Circuit Breaker Symmetrical Breaking Current Explained

This solution explains how to calculate the symmetrical breaking current for a three-phase oil circuit breaker using the provided ratings.

Parameters Provided

The question provides the following details about the oil circuit breaker:

• Type: Three-phase oil circuit breaker
• System Voltage: 33 kV (This is the line-to-line voltage, $V_L$)
• Rated Current: 1200 A (This is the continuous current rating)
• Rated Capacity: 2000 MVA (This is the three-phase breaking capacity, $S$)
• Rated Time: 3 s (This typically refers to the circuit breaker's interrupting time rating)

Formula for Symmetrical Breaking Current

The symmetrical breaking current ($I_b$) is the RMS value of the AC component of the current during the interruption process. It is calculated using the three-phase breaking capacity ($S$) and the line-to-line voltage ($V_L$) of the system. The formula is:

$$ I_b = \frac{S}{\sqrt{3} \times V_L} $$

Where:

• $I_b$ is the symmetrical breaking current in kiloamperes (kA).
• $S$ is the three-phase breaking capacity in megavolt-amperes (MVA).
• $V_L$ is the line-to-line voltage in kilovolts (kV).
• $\sqrt{3}$ represents the factor for three-phase power calculations.

Calculation Steps

Let's use the given values in the formula:

1. Substitute Values: Plug the given MVA rating and voltage into the formula.
   • $S = 2000$ MVA
   • $V_L = 33$ kV

   $$ I_b = \frac{2000 \text{ MVA}}{\sqrt{3} \times 33 \text{ kV}} $$

2. Calculate the Denominator: First, calculate the product of $\sqrt{3}$ and the voltage.

   $$ \sqrt{3} \times 33 \approx 1.732 \times 33 \approx 57.156 $$

3. Divide Capacity by Denominator: Now, divide the MVA rating by the result from the previous step.

   $$ I_b = \frac{2000}{57.156} \text{ kA} $$

4. Final Result: Perform the division to find the breaking current.

   $$ I_b \approx 35.00 \text{ kA} $$

Result and Option Matching

The calculated symmetrical breaking current is approximately 35 kA. Comparing this result with the given options:

• 1200 A (Incorrect - This is the rated current)
• 3600 A (Incorrect)
• 35 kA (Correct)
• 104.8 kA (Incorrect)

Therefore, the symmetrical breaking current for the specified oil circuit breaker is 35 kA.