transient lightning

1. IEEE 1997 International Symposium on Electromagnetic Compatibility, August 1997, Austin, Texas, United States
ISBN: 0-7803-4140-6
385
Frequency and Transient Behavior of Grounding Systems
II - Practical Application Examples
Carlos Portela
COPPE/UFRJ, Federal University of Rio de Janeiro, Brazil
R. Eng. Cesar Grillo, 249, CEP 22640-150
Rio de Janeiro, RJ, BRAZIL
Abstract: In this paper, it is presented the application of
methodology and computational procedures described in a joint
paper [1], to basic concrete problems of electromagnetic
compatibility, including:
- Effects of lightning discharges in electrical grounding systems,
and definition of risks for human safety, for equipment damaging
and of non correct operation of control and protection schemes.
- Procedures to limit consequences of lightning.
- Interference, through ground systems, in sensitive circuits,
considering frequency dependence of interaction of power
equipment with sensitive elements, and surge type phenomena.
- Procedures to limit interference.
INTRODUCTION
The main purpose of this paper is to illustrate the application of
methodology described in [1], and to discuss some of its
applications, including:
- Behavior of grounding systems, in frequency domain, and for fast
transients, including lightning strokes.
- Effects of lightning strokes related to human and equipment
safety, induction and interference, through grounding systems.
We consider a concrete grounding mesh example. In some points
of this mesh, we consider injected either a sinusoidal current, of
frequency varying in the range [ 0 , 1 MHz ] , or a current impulse.
The shape of such impulses is representative of lightning strokes.
Examples of effects of such currents are presented and discussed.
1. GROUNDING MESH EXAMPLE
We consider a grounding mesh formed with 7176 m of copper
conductors, disposed horizontally, 0.5 m below soil surface, as
indicated in figure 1, in which x , y are the horizontal coordinates.
In figure 1-a, all grounding mesh is represented, and, in figure 1-b,
only a part (“part A”), near a corner (“zoom”). The soil parameters,
σ , ω ε , in function of frequency, are represented in figure 2.
Figure 1. Grounding mesh horizontal coordinates.
2. FREQUENCY BEHAVIOR
To illustrate frequency behavior of ground mesh, it is represented,
in figures 3 , 4 , in three-dimensional form, the transversal
voltage in part A of mesh, for a 1 A current injected in point M1 of
mesh (with coordinates x = 0 , y = 0 ) . Figure 3 is for frequency
f = 1 pHz , and figure 4 for f = 1 MHz . In figures 3 and 4-a it is
represented the amplitude of voltage (ranging between 4.63436 V
and 4.63366 V , in figure 3, for f = 1 pHz , and between 0.36 V and
37.99 V in figure 4-a, for f = 1 MHz ). In figure 4-b it is
represented the phase of voltage, for f = 1 MHz (referred to phase
of injected current, assumed 0 ). The phase range is -π , +π ; the
apparent discontinuity results from the fact that, when phase is
lower than -π , it is added 2 π n , to obtain a phase between -π and
+π . The observation point, for 3D representation, is different in
figures 4-a and 4-b .
Figure 2. Soil parameters. Figure 3. Transversal node
voltages, for f = 1 pHz .
Fig. 4-a - Amplitude Fig. 4-b - Argument
Figure 4. Transversal node voltages, for f = 1 M H z .
These results show clearly the important difference between
grounding systems behavior for power frequency and slow
phenomena, and for high frequency and fast transients. For slow
transients, in dominant frequency spectrum, the behavior is of the
type of figure 3, and almost frequency independent. For fast
transients, in significant spectrum, the behavior is strongly
frequency dependent, covering, e.g., conditions of the type of

