospheric

discharges on exposure levels. Thus, this paper

provided valuable insights into a critical aspect of

electrical infrastructure safety, shedding light on

potential risks and offering a basis for further

research and safety measures.

Declaration of Generative AI and AI-assisted

Technologies in the Writing Process

During the preparation of this work the authors used

CLAUDE in order to study the state of the art and

the missing development in order to give a new

approach our proposal. After using this tool/service,

the authors reviewed and edited the content as

needed and take full responsibility for the content of

the publication.

References:

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155653–155663, Nov. 2021. doi:

10.1109/ACCESS.2021.3115824.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

Conceptualization G.G., F.R., S.R.; methodology,

software, validation, formal analysis G.G., F.R.,

S.R.; investigation, G.G., F.R.; writing—original

draft preparation, G.G., F.R.; writing—review and

editing, G.G., F.R., S.R. The authors have read and

agreed to the published version of the manuscript.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

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APPENDIX

Fig. 2: Fault oscillographs. Failure 1 Phase C, failure 2 Phase A, failure 3 Phase B, failure 4 Phase B. Phases A,

B, and C are assigned downstream. Monotonic time and gradient calculated in the middle of the indicator's blue

and yellow cursors

Fig. 3: Results of the calculation of the magnetic field derivatives in a homogeneous monotonic time for all

faults, in contrast to the thresholds of perception, muscular stimulation, and intolerable stimulation

Fig. 4: Lightning signals in the time domain

Failure-event 1 Failure-event 2 Failure-event 3 Failure-event 4

0.5 1 1.5 2 2.5 3 3.5 4

dB/dt intensity[kT/s]

Distance[cm]

Perception and stimulation thresholds Vs dB/dt - rise time=8.3 ms

dB/dt_1.89kA_t=8.3ms dB/dt_2.65kA_t=8.3ms dB/dt_4.38kA_t=8.3ms

dB/dt_10.7kA_t=8.3ms dB/dt_40A_t=8.3ms Threshold_perception

Threshold_Muscle Stimulation Threshold_Intolerable Stimulation

100

150

200

020 40 60 80 100 120 140 160 180 200

I_Peak [kA]

t[µs]

Lightning currents - front signal

ip(24 kA) i(45.3 kA) i(85 kA) i(200 kA)

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Fig. 5: On the left diagram is the lightning strike and field emission in the strip. The right fronts of ray signals

were determined for the calculations

Fig. 6: Results of the magnetic field derivatives for fast front time and their comparison with the thresholds of

perception, stimulation, and intolerable stimulation

Fig. 7: Left simulation model with concrete block and down conductor. Right model excitation function

Distance

Easement strip

-40

110

160

210

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

I_Peak [kA]

t[µs]

Lightning currents - front signal

ip(24 kA) i(45.3 kA) i(85 kA) i(200 kA)

0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

dB/dt intensity[kT/s]

Millares

Distance[m]

Perception and stimulation thresholds Vs dB/dt - rise time=0.32 µs

dB/dt_24kA_t=0.32µs dB/dt_45.3kA_t=0.32µs dB/dt_85kA_t=0.32µs

dB/dt_200kA_t=0.32µs Threshold_perception Threshold_Muscle Stimulation

Threshold_Intolerable Stimulation

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Fig.8: Simulation results, left magnetic field distribution in space. Right absolute magnetic field signal in [A/m]

at test point 14 cm from the down conductor

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