Annex A of IEC 62305-4 allows estimating the magnetic field lightning creates inside a protection zone and the voltage it induces in a cable loop. For a direct strike it uses the mesh width of the shield and the distances to wall and roof. For a nearby strike it uses the external field and the shielding factor SF. The induced voltage is proportional to the loop area and to the rate of change of the field.
Short answer. Annex A of IEC 62305-4 gives a method for estimating, without simulation, the magnetic field a lightning stroke produces inside a protection zone and the voltage it induces in a loop formed by cables. The result is compared with what the equipment can withstand. The formulas are first-order approximations, and the standard offers them as a method in the absence of a theoretical study or an experimental measurement of the shield.
Which lightning parameters are used
Table A.1 of the standard takes three lightning components per protection level (I, II, III and IV):
| Component | Waveform | Peak current by level I – II – III – IV |
|---|---|---|
| First positive stroke (IF) | 10/350 µs | 200 – 150 – 100 – 100 kA |
| First negative stroke (IFN) | 1/200 µs | 100 – 75 – 50 – 50 kA |
| Subsequent strokes (IS) | 0.25/100 µs | 50 – 37.5 – 25 – 25 kA |
Magnetic induction depends mainly on the rise front of the field. The standard represents it with damped oscillations: 25 kHz for the first positive stroke (time to peak 10 µs), 250 kHz for the first negative (1 µs) and 1 MHz for subsequent strokes (0.25 µs). These are the same waveforms as the IEC 61000-4-9 and IEC 61000-4-10 tests.
Field inside the zone from a direct strike
If lightning strikes the structure, the current flows through the zone’s own shield (Annex A.4.1.1). At a point in LPZ 1 the peak field is:
H1 = kh × I0 × wm / (dw × √dr)
where I0 is the lightning current (A), wm the mesh width of the shield (m), dw the shortest distance from the point to the wall (m), dr the shortest distance to the roof (m) and kh a configuration factor, typically 0.01 (1/√m). The note in the standard says the field is divided by 2 if there is a meshed bonding network under clause 5.2. Equations A.2 to A.4 apply the formula to each lightning component with its peak current.
Table A.2 gives examples with I0/MAX = 100 kA and a 2 m mesh:
| Shield (L × W × H) | H1/MAX at the centre | H1/MAX near the wall (dw = ds/1) |
|---|---|---|
| 10 × 10 × 10 m | 179 A/m | 447 A/m |
| 50 × 50 × 10 m | 36 A/m | 447 A/m |
| 10 × 10 × 50 m | 80 A/m | 200 A/m |
The distance to the roof is taken as half the height, and the distance to the wall as half the length at the centre, or as the safe distance ds/1 in the worst case. The field is clearly much higher next to the wall than at the centre.
Field from a nearby strike
If lightning strikes nearby, the external field is approximated as a plane wave:
H0 = I0 / (2 × π × sa)
where sa is the distance between the point of strike and the centre of the protected volume. Inside LPZ 1, the field is reduced by the shielding factor SF (in dB) of the shield, which comes from Table A.3 of the standard (copper or aluminium: SF = 20 × log(8.5 / wm), with wm in metres):
H1 = H0 / 10^(SF/20)
The unfavourable case is the highest current at the shortest possible distance. That distance sa depends on the height H and length L of the structure and on the radius r of the rolling sphere corresponding to the peak current: r is 313 m for level I (200 kA), 260 m for II (150 kA) and 200 m for III and IV (100 kA). For H less than r, the standard gives:
sa = √(2 × r × H − H²) + L / 2
and for H greater than or equal to r, sa = r + L / 2. At shorter distances, lightning strikes the structure directly.
With a copper grid with a 2 m mesh (SF = 12.6 dB) and I0/MAX = 100 kA, Table A.5 gives:
| Shield (L × W × H) | sa | H0/MAX | H1/MAX |
|---|---|---|---|
| 10 × 10 × 10 m | 67 m | 236 A/m | 56 A/m |
| 50 × 50 × 10 m | 87 m | 182 A/m | 43 A/m |
| 10 × 10 × 50 m | 137 m | 116 A/m | 27 A/m |
In LPZ 2 and subsequent zones almost no partial lightning currents flow, and the reduction from one zone to the next is assessed as for a nearby strike: Hn+1 = Hn / 10^(SF/20), with the SF of the inner zone’s shield.
Voltage and current induced in a loop
To estimate the induced voltage, the standard considers rectangular loops (Figure A.14): width b and length l, formed by power or signal lines and the equipment. If the loop has another shape, it is transformed into a rectangle of the same area.