2. 386
figures 3 and 4; otherwise, the electromagnetic behavior of
grounding system is quite sensitive to the point in which ground
current is applied.
To obtain frequency domain behavior, necessary for the study of
lightning discharges behavior, simulation has been done for eight
frequencies, in range [ 0 , 1 MHz ] , for a complete mesh
simulation, covering current injection in any node of ground mesh
and any intermediate individualized point.
3. EXAMPLES OF FREQUENCY DEPENDENCY OF INDUCED
EFFECTS, AND OF LIGHTNING EFFECTS
In order to illustrate some types of immediate results of proposed
method, a few examples are presented, in what concerns frequency
dependency of induced effects, in range [ 0 , 1 MHz ], and of
lightning effects. For lightning, an impulse current, with chosen
relative shape, is injected in mesh.
The presented examples consider an impulse current with relative
shape as represented in figure 5, and 1 A amplitude. Such relative
shape is representative of typical impulses of negative strokes
(either first or subsequent impulses) [2 , 3]. Positive strokes,
although with higher amplitude (in statistical sense), have more
favorable front of wave shapes. For a complete study, the relative
shape parameters may be considered in a range, to have higher
accuracy in statistical risk evaluation obtained from simulation.
For a certain amplitude of impulse, I (in Ampere), the voltage
magnitudes represented in figures must be multiplied by I, as
curves refer to an impulse amplitude I = 1 A .
Figure 5. Relative shape of current impulse injected i n
m e s h .
Table 1 - Definition of examples
Ex. nº Fig. nº Injec.
point
Quantity represented in figure
1 7 M1 Transversal voltage of point M1
2 8 M1 Difference between transversal
voltages of points M1 , S6
3 9 M1 Difference between transversal
voltages of points S1 , S5
4 10 M1 Induced longitudinal voltage in a
segment between points S1 , S3
5 11 M2 Transversal voltage of point M2
6 12 M2 Difference between transversal
voltages of points M2 , S4
7 13 M2 Difference between transversal
voltages of points S1 , S5
8 14 M2 Induced longitudinal voltage in a
segment between points S2 , S3
In table 1 we indicate the conditions identifying the eight
examples. Points, at mesh and at ground surface level, used to
define examples in table 1, have coordinates indicated in table 2
(horizontal coordinates x , y as represented in figure 6).
x - Points at
grounding
mesh, Mi
O - Points at
soil surface,
Sj
Figure 6. Position of points M1, M2, S1, … , S 6
Table 2. Coordinates of points M1, M2, S1, …, S 6
Point Horizontal coordinates
x [m] y [m]
Points at grounding M1 0 0
mesh M2 30 -30
Points at soil surface S1 0 0
S2 30 -30
S3 30 0
S4 26 -26
S5 0 1
S6 4 -4
For each of examples 1 to 8, it is presented a figure with three
graphics. In the first of them, it is represented the immittance,
W , relating the quantity analyzed to the injected current in ground
mesh, in complex representation, in the frequency range
[ 0 , 1 MHz ] . The two curves of each graphic represent the real and
imaginary components of W , and are identified by Re and Im. In
second and third graphics of each figure, it is represented the
analyzed quantity, in function of time, for the assumed current
impulse injected in grounding mesh. These two graphics differ
only in the scale and time range.
Examples 1 and 5 are representative of transferred voltages outside
mesh area and of equivalent impedances, to a remote point, for
currents injected in mesh. Examples 2 and 6 are representative of
transferred voltages to short distances, within mesh area;
examples 3 and 7, of step voltages; examples 4 and 8, of induced
voltages in protection, control and data transmission cables, and
also in power circuits.
In order to have a more compact evaluation of severity for people
and equipment safety, and induced effects, for different purposes, it
is convenient to consider the following severity parameters,
being ua the voltage applied to a person or equipment and ic the
current across the body of affected person, for a lightning stroke
of amplitude I and instantaneous value i :
ˆUa
- crest value of | ua | ˆIc
- crest value of | ic |

3. 387
Su1 = | dtau |∫ Si1 = | dtci |∫ (1)
Su1.4 = | dta
1.4
u |∫ Si1.4 = | dtc
1.4
i |∫ (2)
Su2 = | dta
2
u |∫ Si2 = | dtc
2
i |∫ (3)
For a relative shape of stroke current as in figure 5 , and
I = 100 kA (that has a probability of being exceeded of about 0.03
for first negative lightning impulses), if voltages of considered
examples apply to an equipment of infinite impedance, we have
the values indicated in table 3,
Table 3. Parameter values for a 100 kA impulse
Example ˆUa Su1 Su1.4 Su2
[kV] [Vs] [V
1.4
s] [V
2
s]
1 1 842 28.5 4 917 12.4 10
6
2 648 2.84 230 273 10
3
3 309 2.43 170 129 10
3
4 948 2.21 223 467 10
3
5 994 27.4 4 451 9.75 10
6
6 428 1.71 110 86.4 10
3
7 85.4 2.28 141 76.1 10
3
8 361 0.521 43.1 53.5 10
3
Fig. 7. Example 1 Fig. 8. Example 2
Fig. 9. Example 3 Fig. 10. Example 4
4. HUMAN SAFETY CONDITIONS
There is limited information about safe limits for effects of short
duration current impulses, of arbitrary shape, in human body, and
any reasonable criteria must be chosen with careful judgment. The
conditions we have considered and indicate bellow, are based in
[4], and some additional aspects discussed in [5], and apply only
to very short duration impulse currents in human body, for healthy
adults, and circulation current conditions of touch, transfer and
step types. In following expressions: ic is the current through the
body; uc is the voltage applied to the body (excluding voltage in
gravel and soil consequent of current through the body); u is the
touch or transferred voltage “if” no current would circulate in the
body (or if the body would have infinite impedance); Z1 is the
body impedance, between one hand and both feet (for touch and
transfer conditions), or between both feet (for step conditions); Z2
is the contact impedance with soil, considering a layer of gravel,
for touch, transfer and step conditions; i is the impulse current
injected in ground mesh.
In figure 15 we represent, in schematic form, the main parameters
for transfer or touch conditions.
Safety condition for ventricular fibrillation
We consider, for safety condition for ventricular fibrillation (for
healthy adults, and circulation current conditions of touch, transfer

