Page 250 - Electrical Safety of Low Voltage Systems

Testing the Electrical Safety
233
FIGURE 14.11
Phasor diagram of
voltages and
currents of the
fault-loop test
circuit in TN
systems.
Thus, by solving Eq. (14.9) for Z Loop , we obtain
V ph − V V ph − V
Z = R × = (14.10)
Loop
V I
where I is the test current flowing through R.
The above Eq. (14.10) is a complex number in which voltages and
currents are also symbolized via phasors. Each phasor has a magni-
tude (i.e., the r.m.s. values of the quantity) and an angular phase (i.e.,
the argument of the complex number), and both must be considered
in the determination of Z Loop .
To clarify this concept, let us represent all the phasor quantities in
Eq. (14.10) by applying the Kirchhoff’s voltage law to the fault-loop,
as follows:
V − RI = Z I = R Loop I + jX Loop I (14.11)
ph Loop
The phasor diagram in Fig. 14.11 graphically represents Eq. (14.11).
It can be noted that V ph and V are not in phase, but displaced by
the angle . Thus, the loop-tester must return the following value:
|V ph − V|
|Z Loop |= (14.12)
|I|
where the numerator is the magnitude of the vectorial difference be-
tween the complex numbers representing the voltages, and the de-
nominator represents the magnitude of the current phasor.
If X Loop were negligible with respect to the resistance (e.g., X Loop ≤
0.1|Z Loop |), the fault-loop would essentially be resistive and the test
might just assess the fault-loop resistance. This may happen when the
fault-loop is madeof conductors havingsmall cross-sectionalarea (i.e.,
2
S ≤ 95 mm ), or the circuit is far from large transformers or generators.
V ph and V would then be practically in phase with each other, thereby,
allowing the simplification of Eq. (14.12) as follows:
|V |−|V|
ph
|Z Loop | = R Loop = (14.13)
∼
|I|