# What is the Importance of X/R Ratio?

Electrical Engineers need to know the importance of X/R ratio in doing fault calculations. This ratio can actually determine the peak asymmetrical fault current. Accordingly, the asymmetrical fault current can be way higher than the symmetrical fault current.

#### Fault Currents

Fault calculation is important in electrical design since it determine whether or not the ratings of the protective devices and cable is suitable to handle the worst scenario that an electrical system can encounter. Also, the value of fault current in the system can help to determine the right specification of current transformer used in protective relaying.

The fault calculation can be done using manual method for small installations but it is practical to use computer software to hasten the process. Also, the computer tools can easily perform the coordination among protective devices and between protective devices and cable.

Ohm's Law tells us that the current is equal to the voltage divide by the value resistance (or impedance). In this case, the relationship of the voltage and current is inversely proportional. When the impedance of the circuit will approach to zero as a manifestation of short circuit condition, the value of current will tend to approach the highest possible value which create thermal stress to the cable and transformers causing breakdown of the insulating materials. In the same way, the short circuit condition will also produce high magnetic forces that has the capability to bend busbars in switchgears and panel boards. The enormous value of magnetic force has a value proportional to the square of fault currents.

#### Protective Device

Normally, the protective devices installed in several low voltage system uses circuit breaker and fuses. These devices are tasked to eliminate the short circuit as quick as possible. Medium and high voltage system has an additional means to protect the circuit.

#### The Importance of X/R Ratio

The equipment like transformer, motor, generator and transmission lines are inherently inductive which gives a small value of X/R ratio. When there is a short circuit in the system, the RMS value of the symmetrical fault current is determined by the system source voltage and the total system impedance to the point of fault. However, almost all faults involve significant asymmetry in at least one phase. This asymmetry is treated in analysis as a dc component, which must be combined with the ac symmetrical component to give a new current value, the RMS asymmetrical value. It is the value of the RMS asymmetrical current at the moment of contact part which a circuit breaker must interrupt.

It is important to note that the dc component of the fault current decays rather rapidly, reaching an insignificant value in a matter of 3 to 5 cycles of the power frequency. In this process, the rate of decay is determined by the X/R ratio of the circuit at the point of fault. That means, if the value of the ratio is higher then the DC component decay is slower which prolongs the danger as a result of the fault.

Modern circuit breakers are tested with a prescribed standard values of X/R. For example, the circuit breakers both low and high voltage, the ANSI standards require this X/R ratio to be 6.6 or
higher, corresponding to a power factor of 15% or less. For a given level of symmetrical fault current and
a given circuit breaker contact part time, this X/R ratio establishes the value of asymmetrical fault current
the breaker is required to interrupt. A higher X/R ratio, with its slower decay rate, will result in a higher
asymmetrical fault current at contact part time. If the X/R ratio is too high, the asymmetrical fault current
may exceed the breaker's interrupting capability.

¿How is the X/R ratio calculated with simulation software (E.G. Digsilent)?

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