4. 388
Fig. 11. Example 5 Fig. 12. Example 6
and step types), a limit, M[Si1.4], of severity parameter Si1.4 :
Si1.4 = | dtc
1.4
i |∫ ≤ M[Si1.4] = 1.52 10
-3
A
1.4
s (4)
This criterion is assumed to imply a negligible probability of
ventricular fibrillation for an healthy adult. However, it does not
assure the absence of pain and other physiological effects,
including reversible auricular fibrillation.
For a probability of ventricular fibrillation of about 0.05, the
limit increases to 2.96 10
-3
A
1.4
s .
Also for very short duration impulses, the following threshold
conditions are considered.
Perception threshold
For perception threshold, we consider
Si1 = | dtci |∫ ≤ Ma[Si1] = 0.36 to 0.9 µC (5)
Pain threshold
For pain threshold, we consider
Si1 = | dtci |∫ ≤ Mb[Si1] = 7.6 µC (6)
Assumptions and criteria for risk evaluation
We do the following assumptions (approximate), for risk
evaluation [5 , 6]:
Fig. 13. Example 7 Fig. 14. Example 8
Figure15. Schematic
representation o f
touch or transfer
conditions.
Figure 16. Probability, P , o f
| dt
1.4
i |∫ to be exceeded, for
first impulses of negative
ligthninig strokes.
∫ | | dtc
1.4
c
i
Iˆ .1 4
≅
∫ | | dt
1.4
u
Uˆ .1 4
= τ1.4 (7)
R ≅ K cˆU
-0.2
(being K = 2.9 10
3
, for R in Ω and cˆU in V) (8)
| Z1 | = | k | R =
c
c
ˆ
ˆ
U
I
(being | k | = 0.817 ) (9)
Z2 = K1 . F1 . ρceqb for touch and transfer conditions (10)
Z2 = K2 . F2 . ρceqb for step conditions (11)

5. 389
with
ρceqb =
1
i gravel
((σσ εε ))+ ω
(12)
K1 = 1.27 m
-1
(13)
K2 = 4.46 m
-1
(14)
F1 = F1
gravel
soil
( i )
( i )
h,
σσ εε
σσ εε
+
+






