For the proper coordination of protective devices on a distribution
system, it is essential that the magnitude be known of the fault current
which they may be called upon to handle. For dc systems, the calculation
is a relatively simple application of Ohm’s law; for ac systems, the
procedures are more complex, but for most problems, practical solutions
permit simplified procedures.
For ac systems, four general types of faults can be considered: three
phases short-circuited together (with or without a ground), phase to
phase to ground, phase to phase, and single phase to ground.
Actual Fault Current
The actual fault current may be broken into two components, ac
and dc. The simplified equations give values of the ac, or steady-state,
component, which remains constant throughout the duration of the
fault. The value of this current follows Ohm’s law and is equal to the
voltage divided by the impedance of the circuit from the source to the
point of fault.
Standard measurement of the two components is taken at one-half cycle after the start of the fault.
The total (root mean square) fault current is the square root of the sum
of the squares of the two components; this composite rms current is not
symmetric, and is known as the asymmetric current.
The magnitude of the total fault current during the transient period,
therefore, depends on the type of fault and the time of its initiation.
After the transient period, the magnitude of the fault current depends
only on the type of fault.
The time of fault initiation is measured angularly along the voltage
wave, i.e., as a number of degrees from a known point, such as peak voltage
or voltage zero. Since there is usually a phase angle between voltage
and current, a fault will occur at a different point on the current wave.
If it occurs at the ac component peak, maximum transient current
occurs. This dc component is equal to the difference between the instantaneous
values of the ac fault current and the ac load current. Maximum
transient current occurs at the ac component peak, but maximum rms
fault current occurs at voltage zero. The transient component is zero
when the fault occurs at the time the instantaneous values of the load
current and steady-state current are equal. Between the maximum and
zero transient points, a transient component will exist in which the rms
fault current is less than the rms current when the fault occurs at voltage
zero. Since protective devices operate during transient periods, they are
designed to interrupt the maximum possible fault current.
Factors of Asymmetry
As the reactance to resistance ratio (X/R) and the power factor of
a faulted circuit change, the magnitude of the asymmetric current will
vary with respect to the symmetric current. As this ratio increases and
the power factor decreases, the asymmetric current will increase. A ratio,
known as the factor of symmetry, of the asymmetric to the symmetric
current can be found for different X/R ratios and corresponding power
factors.
When the symmetric current and the X/R ratio are known, the
maximum asymmetric current can be found. This is useful in the design
of fuse cutouts which are rated asymmetrically.
