Why the reactance of a system under fault condition is low and faults currents may raise dangerously high value. ? (With simple example)
2 Answers
When a fault occurs in an electrical system, such as a short circuit, the reactance (which is a form of opposition to current in an AC circuit) of the system drops to a very low value. This happens because the fault essentially creates a direct path for current to flow, bypassing the regular circuit impedance (resistance and reactance). Let's break this down with a simple explanation and example.
### Key Concepts:
1. **Reactance and Impedance**: In an AC system, the total opposition to current is called **impedance** (Z), which has two components: **resistance (R)** and **reactance (X)**. Reactance can be due to inductance (from coils) or capacitance. The formula for impedance is:
\[
Z = \sqrt{R^2 + X^2}
\]
2. **Normal Operation**: Under normal operating conditions, the current in the system is limited by the system's impedance. This means that the combination of resistance and reactance limits how much current flows through the system.
3. **Fault Condition**: When a fault occurs, particularly a short circuit, the path the current can take becomes much simpler — the current can bypass much of the impedance, especially the reactance. This leads to a **low reactance** condition, which drastically reduces the impedance of the system.
### Simple Example
Consider a simple electrical system with the following:
- A power source (such as a generator or transformer).
- A load (which could be any device consuming electricity).
- The system has an impedance that limits the current flow during normal conditions.
Let’s say, under normal conditions, the system has a resistance (R) of 1 ohm and a reactance (X) of 2 ohms. The total impedance (Z) of the system is:
\[
Z = \sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.24 \, \text{ohms}
\]
Now, assume the system is operating with a voltage of 220V. The current (I) can be calculated using Ohm's law:
\[
I = \frac{V}{Z} = \frac{220}{2.24} \approx 98 \, \text{amps}
\]
This is the normal current flow in the system.
### What Happens During a Fault?
If a fault, like a short circuit, occurs, the path for the current bypasses most of the load and impedance. In the worst-case scenario (such as a three-phase short circuit), the reactance may drop significantly close to zero, and the only remaining opposition to the current is the very small resistance of the wires and connections.
For simplicity, let's assume that during the fault, the reactance (X) drops to near zero and the resistance (R) reduces to 0.1 ohms (representing the small resistance of wires). Now the total impedance becomes:
\[
Z = \sqrt{0.1^2 + 0^2} = 0.1 \, \text{ohms}
\]
Using Ohm's law again, the current during the fault is:
\[
I_{\text{fault}} = \frac{V}{Z} = \frac{220}{0.1} = 2200 \, \text{amps}
\]
### Conclusion:
- **Normal Condition**: Current was 98 amps with impedance of 2.24 ohms.
- **Fault Condition**: Current rises to 2200 amps with impedance of just 0.1 ohms.
The reason for this drastic increase in current is that the impedance (especially the reactance) becomes very small during a fault, allowing current to flow much more easily. This enormous current can cause significant damage to equipment and pose a safety hazard if not quickly interrupted by protective devices like circuit breakers.
This is why fault currents can reach dangerously high values during a fault, and why systems are designed with protective devices to quickly stop this current before damage occurs.
### Key Concepts:
1. **Reactance and Impedance**: In an AC system, the total opposition to current is called **impedance** (Z), which has two components: **resistance (R)** and **reactance (X)**. Reactance can be due to inductance (from coils) or capacitance. The formula for impedance is:
\[
Z = \sqrt{R^2 + X^2}
\]
2. **Normal Operation**: Under normal operating conditions, the current in the system is limited by the system's impedance. This means that the combination of resistance and reactance limits how much current flows through the system.
3. **Fault Condition**: When a fault occurs, particularly a short circuit, the path the current can take becomes much simpler — the current can bypass much of the impedance, especially the reactance. This leads to a **low reactance** condition, which drastically reduces the impedance of the system.
### Simple Example
Consider a simple electrical system with the following:
- A power source (such as a generator or transformer).
- A load (which could be any device consuming electricity).
- The system has an impedance that limits the current flow during normal conditions.
Let’s say, under normal conditions, the system has a resistance (R) of 1 ohm and a reactance (X) of 2 ohms. The total impedance (Z) of the system is:
\[
Z = \sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.24 \, \text{ohms}
\]
Now, assume the system is operating with a voltage of 220V. The current (I) can be calculated using Ohm's law:
\[
I = \frac{V}{Z} = \frac{220}{2.24} \approx 98 \, \text{amps}
\]
This is the normal current flow in the system.
### What Happens During a Fault?
If a fault, like a short circuit, occurs, the path for the current bypasses most of the load and impedance. In the worst-case scenario (such as a three-phase short circuit), the reactance may drop significantly close to zero, and the only remaining opposition to the current is the very small resistance of the wires and connections.
For simplicity, let's assume that during the fault, the reactance (X) drops to near zero and the resistance (R) reduces to 0.1 ohms (representing the small resistance of wires). Now the total impedance becomes:
\[
Z = \sqrt{0.1^2 + 0^2} = 0.1 \, \text{ohms}
\]
Using Ohm's law again, the current during the fault is:
\[
I_{\text{fault}} = \frac{V}{Z} = \frac{220}{0.1} = 2200 \, \text{amps}
\]
### Conclusion:
- **Normal Condition**: Current was 98 amps with impedance of 2.24 ohms.
- **Fault Condition**: Current rises to 2200 amps with impedance of just 0.1 ohms.
The reason for this drastic increase in current is that the impedance (especially the reactance) becomes very small during a fault, allowing current to flow much more easily. This enormous current can cause significant damage to equipment and pose a safety hazard if not quickly interrupted by protective devices like circuit breakers.
This is why fault currents can reach dangerously high values during a fault, and why systems are designed with protective devices to quickly stop this current before damage occurs.
In a fault condition, such as a short circuit, the reactance of the system becomes very low because the fault provides a path of very low impedance. Reactance (opposition to AC current) is inversely related to impedance, so when impedance drops, reactance also drops.
**Example:** Imagine an electrical circuit with a resistor and an inductor (which provides reactance). Under normal conditions, the inductor's reactance limits current flow. If a short circuit happens across the inductor, the reactance is nearly zero because the short circuit bypasses the inductor. This drastically reduces the impedance of the circuit, allowing a large amount of current to flow, which can cause dangerously high fault currents.
**Example:** Imagine an electrical circuit with a resistor and an inductor (which provides reactance). Under normal conditions, the inductor's reactance limits current flow. If a short circuit happens across the inductor, the reactance is nearly zero because the short circuit bypasses the inductor. This drastically reduces the impedance of the circuit, allowing a large amount of current to flow, which can cause dangerously high fault currents.