ω
ω
≅ F1
gravel
soil
( i )
( i )
h,
σσ εε
σσ εε
+
+






ω
ω
(15)
F2 = F2
gravel
soil
( i )
( i )
h,
σσ εε
σσ εε
+
+






ω
ω
≅ F2
gravel
soil
( i )
( i )
h,
σσ εε
σσ εε
+
+






ω
ω
(16)
h depth of gravel layer
F1 , F2 functions defined, in graphic form, in [6]
Due to uncertainty about some parameters, it is justified to avoid a
detailed frequency analysis for Z1 and Z2 , and to consider them, in
absolute assumed average value, for a frequency f = 150 kHz
(chosen for examples discussed below).
Due to limited accuracy of statistical parameters of lightning
current impulses shape, it is also justified to assume that, for
statistical distribution analysis,
| dt
1.4
u |∫ = H1.4 |
1.4
dti |∫ (17)
(with H1.4 constant, equal to H1.4 for “representative”
stroke current shape)
With previous assumptions, we have, for limit conditions for
ventricular fibrillation:
ˆIc
≅
i1.4
1.4
1.4
M[S ]
ττ
(18)
cˆU = | | c
1.2 k K Iˆ (19)
|
1.4
dti |∫ =
( | | | | )1 2
1.4
1.4
Z Z
H
+
| dtc
1.4
i |∫ (20)
The probability to exceed the safety limit for ventricular
fibrillation is, so, the probability that
E1.4 = |
1.4
dti |∫ > D (21)
being
D =
( | | | | )1 2
1.4
1.4
Z Z
H
+
M[Si1.4] (22)
M[Si1.4] = 1.52 10
-3
A
1.4
s (23)
For a representative lightning impulse shape, by simulation, we
obtain H1.4 and | Z1 | . From gravel and soil parameters, we obtain
| Z2 | . So, we have D value. From the statistical distribution of
lightning parameters, we obtain the approximate probability that
safety condition for ventricular fibrillation is not satisfied, for
assumed touch, transfer or step conditions. In figure 16 , we
represent the estimated statistical distribution of E1.4 , being P
the probability that E1.4 is exceeded for the first impulse of a
negative lightning stroke. This estimated distribution is based,
essentially, in [2].
In a similar way, other safety conditions, e.g., for some defined
probability of ventricular fibrillation, or for perception or pain
threshold, can be obtained.
For the examples of this paper, based in [7], we consider, for
gravel, at f = 150 kHz :
σ = 170 µS/m ω ε = 120 µS/m (24)
and, so,
F1 = F1(0.245) ≅ 0.625 (25)
F2 = F2(0.245) ≅ 0.672 (26)
| Z2 | ≅ 3814 Ω for touch and transfer conditions (27)
| Z2 | ≅ 14 403 Ω for step conditions (28)
In table 4 we indicate the following parameters for limit
conditions for ventricular fibrillation, for examples 1 to 8, (with
lightning impulse current with amplitude for limit condition, and
relative shape of examples): current amplitude at human body, ˆIc
,
voltage amplitude applied to body, cˆU , parameter D ,
probability that safety condition is not respected, P , for first
impulses of negative lightning flashes, in conditions of each
example. Subsequent negative impulses are less severe than the
first ones, in a statistical sense. For positive lightning impulses,
the relative shape is quite different of the current shape of
presented examples, and risk evaluation must be based in a
different shape. The method, however, is identical, only with
different current shape.
Table 4. Risk parameters for first impulses o f
negative lightning strokes
Ex. nº ˆIc
[A] cˆU [kV] D [A
1.4
s] P
1 41.2 14.4 18.85 0.99
2 129.3 37.3 394.4 0.27
3 76.6 24.1 3193 0.01
4 193.3 52.2 404.1 0.27
5 23.9 9.14 21.06 0.98
6 145.2 41.1 827.6 0.10
7 24.2 9.22 3871 <0.005
8 238.1 62.1 2089 0.02
Examples 1 and 5 are representative of transferred voltages outside
mesh area. The values of table 4, for these examples, apply to
contact impedance, of affected person, through gravel and soil, as
in mesh area. Till in this conditions, the risk is too high. Local
conditions, at the point where affected person stands, must be
considered. Such local conditions may be more unfavorable than
in mesh area, in what concerns contact impedance.
Anyhow, a lightning stroke, at any point of grounding mesh,
implies in high risk, for people exposed to transferred voltage
outside mesh area. So, conditions that allow a person to be
submitted to such transferred voltages must be avoided. Namely,
no power or telephone cables may connect grounding mesh area to
outside points, unless very special protective measures are taken.

