Page 700 - Industrial Power Engineering and Applications Handbook

20/660 Industrial Power Engineering and Applications Handbook
20.2 Analysis of ungrounded and = JIi2 + Ip" + 2. I; .I; . COS. 60" (as in Section
grounded systems 15.4.3)

This is related more to an HT system.
= 1; (but this current may not be enough to trip
20.2.1 Analysis of an ungrounded system
a protective relay)
This is common to
The voltage across the healthy phases is now fi times
A three-phase three-wire, star connected isolated neutral or 73% more than the phase to neutral voltage under
system, healthy conditions.
A delta connected system, or Under certain line to ground impedance conditions,
A three-phase four-wire, ungrounded system. when the ground circuit may also contain some inductive
reactance, the voltage of the healthy phases may rise
An ungrounded a.c. system is more often subject to over- further, much above the system voltage, due to resonance
voltages. The reason is that even when the system is not and ferro-resonance effects (see below). All this in turn
connected to ground, it makes a ground connection through may tend to swing the system to an unstable state. It may
the coupling of the leakage ground capacitances, as also cause arcing grounds* at the supporting insulators,
illustrated in Figure 20.2. For all purposes these capaci- leading to voltage surges, travelling in both directions
tances may be regarded as equal and uniformly distributed, along the line, and may be enough to cause damage to
providing a balanced system. In the event of a ground the line insulators and the terminal equipment.
fault, this circuit is closed as shown and a capacitive The magnitude of overvoltage will depend upon the
current, I',, flows back to the healthy phases via these actual inductive reactance introduced through the ground
capacitances Cg, Analysing the circuit of Figure 20.2, circuit. The unintentional introduction of an impedance
the following may be derived: into the ground leakage capacitive circuit is generally a
result of a ground fault in the main equipment such as a
If C, = electrostatic or leakage capacitance to the gcncrator, a transformer, power capacitors or an induction
ground per phase, providing the return path to motor and when one or more of their phase windings
the fault current Ig, in the event of a ground forms a part of the ground circuit, as illustrated in Figure
fault on the system. This current will be 20.3. Under such conditions, they will introduce their
capacitive in nature. own inductive, capacitive or resistive impedances or a
Xcg = ground capacitive reactance per phase combination of them into the ground circuit and alter the
parameters of the ground capacitive circuit. Figure 20.5
illustrates the system of Figure 20.2, drawn simply on a
singlc phase basis. The current through the ground circuit
Under transient conditions, f becomes surge frequency, will be zero when the system is healthy, the ground leakage
fs and capacitances finding no return path (Figure 20.6). It is
not necessary that the equipment itself should develop a
1
Xc, becomes, ground fault and then only its impedance will be inducted
2xfs . C, into the ground circuit. It may be introduced into the
1 circuit even when there is a line or a system ground
where fs = fault, as illustrated in Figure 20.4. The ground circuit
27c J l may give rise to dangerous voltages in the healthy phases,
L being the inductance of the circuit. as analysed below.
If I, = ground fault current
V, = ground potential, which is the same as zero (1) When the external impedance is a resistance
sequence voltage or residual voltage or a capacitive reactance
Vt = line voltage and
Vp = phase voltage Referring to Figure 20.5, if Z; is the external impedance
introduced into the natural leakage ground circuit, as a
then on a ground fault, say, in phase R, the voltage across consequence of a ground fault, as shown in Figures 20.3
this phase will reduce to zero, while the ground potential
across the healthy phases will rise to V, from a zero level
earlier. It will cause a fault current Zi, in the healthy * Arcing grounds: This occurs during a temporary ground fault on
phases also, through the ground leakage capacitances an ungrounded HT system. It causes an arc between the line conductor
such that I: = VI/X,, (assuming the ground circuit has and the ground, which may be direct or through the flashover of the
line insulators, due to overvoltage. The ground leakage capacitors
no other impedance) and the ground fault current through that may be considered as charged with the line voltage are discharged
the grounded circuit, to the ground on developing a ground fault. The supply voltage
_- would charge them again and so the process will repeat until the
I, = I, + I, fault exists. The repeated discharges and charges of ground capacitors
during the fault produce arcs and are termed arcing grounds, giving
= r,' + I,' (both phasors being 60" apart) rise to voltage surges.