150 HANDBOOK OF ELECTRICAL ENGINEERING
Suppose the generator is connected to a nearby switchboard. The generator and busbar section
circuit breakers will need to at least withstand the fault current given in (7.1). The equation consists
of three essential parts:-
- Fundamental AC part.
- DC part.
- Double frequency AC part.
7.2.8 Fundamental AC part
This starts with high values of sinusoidal current that are determined byXd′′. After about 20 cycles the
current will have decayed to a value determined byXd. This part is symmetrically distributed above
and below the zero axis. During the sub-transient and transient early period the automatic voltage
regulator (AVR) action in the generator may be ignored since it will not have had time to respond.
However, during the later period in the steady state the AVR will have caused the field current to
reach and stay at its ceiling (maximum) value. This means thatVpkin (7.1) will have effectively risen
by up to 170% of its prefault value. This aspect is more significant for the breaking duty of the circuit
breakers. Reference 4 gives a method of calculating the decrement of short circuit for a generator,
which includes a modification to the basic equations so that the effect of the AVR and exciter can
be included. Figure 12.3 implements this method and shows the effect of AVR response in terms of
the rms fault current. The method is well suited for programming in a small desktop computer.
7.2.9 DC part
It is a particular characteristic in the solution of differential equations involving resistances and
inductances that a DC component accompanies the symmetrical AC component. The magnitude of the
DC component can equal that of the peak AC component since both are determined byXd′′. The decay
of the DC component can be reasonably slow and is determined byTawhich is a function ofXd′′and
the armature winding resistanceRa. With machines that have significant values ofX′′dand particularly
low values ofRa, the value ofTacan become relatively high. WhenTais high in relation toTd′′and
Td′it is possible that the initial AC decay is faster than the DC decay. When this happens the AC
instantaneous current does not reach zero until several cycles have passed. This puts an extra strain on
the circuit breaker and can cause problems at the point when it starts to open to clear the fault current.
Hence the circuit breakers and the busbars in the switchboard may have to be derated for the
breaking duty. The amount of DC component, or ‘off-set’ as it is often called, depends upon the point
in time set byφowhen the fault is applied. The occurrence of 100% off-set is seldom but cannot be
ignored. The design and selection of the switchboard should be based on 100% off-set, especially if
it is fed by generators and feeds a group of high voltage motors.
7.2.10 Double frequency AC part
A small double frequency part occurs due to sub-transient saliency of the rotor pole surfaces. Often the
data from the manufacturer are not good enough to distinguish betweenXd′′andXq′′. The quadrature
axis parameters are difficult to obtain from the normal factory tests. It is usually adequate to assume
thatX′′qequalsX′′dand so the double frequency component becomes zero and can therefore be ignored.