6. 390
Examples 2 and 6 are representative of transferred voltages to
short distances, within mesh area; example 2 for a lightning
stroke near the corner of mesh, and, example 6, at 30 m of mesh’s
borders. The comparison of these examples shows the influence of
the point of mesh at which lightning stroke is applied, and also of
the point where affected person is located. For unfavorable
conditions, it is important to take constructive measures that
restrain the incidence of high amplitude strokes near the border of
grounding mesh, and force the lightning impulse to divide, going
to several points of mesh. It is possible to obtain such behavior
by adequate design of structures, masts and aerial cables.
Examples 3 and 7 are representative of step voltages, also for the
two different mesh’s points to which lightning impulse is applied.
They show that step voltage conditions are much less severe than
transfer and touch conditions. They also illustrate and the
influence of the point of mesh to which lightning stroke is
applied.
Examples 4 and 8 are representative of induced voltages in
protection, control and data transmission cables, and also in
power circuits. In both cases, the cable is 30 m length, at ground
level. The lightning incidence points are different (as in previous
cases). Values of table 4, for these examples, apply to people
safety conditions of eventual transferred voltages equal to the
induced voltages (what can occur in several circumstances). They
show the influence of lightning incidence point, and demonstrate
that induced voltages in power, protection, control and data
transmission circuits, must be considered carefully, for people’s
safety.
5. EQUIPMENT SAFETY CONDITIONS
The safety equipment conditions, namely related to lightning
impulses in grounding mesh, depend on overvoltages of impulse
type that the equipment can support. Anyhow, the conditions of
presented examples, namely those shown in table 3, that consider
a lightning impulse of 100 kA amplitude, show that very severe
overvoltages can occur.
Values of table 3, for examples 4 and 8, that consider a lightning
impulse of 100 kA amplitude, also show the importance of induced
voltages, for equipment safety and for wrong operation risk (of
protection, control and data transmission circuits). They also
demonstrate the absolute need to limit the consequences of induced
lightning effects. Corrective measures include adequate shielding,
multiple connection of shielding circuits to grounding mesh,
careful definition of equipment requirements, for short duration
surges, and surge protection equipment.
6. INTERFERENCE EFFECTS IN FREQUENCY DOMAIN
The first of each group of three graphics of figures 7 to 14, for
examples 1 to 8, indicate directly the transfer impedance for each
example, equal to the ratio of voltage considered in example to
injected current in grounding mesh. For examples 1 to 4, injection
point is one corner of mesh, and for examples 5 to 8, a point at 30
m of mesh’s borders.
For example 8, the transfer impedance to a cable 30 m long, at
ground surface, is 8.90 Ω at 250 kHz and 21.8 Ω at 1 MHz . These
values, and the graphics indicated above, show that inductive
effects of currents injected in grounding mesh may be important
for operation reliability of digital equipment, including digital
protection and control.
7. CONCLUSION
The presented examples show that the methods proposed and
described in [1] allow to consider the behavior of grounding
meshes and circuits, and its interaction with power, protection,
control and data processing circuits and equipment, including the
following aspects:
- Frequency dependence of soil parameters.
- Frequency range of, at least, [ 0 , 1 MHz ] , and probably,
larger, e.g., [ 0 , 10 MHz ] .
- Fast transients, including lightning and its effects.
- Human safety for fast transients.
- Equipment safety.
- Large grounding meshes, including those of largest power
stations, substations, telecommunication and industrial
installations.
REFERENCES
[1] Portela, C., Frequency and Transient Behavior of Grounding
Systems - I Physical and Methodological Aspects, Proceedings
1997 International Symposium on Electromagnetic
Compatibility, August 1997, Austin, Texas, United States.
[2] Berger, K., Anderson, R., Parameters of Lightning Flashes,
Electra nº 41, p. 23-37, 1975.
[3] Portela, C., Transient Regimen, vol. 1 - 4 , edition of
ELETROBRAS and COPPE, 1984 (in Portuguese).
[4] International Electrotechnical Commission, IEC, Technical
Committee Nº 64, Effects of Current Passing Through the Human
Body, Part 5, Unidirectional Single Impulse Currents of Short
Duration, September 1984.
[5] Portela, C., Basic Aspects of People Safety Conditions for
Lightning Discharges in Substations and Transmission Lines,
Proceedings VIII SNPTEE, National Seminar on Production and
Transmission of Electric Energy, paper SP/GSP/34, 20 p. , São
Paulo, Brazil, 1986 (in Portuguese).
[6] Portela, C., Determination of Contact Resistances with Soil,
considering Gravel or Covering Layers, Proceedings XI SNPTEE,
National Seminar on Production and Transmission of Electric
Energy, paper RJ/GSI/21, 6 p. , Belo Horizonte, Brazil, 1987 (in
Portuguese).
[7] Visacro Fº, S., Portela, C., Scoralick, M., Bispo, P.,
Investigation of Gravel Behavior in its Application as a Safety
Element in Electrical Installations, Proceedings XI SNPTEE,
National Seminar on Production and Transmission of Electric
Energy, paper RJ/GSI/21, 6 p. , Rio de Janeiro, Brazil, 1991 (in
Portuguese).
[8] Portela, C., Ground Meshes Transient Analysis - Example of
Results Obtained with TRANSMATER ®, 211 pp. 1966 (in
Portuguese).