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D.3 Current sharing

The parameters given in the Table D.1 are relevant to the lightning current at the point of strike. In fact, the current flows to earth through more than one path, as several down- conductors and natural conductors are normally present in an external LPS. Additionally, different lines normally enter the protected structure (water and gas pipes, power and telecommunication lines, etc.). For the determination of the parameters of the actual current flowing in specific components of an LPS, the sharing of the current has to be taken into account. Preferably, current amplitude and shape through a component at a specific location of the LPS should be evaluated. Where an individual evaluation is not possible, the current parameters may be assessed by means of the following procedures.

For the evaluation of the current sharing within the external LPS, the configuration factor k_c (see Annex C of IEC 62305-3:2010) may be adopted. This factor provides an estimate of the share of the lightning current flowing in down-conductors of the external LPS under worst-case conditions.

For the evaluation of the current sharing in presence of external conductive parts and power and telecommunication lines connected to the protected structure, the approximate values of k_e and k’_e considered in Annex E may be adopted.

The above-described approach is applicable for the evaluation of the peak value of the current flowing in one particular path to earth. The calculation of the other parameters of the current is carried out as follows:

/

(D.1)

(D.2)

(D.3)

(D.4)

p = kxl

Q_p = к x Q

W!R = A-² >{ W !R)

where

x_p is the value of the quantity considered (peak current /_p, charge Q_p, specific energy (14//R)_p, current steepness (d/7df)_p) relevant to a particular path to earth "p";

x is the value of the quantity considered (peak current /, charge Q, specific energy (W/R), current steepness (d/7dt)) relevant to the total lightning current;

к is the current sharing factor:

k_c for external LPS (see Annex C of IEC 62305-3:2010);

k_e, k’_e in the presence of external conductive parts and power and telecommunication lines entering the protected structure (see Annex E).

D.4 Effects of lightning current causing possible damage

D.4.1 Thermal effects

Thermal effects linked with lightning current are relevant to the resistive heating caused by the circulation of an electric current flowing through the resistance of a conductor or into an LPS. Thermal effects are also relevant to the heat generated in the root of the arcs at the attachment point and in all the isolated parts of an LPS involved in arc development (e.g. spark gaps).

D.4.1.1 Resistive heating

Resistive heating takes place in any component of an LPS carrying a significant part of the lightning current. The minimum cross-sectional area of conductors must be sufficient to prevent overheating of the conductors to a level that would present a fire hazard to the surroundings. Despite the thermal aspects discussed in D.4.1, the mechanical withstand and durability criteria have to be considered for parts exposed to atmospheric conditions and/or corrosion. The evaluation of conductor heating due to lightning current flow is sometimes necessary when problems can arise because of the risk of personal injury and of fire or explosion damages.

Guidance is given below to evaluate the temperature rise of conductors subjected to the flow of a lightning current.

An analytical approach is presented as follows:

The instantaneous power dissipated as heat in a conductor due to an electrical current is expressed as:

P(t) = /²(t) x R (D.5)

The thermal energy generated by the complete lightning pulse is therefore the ohmic resistance of the lightning path through the LPS component considered, multiplied by the specific energy of the pulse. This thermal energy is expressed in units of Joules (J) or Watt-seconds (Wxs).

W-Rx jz²(/)xd/ (D.6)

In a lightning discharge, the high specific energy phases of the lightning flash are too short in duration for any heat generated in the structure to be dispersed significantly. The phenomenon is therefore to be considered adiabatic.

The temperature of the conductors of the LPS can be evaluated as follows:

W

1

(D.7)

_їїхор₍₁
0-00=— exp( —- )-l

a q^zxyxC_w

Characteristic values of the physical parameters reported in Equation (D.7), for different materials used in the LPS are recorder in Table D.2 where

0-0_o is the temperature rise of the conductors (K);

a is the temperature coefficient of the resistance (1/K);

W/R is the specific energy of the current impulse (J/Q);

p₀ is the specific ohmic resistance of the conductor at ambient temperature (Qm);

q is the cross-sectional area of the conductor (m²);

у is the material density (kg/m³);

C_w is the thermal capacity (J/kgK);

C_s is the latent heat of melting (J/kg);

0_S is the melting temperature (°С).Table D.2 - Physical characteristics of typical materials used in LPS components

^a Austenitic non-magnetic.

Table D.3 reports, as an example of application of this equation, the temperature rise of conductors made of different materials, as a function of the kV/R and of the conductor cross-sectional area.

Table D.3 - Temperature rise for conductors of different sections as a function of W/R

The typical lightning stroke is characterized by a short duration stroke (time to half value of a few 100 p.s) and high current peak value. Under these circumstances, the skin effect should also be taken into consideration. However, in most of the practical cases linked with LPS components, the material characteristics (dynamic magnetic permeability of the LPS conductor) and the geometrical configurations (cross-sectional area of the LPS conductor) reduce the contribution of the skin effect to the temperature rise of the conductor to negligible levels.