Nearby strike or LPZ 2 and subsequent zones (homogeneous field, Annex A.5.3). The maximum open-circuit voltage is:
UOC/MAX = μ0 × b × l × H1/MAX / T1
with μ0 = 4π × 10⁻⁷ Vs/(Am) and T1 the front time of the field. The maximum short-circuit current is ISC/MAX = μ0 × b × l × H1/MAX / LS, where LS is the self-inductance of the loop and the wire resistance is neglected, which is the unfavourable case. With the field in A/m, length and width in m and voltages in V, the standard develops the coefficients: UOC/F/MAX = 0.126 × b × l × H1/F/MAX for the first positive stroke (T1 = 10 µs), 1.26 × b × l × H1/FN/MAX for the first negative (1 µs) and 5.04 × b × l × H1/S/MAX for subsequent strokes (0.25 µs).
Direct strike to the structure (Annex A.5.2). The voltage also depends on the distance from the loop to the wall and roof of the shield, and uses a logarithmic function of l / dl/w. Each lightning component has its own equation with its own coefficients.
Example using the standard’s figures
Take shield type 1 in Table A.5 (2 m copper grid, 10 × 10 × 10 m structure) and a nearby level III strike, with H1 = 56 A/m for 100 kA. A loop 1 m wide and 10 m long (10 m² area) would give:
- First positive stroke, IF = 100 kA: 0.126 × 1 × 10 × 56 ≈ 71 V.
- First negative stroke, IFN = 50 kA (28 A/m): 1.26 × 1 × 10 × 28 ≈ 353 V.
- Subsequent strokes, IS = 25 kA (14 A/m): 5.04 × 1 × 10 × 14 ≈ 706 V.
Although the subsequent stroke has the lowest current, it produces the highest induced voltage, because its front is the fastest. If the loop is reduced to 1 m × 1 m (a tenth of the area), the voltage falls to a tenth. The values are compared with the withstand voltage of the equipment and its interfaces, for example with the overvoltage categories of IEC 60664-1 and the test levels of IEC 61000-4-5. This example illustrates the method; it does not replace the calculation for a real installation.
- Can lightning strike the structure that forms the zone?
- Yes: Is the zone LPZ 1?
- Yes: Field with kh, wm, dw and dr (Eq. A.1 to A.4), inside the safe volume ds/1
- No: Start from the field in the previous zone and reduce it with the shield SF (Eq. A.19)
- No: Does lightning strike near the structure?
- Yes: External field H0 = I0 / (2π·sa) and reduction with SF (Eq. A.7 and A.11)
- No: Assess the surge conducted along the line, with the SPDs at the entrance
- Yes: Is the zone LPZ 1?
Limits of the method
- These are first-order approximations. The standard warns that the real field inside the shield is more complex than that of the formulas, with sign changes in its components, and that measurements show a smaller rise of the field near the wall than calculated.
- They are valid only inside the safe volume, at distances from the wall greater than the mesh width wm.
- A shield can be verified with a low-level measurement, using a current generator of the same waveform and a field probe (Annex A.4.3).
Guides in the same series
The induced voltage is used to select the shielding and cable routing: see magnetic shielding and cable routing and SPM against LEMP. The zones in which the field is assessed are defined in lightning protection zones (LPZ). The risk to sensitive equipment is assessed in lightning risk management, and the SPDs that limit the voltage reaching it are in coordinated SPDs.
When to call us
Estimating the induced voltage in an installation requires the building dimensions, the shield mesh, the routing of each cable and the withstand levels of the equipment. If you need to review a control room, a plant or a substation, our engineering design and studies team can support you on the secondary design and the earthing. Write to us through the contact page.
Related guides
- IEC 62305: lightning protection, what each part covers
- Magnetic shielding and cable routing against lightning
- SPM against LEMP: what they are and how they are managed
- Lightning protection zones: LPZ 0A, 0B, 1 and 2
- Electromagnetic compatibility of switchgear
References
- IEC 62305-4:2010, Protection against lightning, Part 4: Electrical and electronic systems within structures: Annex A, clauses A.3 to A.5 (Equations A.1 to A.42, Figures A.7 to A.14, Tables A.1 to A.5).
- IEC 60664-1, IEC 61000-4-5, IEC 61000-4-9 and IEC 61000-4-10.
Frequently asked questions
Which stroke produces the highest induced voltage in a loop?
With the currents of IEC 62305-4 for protection levels III and IV, subsequent strokes, with a very short front (0.25 µs), induce more voltage than the first stroke, even though their current is lower. The voltage depends on how fast the field rises, not only on its peak value.
Why must equipment be kept at a certain distance from the shield wall?
Because near the wall, where partial lightning currents flow, the field is higher. The formulas of Annex A are valid only inside a safe volume that keeps a distance ds from the wall: ds = wm × SF / 10 if SF is 10 dB or more, and ds = wm if it is less.
What if the loop is a shape other than a rectangle?
The standard says to transform the loop into a rectangle of the same area and apply the formulas with the dimensions of that rectangle, width b and length l. That is why the routing of cables, which changes the area, changes the induced voltage in the same proportion.