Rodolfo Araneo

Electrical Safety Engineering of Renewable Energy Systems


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the temperature and/or duration are not sufficient to cause necrosis of the epidermis but only reddening of the skin. TA 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.

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 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.

      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.

      Equation 1.5 yields:

      J with rightwards arrow on top equals fraction numerator i over denominator 2 pi r squared end fraction r with hat on top comma f o r space r greater than r subscript o (1.6)

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

      F equals I subscript r e f end subscript over I subscript h (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:

      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

      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.