Page 288 - Handbook of Electrical Engineering

274 HANDBOOK OF ELECTRICAL ENGINEERING

The quadrature axis reactances are those that can be represented on an axis at right angles
to the pole or direct axis. These reactances do not normally appear in the hand calculation of fault
currents.
When generators are being considered it is usually necessary to know the form and magnitude
of fault currents when a fault occurs close to the main terminals of the generators. Several aspects
of the fault current are of interest:
• The peak value of the fault current during the first cycle of instantaneous current. This value
determines the ‘peak asymmetrical’ duty of the switchgear connected to the generator. This value
is determined by the sub-transient reactance.
• The rms value of the symmetrical component of the fault current during the first cycle. This is
the first result obtained from the calculation process and from this is then calculated, or estimated,
the peak value mentioned above (due to the phenomenon called ‘current doubling’). This value is
determined by the sub-transient reactance.
• The rms value of the symmetrical component of the fault current several cycles after the fault
occurs. This value determines the ‘symmetrical breaking’ duty of the switchgear connected to the
generator. This value is determined by the transient reactance
• Occasionally a critical situation occurs in which the alternating fault current does not reach a zero
value, or becomes negative, until several cycles have passed, see sub-section 7.2.10 and Figure 7.1.
This is very important because the basis of interrupting fault current in a circuit breaker is highly
dependent on current zeros and crossing points occurring naturally in the circuit. When a current
zero occurs, the arc-gap has a short time to become de-ionised and the dielectric strength of the
insulating medium in the gap to be restored. While arcing occurs, these two processes cannot take
place and energy is released in the arc. If this process is overly delayed then too much energy will
be released in the arc and damage due to overheating can occur.
• The switchboard must be specified to withstand this peculiar situation and it is the task of the
engineer to investigate the possibility of it taking place, see sub-section 7.2.11. The controlling
factor that determines whether or not it takes place is the X-to-R ratio of the source impedance of the
generator and its connecting components (cables, busbars and transformers) up to the switchboard.
If X is very much larger than R then the phenomenon described may occur. The time constant T a
of the generator influences the time taken for a zero-crossing to occur.

11.5 CALCULATION OF FAULT CURRENT DUE TO FAULTS
AT THE TERMINALS OF A GENERATOR

11.5.1 Pre-Fault or Initial Conditions

Since the peak value of the fault current reduces in time due to the effects of the sub-transient and
transient reactances, it is necessary to establish a driving voltage suitable for each part of the process
and calculation. The concept used is one which assigns an emf ‘behind’ an appropriate impedance
of, in the case of generators, an appropriate reactance.
This is shown diagrammatically in Figure 11.5.