Circuit Breaker Symmetrical Breaking Current Calculation

The symmetrical breaking current is a crucial parameter for any circuit breaker, especially for an oil circuit breaker, as it defines the maximum symmetrical fault current that the breaker is designed to successfully interrupt. This value is directly derived from the breaker's MVA (Mega Volt-Ampere) rating and the system voltage. The MVA rating signifies the total apparent power the circuit breaker can safely handle during fault conditions.

Understanding Circuit Breaker Specifications

We are provided with the following key specifications for the three-phase, 33 kV oil circuit breaker:

• Rated Voltage (V): 33 kV (This is the line-to-line voltage of the system).
• MVA Rating (S): 2000 MVA (This is the three-phase fault breaking capacity of the circuit breaker).
• Rated Current (I_rated): 1200 A (This indicates the continuous current the breaker can carry without overheating, and is not directly used for calculating symmetrical breaking current from MVA).
• Breaking Time (t): 3s (This specifies the maximum time from the instant of fault initiation until the fault is cleared by the breaker).

Our goal is to accurately determine the symmetrical breaking current using the given MVA rating and the system voltage.

Formula for Symmetrical Breaking Current

For a three-phase electrical system, the relationship between apparent power (MVA), line-to-line voltage (kV), and line current (kA) is given by the formula:

$$S = \sqrt{3} \times V_{L-L} \times I$$

Where:

• \(S\) represents the MVA rating of the circuit breaker.
• \(V_{L-L}\) is the line-to-line voltage of the system in kiloVolts (kV).
• \(I\) is the symmetrical breaking current in kiloAmperes (kA).

To calculate the symmetrical breaking current (\(I\)), we can rearrange the formula as follows:

$$I = \frac{S}{\sqrt{3} \times V_{L-L}}$$

Calculating the Symmetrical Breaking Current

Now, let's substitute the provided values into the rearranged formula:

• MVA Rating (\(S\)) = 2000 MVA
• Rated Voltage (\(V_{L-L}\)) = 33 kV
• The approximate value of \(\sqrt{3}\) is 1.732.

Performing the calculation:

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

$$I = \frac{2000}{1.732 \times 33}$$

$$I = \frac{2000}{57.156}$$

$$I \approx 34.99 \text{ kA}$$

When rounded to the nearest whole number, the symmetrical breaking current is approximately 35 kA.

Comparing with Given Options

Let's check our calculated value against the provided options:

Option Number	Value	Matches Calculation
1	1200 A	No
2	35 kA	Yes
3	104.8 kA	No
4	3600 A	No

Based on our calculation, the symmetrical breaking current for the 33 kV oil circuit breaker with a 2000 MVA rating is approximately 35 kA, which corresponds to option 2.