The component of the lightning flash most relevant to this heating mechanism is the first return stroke.

D.4.1.2 Attachment point thermal damage

Attachment point thermal damage can be observed on all components of an LPS on which an arc development takes place, i.e. air-termination systems, spark gaps, etc.

Material melting and erosion can occur at the attachment point. In fact, in the arc root area there is a large thermal input from the arc root itself, as well as a concentration of ohmic heating due to the high current densities. Most of the thermal energy is generated at or very close to the surface of the metal. The heat generated in the immediate root area is in excess of that which can be absorbed into the metal by conduction and the excess is irradiated or lost in melting or vaporizing of metal. The severity of the process is linked to the current amplitude and to the duration.

D.4.1.2.1 General

Several theoretical models have been developed for the calculation of thermal effects on metal surfaces at the attachment point of a lightning channel. For sake of simplicity, this standard will report only the anode-or-cathode voltage drop model. The application of this model is particularly effective for thin metal skins. In all cases, it gives conservative results as it postulates that all the energy injected in the lightning attachment point is used to melt or vaporize conductor material, neglecting the heat diffusion within the metal. Other models introduce the dependence of the lightning attachment point damage on the duration of the current impulse.

D.4.1.2.2 Anode-or-cathode voltage drop model

The energy input W at the arc root is assumed as given by the anode/cathode voltage drop u_ac multiplied by the charge Q of the lightning current:

W

(D.8)

= ju_a, _c (t) /(t) dt = u_a, cj |/(t)| dt
о о

As u_ac is fairly constant in the current range considered here, the charge of the lightning current (Q) is primarily responsible for the energy conversion in the arc root.

The anode-or-cathode voltage drop u_ac has a value of a few tens of volts.

A simplified approach assumes that all of the energy developed at the arc root is used only for melting. Equation (D.9) uses this assumption but leads to an overestimate of the melted volume.

У C_wx(0s-0i>) ⁺ Cs

where

V is the volume of metal melted (m³);

u_{a c} is the anode-or-cathode voltage drop (assumed as constant) (V);

Q is the charge of the lightning current (C);

у is the material density (kg/m³);

C_w is the thermal capacity (J/kgK);

0_S is the melting temperature (°С);

0_U is the ambient temperature (°С);

C_s is the latent heat of melting (J/kg).

Characteristic values of the physical parameters reported in this equation, for different materials used in an LPS, are recorded in Table D.2.

Basically, the charge to be considered is the sum of the charge of the return stroke and the lightning continuing current. Laboratory experience has revealed that the effects of the return stroke charge are of minor importance when compared to the effects of the continuing current.D.4.2 Mechanical effects

Mechanical effects caused by the lightning current depend on the amplitude and the duration of the current as well as on the elastic characteristics of the affected mechanical structure. Mechanical effects also depend on the friction forces acting between parts of the LPS in contact with one another, where relevant.

D.4.2.1 Magnetic interaction

Magnetic forces occur between two current-carrying conductors or, if only one current­carrying conductor exists, where it forms a corner or a loop.

When a current flows through a circuit, the amplitude of the electrodynamic forces developed at the various positions of the circuit depend on both the amplitude of the lightning current and the geometrical configuration of the circuit. The mechanical effect of these forces, however, depends not only on their amplitude but also on the general form of the current, its duration, as well as on the geometrical configuration of the installation.

D.4.2.1.1 Electrodynamic forces

Electrodynamic forces developed by a current, /, flowing in a conductor having long parallel sections of length I and distance d (long and small loop), as shown in Figure D.1, can be approximately calculated using the following equation:

F(0 = y-x/²(t)x-^ = 2x1(F⁷x/²(t)x-^ (D.10)

where

F(t) is the electrodynamic force (N);

/ is the current (A);

//₀ is the magnetic permeability of free space (vacuum) (4л x 10~⁷ H/m);

I is the length of conductors (m);

d is the distance between the straight parallel sections of the conductor (m).

Figure D.1 - General arrangement of two conductors
for the calculation of electrodynamic forc

e

In an LPS an example is given by a symmetric corner arrangement of conductors, forming an angle of 90°, with a clamp positioned in the vicinity of the corner as shown in Figure D.2. The diagram of the stresses for this configuration is reported in Figure D.3. The axial force on the horizontal conductor tends to pull the conductor out of the clamp. The numerical value of the force along the horizontal conductor, considering a peak current value of 100 kA and a length of a vertical conductor of 0,5 m, is shown in Figure D.4.

