Page 114 - Electrical Safety of Low Voltage Systems

TT Grounding System 97

As explained in Chap. 4, in low-voltage systems, we conserva-
tively consider persons exposed to the prospective touch voltage V ST ,
instead of the touch voltage V T (V ST > V T ). Consequently, we discon-
nect the branch containing (R B + R BG ) in Fig. 6.2, as we calculate the
touch voltage prior to the person’s contact.
3
By applying Millmann’s theorem to the circuit in Fig. 6.1, we
obtain the magnitude of the prospective touch voltage V ST :

(V ph /R N ) R GT 1
V ST = = V ph × = V ph ×
(1/R GT ) + (1/R N ) R GT + R N 1 + (R N /R GT )
(6.1)

The negligibility of the phase and protective conductors’
impedances in Eq. (6.1) show that the location of the fault, directly
related to the aforementioned impedances, has no influence on the
magnitude of the prospective touch voltage. V ST , therefore, is a con-
stant value regardless of where the ground fault occurs, but does de-
pend on the system ground resistance of the distributor R N , which is
generally unknown to the designer and is out of his/her control.
In order for V ST to be harmless to persons, R N should ideally be
very large and R GT very low. Figure 6.3 shows the prospective touch
voltage V ST as a function of R GT for three increasing values of R N
(1, 10, and 100 ) in correspondence with a phase-to-ground voltage
V ph of 230 V.
It is clear that a larger R N improves safety for any fixed value
of the user ground. In practice, in urban areas, the utility grounding
system at the supply substation may be interconnected in parallel to
the earths of other substations via the metal sheath/armor of cables
and/or the overhead lightning protection wire. Therefore, the value of
R N is typically very low (i.e., fraction of ohms). This may not be true in
rural environments, where pole transformers may only be grounded
locally and have an earth resistance R N of tens of ohms.
It is important to note that in urban areas, the protection offered
by the sole user’s grounding system does not guarantee the safety of
persons, because, as shown in Fig. 6.3, for R N = 1, the prospective
touch voltage is not sufficiently low to be harmless and nearly coin-
cides with the phase-to-ground potential as R GT increases. To clarify
this concept, let us calculate by applying the voltage divider, the value
that R GT should reach in order to limit V ST to the nondangerous value
of 25 V (see Fig. 5.19), when V ph equals 230 V and R N equals 1 :

R GT
25 = 230 × ⇒ R GT = 0.12 (6.2)
R GT + 1
The above value is rather difficult to achieve for the users, whose
earth resistance ranges in the order of tens of ohms, depending on