Page 49 - Electrical Safety of Low Voltage Systems

32 Chapter Three

where the subscript i indicates the ith PM and n indicates the total
number of PMs.

3.3 Risk of Indirect and Direct Contact
How can we evaluate the risk a person is subject to when interact-
ing with electrical items? Basically, three simultaneous adverse events
must occur to expose a person to damage (i.e., physical injuries, death)
caused by indirect contact:

1. A surface potential must appear on the equipment enclosure
2. Person must touch the enclosure
3. The surface potential’s magnitude must exceed the safe limits

The above conditions are tied together by a logic “AND” and so re-
moving just one of them makes the hazard disappear.
The logic AND corresponds to the algebraic multiplication sign;
hence, the probability that the above-described events occur, and
therefore the magnitude of the residual risk r(t) at any given time
after PMs have been applied can be evaluated by Eq. (3.5).

r(t) = [1 − S(t)]k(t)v(t) (3.5)

where [1−S(t)] is the probability that the enclosure is energized due
to an internal fault, which “perforates” the basic insulation. This term
is also referred to as insecurity.
k(t) is the probability that a person touches the faulted enclosure.
For example, hand-held devices can perform their function only if
held, and therefore, k(t) = 1; the same applies to restrictive locations
(e.g., metal tanks), where workers may be in permanent bodily contact
3
with electrical equipment due to limited freedom of movement. On
the contrary, appliances in ordinary locations (e.g., dishwashers) can
operate even in the absence of persons, ergo the probability that they
are touched during a fault is very low, and k(t) is well below 1.
v(t) is the probability that the touch voltage exceeds the dangerous
values and/or the maximum durations established by technical stan-
dards in reference to a person’s body resistance. v(t) depends on the
magnitude of the fault potential, which may reach the same value as
the system nominal voltage, if the grounding/bonding is not effective
or is missing.
To reduce r(t), at least one of the factors in Eq. (3.5) must be kept
as close to zero as possible. When k(t) < 1, the preferred approach is to
lower v(t) by limiting the time the fault potential persists on the enclo-
sure by prompt automatic disconnection of supply. If k(t) = 1, Class II
equipment, which lowers the factor [1−S(t)], may be the best choice.