Figure D.2 - Typical conductor arrangement in an LPS

/ (m)

Figure D.3 - Diagram of the stresses F for the configuration of Figure D.2

IEC 2634/10

NOTE The peak current value is 100 kA and the length of the vertical conductor is 0,5 m.

Figure D.4 - Force per unit length F’ along the horizontal conductor of Figure D.2

D.4.2.1.2 Effects of electrodynamic forces

In terms of amplitude of applied force, the instantaneous value of the electrodynamic force F(f) is proportional to the square of the instantaneous current /(f)². In terms of the stress development within the mechanical LPS structure, expressed by the product of the elastic deformation <5(t) and the elastic constant к of the LPS structure, two effects should be considered. The natural mechanical frequency (linked with the elastic behaviour of the LPS structure) and the permanent deformation of the LPS structure (linked with its plastic behaviour) are the most important parameters. Moreover, in many cases the effect of the friction forces within the structure are also of significant importance.

The amplitude of the vibrations of the elastic LPS structure, caused by an electrodynamic force developed by the lightning current, can be evaluated by means of second order differential equations; the key factor is the ratio between the duration of the current impulse and the period of natural mechanical oscillation of the LPS structure. The typical condition encountered in LPS applications consists of natural oscillation periods of the structure much longer than that of the applied force (duration of the lightning current impulse). In this case the maximum mechanical stress occurs after the cessation of the current impulse and has a peak value that remains lower than that of the applied force. In most cases, maximum mechanical stress can be neglected.

Plastic deformation occurs when the tensile stress exceeds the elastic limit of the material. If the material composing the LPS structure is soft, for example aluminium or annealed copper, the electrodynamic forces can deform the conductors in corners and loops. LPS components should therefore be designed to withstand these forces and to show essentially an elastic behaviour.

The total mechanical stress applied to the LPS structure depends on the time integral of the applied force and therefore on the specific energy associated with the current impulse. It also depends on the shape of the current impulse and its duration (compared with the period of natural oscillation of the structure). All these influencing parameters must therefore be taken into account during testing.

D.4.2.2 Acoustic shock wave damage

When a lightning current flows in an arc a shock wave is produced. The severity of the shock is dependent upon the peak current value and the rate of rise of the current.

In general, the damage due to the acoustic shock wave is insignificant on metal parts of the LPS but can cause damage to surrounding items.

D.4.3 Combined effects

In practice, both thermal and mechanical effects occur simultaneously. If the heating of the material of the components (rods, clamps, etc.) is sufficient to soften the materials, much greater damage can occur than otherwise. In extreme cases, the conductor could explosively fuse and cause considerable damage to the surrounding structure. If the cross­section of the metal is sufficient to safely handle the overall action, only mechanical integrity need be checked.

D.4.4 Sparking

Sparking is generally important only in flammable environments or in the presence of combustible materials. In most practical cases, sparking is not important for LPS components

.Two different types of sparking can occur, i.e. thermal sparking and voltage sparking. Thermal sparking occurs when a very high current is forced to cross a joint between two conducting materials. Most thermal sparking occur near the edges inside a joint if the interface pressure is too low; this is due primarily to high current density and inadequate interface pressure. The intensity of the thermal sparking is linked to the specific energy and therefore, the most critical phase of the lightning is the first return stroke. Voltage sparking occurs where the current is forced to take convoluted paths, e.g. inside a joint, if the voltage induced in such a loop exceeds the breakdown voltage between the metal parts. The induced voltage is proportional to the self inductance multiplied by the steepness of the lightning current. The most critical lightning component for voltage sparking is therefore the subsequent negative stroke.

D.5 LPS components, relevant problems and test parameters

D.5.1 General

Lightning protection systems are made of several different components, each having a specific function within the system. The nature of the components and the specific stresses to which they are subjected, require special consideration when setting up laboratory tests to check their performance.

D.5.2 Air termination

Effects on air-termination systems arise from both mechanical and thermal effects (as discussed below in D.5.3, but noting that a high proportion of the lightning current will flow in an air-termination conductor which is struck) and also, in some cases, arc erosion effects, particularly in natural LPS components such as thin metal roof or wall skins (where puncture or excessive rear surface temperature rise may occur) and suspended conductors.

For arc erosion effects, two main test parameters should be considered, i.e. the charge of the long duration current and its duration.

The charge governs the energy input at the arc root. In particular, long duration strokes appear to be the most severe for this effect whilst short duration strokes can be neglected.

The duration of the current has an important role in the heat transfer phenomena into the material. The duration of the current applied during the tests should be comparable to those of long duration strokes (0,5 s to 1 s).

D.5.3 Down-conductors

Effects on down-conductors caused by lightning can be divided into two main categories: