### What is X/R Ratio?

The X/R ratio is a measure of the ratio of the inductive reactance (X) to the resistance (R) of an electrical system. Knowing the X/R ratio is important for several reasons. 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.

During a short circuit, the total current comprises two components:

• The AC component, which varies sinusoidally with time and is also known as the symmetrical current, and the DC component, which is non-periodic and decays exponentially with a time constant of L/R (where L/R is proportional to X/R).
• The DC component causes the symmetrical current to become asymmetrical. The X/R ratio impacts the magnitude of the DC component, which in turn affects the total current.

### The Importance of X/R Ratio

Specifically, circuits with a higher X/R ratio will have a longer time constant for the decay of the DC component, leading to a slower decay of the total current. X/R ratio helps in the selection of the appropriate protective devices for the electrical system. The X/R ratio is used to calculate the time-current characteristic curve for protective devices such as circuit breakers and fuses.

A mismatch between the X/R ratio and the protective device can result in improper functioning of the protective device, leading to damage to the equipment or safety hazards to personnel. Secondly, it helps to optimize the electrical system's performance. The X/R ratio affects the voltage drop in the system and the transient response to switching events, such as motor starting or capacitor switching. A proper understanding of the X/R ratio can help in designing the electrical system to operate efficiently under various operating conditions. Thirdly, it helps in troubleshooting the electrical system. An X/R ratio that is too high or too low can indicate problems such as equipment malfunctions or incorrect wiring, which can be corrected to ensure the system is operating optimally.

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.

Overall, knowing the X/R ratio is essential to ensure proper selection of protective devices, optimize system performance, and troubleshoot problems that may arise in the electrical system.

### X/R Ratio in Fault Current Calculation

The X/R ratio plays a critical role in short-circuit calculations because it determines the behavior of the circuit during the short circuit. During a short circuit, the electrical system experiences a transient condition, and the response of the system depends on the X/R ratio of the circuit.

A high X/R ratio indicates that the circuit is more reactive, and the system response to the short circuit will be dominated by the inductance of the system. On the other hand, a low X/R ratio indicates that the circuit is more resistive, and the system response to the short circuit will be dominated by the resistance of the system.

Knowing the X/R ratio is essential in short-circuit calculations as it helps to estimate the magnitude and duration of the short-circuit current, which is critical for the design and operation of protective devices. The protective devices, such as circuit breakers and fuses, are designed to operate within specific current and time limits to prevent damage to equipment and personnel.

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.

### X/R Ratio in Selecting Protective Device

To select the appropriate protective device for a given system, it is essential to determine the X/R ratio of the circuit where the device will be installed. A protective device must have a suitable interrupting capacity that can handle the maximum short-circuit current that can occur in the circuit. The interrupting capacity of a protective device is typically specified in terms of its current rating and its withstand capacity.

The X/R ratio affects the magnitude and duration of the short-circuit current, which, in turn, affects the interrupting capacity required for a protective device. A circuit with a high X/R ratio will have a longer duration of the fault current, and therefore, requires a protective device with a higher interrupting capacity. Conversely, a circuit with a low X/R ratio will have a shorter duration of the fault current, and a protective device with a lower interrupting capacity may be sufficient.

Furthermore, the X/R ratio can also affect the operation of the protective device. For example, a protective device designed for use in a high X/R ratio circuit may have a longer time delay before tripping to account for the longer duration of the fault current. In contrast, a protective device designed for use in a low X/R ratio circuit may have a shorter time delay to account for the shorter duration of the fault current.

In conclusion, the X/R ratio is a critical parameter in electrical power systems that affects the behavior of circuits and components. Its importance lies in its impact on fault calculations, protective device selection, equipment design, power system stability, and fault detection. Knowledge of the X/R ratio is crucial for ensuring the safe and efficient operation of electrical systems, and proper selection of protective devices that can handle the maximum short-circuit current that can occur in the circuit.

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