In power systems, grounding the neutral point is a common practice to manage fault currents. One method is using a Peterson coil, also known as a arc suppression coil or reactor grounding.

The primary purpose of Peterson coil grounding is to limit the magnitude of fault current, specifically during a single line-to-ground fault. This helps in extinguishing the arc at the fault point, preventing damage to equipment and improving system stability.

Understanding Peterson Coil Grounding

When a single line-to-ground fault occurs in a system grounded through a Peterson coil, currents flow from the healthy phases through their capacitance to ground, and a current also flows through the Peterson coil connected between the neutral point and ground.

• Capacitive Current (\(I_C\)): This current flows from the unfaulted phases through the phase-to-ground capacitances to the fault point. Since there are three phases, the total capacitive current is the sum of the capacitive currents from all phases to ground.
• Inductive Current (\(I_L\)): This current flows through the Peterson coil from the neutral point to ground and then to the fault point. The voltage driving this current is the neutral displacement voltage, which is effectively the phase voltage during a single line-to-ground fault on one phase.

Resonance Condition in Peterson Coil Grounding

The Peterson coil is designed so that its inductive reactance (\(X_L\)) is tuned to resonate with the total capacitive reactance (\(X_C\)) of the system to ground. When the system is perfectly tuned, the inductive current flowing through the coil is equal in magnitude to the total capacitive current flowing from the healthy phases to ground.

Under a single line-to-ground fault on one phase (say, phase A), the voltage of the neutral point relative to ground rises to approximately the phase voltage (\(V_p\)). The capacitive current \(I_C\) from the healthy phases (B and C) and the inductive current \(I_L\) flow towards the fault.

The total capacitive current from the three phases is approximately:

\(I_{total\_C} \approx 3 \frac{V_p}{X_C}\)

The inductive current through the Peterson coil is:

\(I_L = \frac{V_p}{X_L}\)

The condition for complete neutralization of the fault current (when inductive fault current becomes equal to capacitive current of the system) is when \(I_L = I_{total\_C}\). So,

\(\frac{V_p}{X_L} = 3 \frac{V_p}{X_C}\)

Assuming \(V_p \neq 0\), we can cancel \(V_p\) from both sides:

\(\frac{1}{X_L} = \frac{3}{X_C}\)

Rearranging this equation to find the ratio \(\frac{X_C}{X_L}\):

\(X_C = 3 X_L\)

\(\frac{X_C}{X_L} = 3\)

This condition, \(\frac{X_C}{X_L} = 3\), represents the ideal tuning for a Peterson coil in a three-phase system during a single line-to-ground fault, where the inductive current through the coil cancels out the total capacitive current from the system to ground, minimizing the fault current.

Analyzing the Options

Let's look at the given options in light of our derivation:

• Option 1: \(\frac{X_C}{X_L}=\frac{1}{\sqrt{3}}\). This does not match our derived condition.
• Option 2: \(\frac{X_C}{X_L}=3\). This matches our derived condition.
• Option 3: \(\frac{X_C}{X_L}=\sqrt{3}\). This does not match our derived condition.
• Option 4: \(\frac{X_C}{X_L}=\frac{1}{{3}}\). This does not match our derived condition.

Therefore, when the inductive fault current becomes equal to the capacitive current of the system in Peterson coil grounding, the ratio of total capacitive reactance to inductive reactance is 3.

Revision Table: Key Concepts

Additional Information: Benefits of Peterson Coil Grounding

Peterson coil grounding offers several advantages:

• Fault Current Reduction: Significantly reduces the magnitude of single line-to-ground fault current.
• Arc Extinction: The low fault current magnitude helps in extinguishing the arc at the fault location naturally, often without tripping circuit breakers.
• Improved System Reliability: By allowing transient ground faults to clear themselves, it reduces the number of outages.
• Reduced Equipment Stress: Lower fault currents result in less thermal and mechanical stress on equipment like transformers and switchgear.
• Prevention of Overvoltages: Helps in preventing dangerous transient overvoltages that can occur with other grounding methods like ungrounded systems.

It's important to note that perfect tuning (\(\frac{X_C}{X_L} = 3\)) is for ideal resonance. In practice, systems might be slightly detuned to avoid continuous arcing or complex fault behavior. However, the principle remains balancing the inductive and capacitive currents.