RFL 9300 RFL Electronics Inc.
August 25, 2000 3 - 6 (973) 334-3100
3.7 PREFAULT LOAD SUBTRACTION
The current flowing through a transmission line is determined by the phase angle difference between the gen-
eration at either bus. This angle difference is generally in the ten to thirty degree range. So long as there is no
internal fault the currents entering the zone of protection will equal the currents leaving it. It’s true that there will
be line-charging current differences but for the purposes of this discussion they can be neglected. For 2-
terminal applications the currents at the terminals are generally well behaved. The time correspondence be-
tween the half-cycle current integrals at the local and remote terminals is fairly easy to maintain.
When an internal fault occurs the generator angles come into play. The fault tends to separate the system and
the current flow to the fault is now a function of the generator voltage and line fault impedance. For phase-to-
phase and 3-phase faults the phase angle between the local and remote terminal currents is approximately
equal to the generator angle difference. This relationship is modified to some degree for ground faults because
of fault resistance. Since both terminals see the same currents, through faults do not present a phase angle
problem. The end result of this discussion is that for 2-terminal systems we can expect phase angle differences
for internal faults but since the CCS “nesting” tolerance approaches 4ms (90 degrees) these angular differences
pose no particular problem for the relay.
When 3-terminal systems are considered the situation changes radically. A fault simulator was used to generate
an external fault on a tie line between terminals M and R in a 3-terminal system similar to that represented by
the single line diagram shown in Figure 3-8. The waveforms shown in Figure 3-9 represent the Phase A current
seen at each of the terminals. The generator angle difference was 40 degrees. Admittedly a generator angle
this large is rare but it’s useful for purposes of illustration. Note that even though the waveforms represent an
external fault there are wide phase angle shifts for the relay to contend with. This phase shift cuts into the 4ms
margin allowed for communications channel delay error between the terminals.
The effects of generator angles and fault impedance can be eliminated if only the fault current component of the
total post fault current is considered. The concept is best illustrated by considering the 3-terminal one-line dia-
gram shown in Figure 3-8. The fault type being considered is a symmetrical 3-phase fault. This is easy to visual-
ize as it consists of only positive sequence currents. The fault is represented in a) by a shorting switch. In b) the
shorting switch has been replaced by a pair of voltage generators with the same value and opposite polarity.
Since the voltage from the fault to neutral is Vf - Vf =0 this is a valid substitution. Using superposition tech-
niques the equivalent network is now broken down into two parts as shown in c) and d). Let’s consider the volt-
age Vf to be the open circuit voltage at the fault point just prior to the fault. In d) we see that voltage source Vf
will oppose the flow of any current in that branch of the circuit. Because the circuit branch with voltage source Vf
has no current flow it can be removed from the circuit and we end up with e) which is equivalent to the original
circuit in a). The only difference is that the reactances have been converted into their Thevenins equivalent
values. Therefore the current flowing in the equivalent circuit represented by e) must be the prefault load cur-
rent.
Now consider c). There is nothing to oppose current flow in the branch containing voltage source Vf. Since
there was no current flowing in this circuit branch prior to the fault this current must be the fault current. The
important point to note here is that the Thevenins equivalent impedance of the three circuit branches are being
driven in parallel by Vf. Regardless of the angle of this voltage, as long as the impedance angles of each branch
are the same, the phase angle of the fault current in each branch will be the same. This will essentially eliminate
the generator angles and fault resistance from consideration.
Prefault load subtraction was applied to the fault waveforms shown in Fig 3-9 with the result shown in 3-10. No-
tice how the waveforms line up essentially restoring the entire 4ms communications error margin to the relay.
When the RFL 9300 relay is configured for 3-terminal operation its control algorithms, for the most part, are
based on transient fault currents obtained using prefault load subtraction.
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