## THE IMPORTANCE OF THE X/R RATIO IN LOW VOLTAGE SHORT CIRCUIT STUDIES

The X/R ratio is important because it determines the peak asymmetrical fault current. The asymmetrical fault current can be much larger than the symmetrical fault current.  In some short circuit studies, the X/R ratio is ignored when comparing the short circuit rating of the equipment to the available fault current at the equipment. What is not always realized is that when low voltage gear is tested, it is tested at a certain X/R ratio.

Purpose of a Short Circuit Study

The purpose of a short circuit study is to determine whether or not electrical equipment is rated properly for the maximum available fault current that the equipment may see. There are essentially four types of faults:

three-phase
single line-to-ground
double line-to-ground
line-to-line

Each of these types of faults can result in different magnitudes of fault current. In all types,
however, there is a common element: an abnormally low-impedance path for current to flow. Such a
condition can lead to extremely high currents.

By Ohm’s Law, voltage equals current times impedance (resistance). Therefore, when the impedance becomes very low and the voltage does not change, the current becomes very high. Large electrical currents produce a lot of heat transfer, which increases the temperature of cables, transformers, etc.

Obviously, fault conditions are undesirable. Therefore, protective devices like circuit breakers and fuses are used to remove the short-circuited part of the system from the power source(s). These devices are meant to interrupt very large electrical current. However, there are limits to how many amps they can interrupt.

In AC electrical systems, impedance has two components. The first is called reactance (X). Reactance depends on two things: (1) the inductance and (2) the frequency. Inductance reflects how hard it is to change the current. All conductors have some inductance, but a more useful example of a component having inductance is a coil of wire. Frequency is fixed at either 60 or 50Hz, depending upon where in the world the electrical system is, so the reactance is solely dependent upon the inductance.

The second component of impedance is the familiar resistance (R). Resistance is a measure of how hard it is for current to flow. When current flows through a material having resistance, heat is transferred from the material to the surroundings.

The resistance and reactance of a circuit establishes a power factor. The power factor (p.f.) is given by the following equation:
p.f. = cos(tan-1(X/R))
If the power factor is unity (1), then the impedance only has resistance. If the power factor is zero, then the impedance only has reactance.

When performing short circuit calculations, it is important to consider the X/R ratio. The higher the X/R ratio, the higher the asymmetrical peak fault current. Therefore, when verifying the ratings of electrical equipment, both the symmetrical short circuit rating and the X/R ratio must be taken into consideration.

If the calculated X/R ratio is larger than the test X/R ratio, then the equipment short circuit rating must be de-rated by a multiplying factor. This multiplying factor equals the ratio of the calculated peak asymmetrical fault current divided by the peak asymmetrical current corresponding to the rated symmetrical current and the test X/R ratio.