Electrical Safety Engineering of Renewable Energy Systems. Rodolfo Araneo

the temperature and/or duration are not sufficient to cause necrosis of the epidermis but only reddening of the skin. T_A is the locus representing the complete trans-epidermal necrosis.

      The surface of photovoltaic arrays in full sun can exceed the ambient temperature by 30°C or more, which may easily produce temperature greater than 60˚C. It is therefore apparent that PV modules’ surface with temperatures exceeding 64˚C can only be contacted for 1 s before skin injury occurs.

IEC 60364-4-42⁶ requires that accessible parts of electrical equipment within arm’s reach do not attain temperatures exceeding the limits given in Table 1.8, to prevent burns caused by contact with heated surfaces.

Table 1.8 Temperature limits in normal service for accessible parts of equipment

Accessible parts	Material of accessible surfaces	Maximum temperatures (°C)
A hand-held part	Metallic	55
	Non-metallic	65
A part intended to be touched but not hand-held	Metallic	70
	Non-metallic	80
A part that does not need to be touched for normal operation	Metallic	80
	Non-metallic	90

      The above temperature limits vary according to whether the part is intended to be hand-held or touched during normal use, and are based on the nature of the material of the accessible surface; they do not apply to equipment for which a maximum temperature is specified in the relevant product standard.

      The temperature limits of Table 1.8 are rather large, and it would be prudent to be well below those values; if not possible, the equipment in question might be fitted with guards to prevent accidental contact.

      1.6 Ground-Potential and Ground-Resistance

A ground electrode is a conductive part, embedded in the soil or in another conductive medium (e.g., concrete), which is in electrical contact with the earth [22].

      A connection to the ground can also be made through metalwork not forming part of the electrical installation, such as structural steelwork, metal, water supply pipes, or other buried metalwork. Such metalwork, however, should not be relied upon as an electrode, as it could be removed or replaced without any warning to users. The safety purpose of ground-electrodes is to effectively dissipate fault-currents into the soil.

      To illustrate the relationship between ground-potentials, ground-resistances, and ground-currents, we study a hemispherical electrode, as this will allow the understanding of the performance of electrodes of different geometry.

We consider a hemisphere of radius r0 embedded in a boundless and uniform soil of resistivity ρ, buried at a sufficient distance from a receiving electrode, and that the ground-current i leaking from this electrode flows radially into the soil (Figure 1.8).

      Figure 1.8 Hemispherical ground-electrode.

      The current density J→, identified as a vector quantity, through a surface S in the soil of infinitesimal thickness dl, r from the center of the hemisphere, is related to the uniform leakage current i through the flux operator expressed in Eq. 1.5.

(1.5)

      Equation 1.5 yields:

       (1.6)

where r^ is the unit vector in the radial direction.

      The electric field E→at any distance r from the center of the hemisphere can be determined as:

       (1.7)

      The ground-potential on the soil surface at any distance r from the center of the hemisphere, which is taken zero at infinity, is:

(1.8)

The ground-potential V(r) features a hyperbolic distribution through the soil, with the coordinate axes as asymptotes (Figure 1.9 ).

      Figure 1.9 Hyperbolic distribution of the ground-potential V(r) over the soil.

      The equipotential surfaces are hemispheres, including the actual surface of the electrode. Points belonging to the same equipotential surface have equal potential both on the surface and deep in the soil. Current lines are perpendicular to such surfaces.

      The ground-potential rise on the surface of the hemisphere, that is, the potential at the distance r0 from its center, is

(1.9)

      We define the resistance RG of the hemisphere-electrode to earth (from now on the ground-resistance) as the ratio of the ground-potential rise VG to the leakage current i (Eq.