1. Introduction
2.Three phase fault calculations
3.Symmetrical component analysis of a three-phase network
4.Equations and network connections for various types of faults
5.Current and voltage distribution in a system due to a fault
6.Effect of system earthing on zero sequence quantities
7. References
1. Introduction
A power system is normally treated as a balanced symmetrical three-phase network. When a fault occurs, the symmetry is normally upset, resulting in unbalanced currents and voltages appearing in the network. The only exception is the three-phase fault, which, because it involves all three phases equally at the same location, is described as a symmetrical fault. By using symmetrical component analysis and replacing the normal system sources by a source at the fault location, it is possible to analyse these fault conditions.
For the correct application of protection equipment, it is essential to know the fault current distribution throughout the system and the voltages in different parts of the system due to the fault. Further, boundary values of current at any relaying point must be known if the fault is to be cleared with discrimination.
The information normally required for each kind of fault at each relaying point is:
a. maximum fault current
b. minimum fault current
c. maximum through fault current
To obtain the above information, the limits of stable generation and possible operating conditions, including the method of
system earthing, must be known. Faults are always assumed to be through zero fault impedance.
Three-phase fault calculations
Three-phase faults are unique in that they are balanced, that is, symmetrical in the three phases, and can be calculated
from the single-phase impedance diagram and the operating conditions existing prior to the fault.
A fault condition is a sudden abnormal alteration to the normal circuit arrangement. The circuit quantities (current and voltage)
will alter, and the circuit will pass through a transient state to a steady state. In the transient state, the initial magnitude of
the fault current will depend upon the point on the voltage wave at which the fault occurs. The decay of the transient condition,
until it merges into steady state, is a function of the parameters of the circuit elements. The transient current may be regarded
as a d.c. exponential current superimposed on the symmetrical steady state fault current. In a.c. machines, owing to armature
reaction, the machine reactances pass through ‘sub transient’ and ‘transient’ stages before reaching their steady state
synchronous values. For this reason, the resultant fault current during the transient period, from fault inception to steady state
also depends on the location of the fault in the network relative to that of the rotating plant.
In a system containing many voltage sources, or having a complex network arrangement, it is tedious to use the normal system voltage sources to evaluate the fault current in the faulty branch or to calculate the fault current distribution in the system.
A more practical method [Ref A3.1: Circuit Analysis of A.C.Power Systems] is to replace the system voltages by a single
driving voltage at the fault point. This driving voltage is the voltage existing at the fault point before the fault occurs.
Consider the circuit given in Figure A3.1 where the driving voltages are E and E , the impedances on either side of fault
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