Symmetrical Fault Calculations: Percentage Reactance at Base kVA

In the study of power systems, especially during symmetrical fault calculations, it is crucial to standardize electrical quantities. The per unit (p.u.) system or percentage system is widely used for this purpose as it simplifies complex calculations by expressing all values relative to a common base. When different components of a power system have their ratings given (e.g., rated kVA), it becomes necessary to convert their parameters, such as percentage reactance, to a single chosen system-wide base kVA.

Base kVA and Per Unit System for Fault Analysis

The concept of a base kVA is fundamental in the per unit system. It is a reference apparent power value chosen for the entire system or a specific zone within it. All power quantities are then expressed as a fraction or percentage of this base value. Similarly, the percentage reactance (%X) of a component indicates its reactance relative to its rated capacity or a specified base.

The per unit value of any quantity is defined as:

• $\text{Per unit value} = \frac{\text{Actual value}}{\text{Base value}}$

For reactance, the per unit value at a specific base kVA and base voltage is given by:

• $\text{X}_{\text{p.u.}} = \frac{\text{Actual X (ohms)} \times \text{Base kVA}}{(\text{Base kV})^2 \times 1000}$

When you change the base kVA, the per unit or percentage reactance value also changes proportionally, assuming the base voltage remains constant. This transformation is vital to ensure all reactances are on a common reference before performing symmetrical fault calculations.

Reactance Base Conversion Formula

To convert the percentage reactance of a component from an initial base (often its rated kVA) to a new base kVA, a specific formula is used. This formula ensures that the relative opposition to current flow is accurately represented under the new base conditions.

The relationship between the per unit reactance at two different base kVAs (assuming constant base voltage) is:

• $\text{X}_{\text{p.u. (new base)}} = \text{X}_{\text{p.u. (old base)}} \times \frac{\text{Base kVA}_{\text{new}}}{\text{Base kVA}_{\text{old}}}$

Since percentage reactance is simply the per unit reactance multiplied by 100, we can write the formula for percentage reactance conversion as:

• $\text{\%Reactance}_{\text{new base}} = \text{\%Reactance}_{\text{old base}} \times \frac{\text{Base kVA}_{\text{new}}}{\text{Base kVA}_{\text{old}}}$

In the context of the question, the 'old base' is the rated kVA of the equipment, and the 'new base' is the desired common base kVA for the system's symmetrical fault calculations.

Therefore, the percentage reactance at base kVA is equal to:

• $\text{\% reactance at base kVA} = \left( \frac{\text{base kVA}}{\text{rated kVA}} \right) \times \text{\% reactance at rated kVA}$

Applying the Percentage Reactance Formula

Let's evaluate the given options based on the derived formula for converting percentage reactance to a common base kVA in symmetrical fault calculations.

Based on the principles of base conversion in power system analysis, the correct way to find the percentage reactance at base kVA from its value at rated kVA is to use the direct proportionality with the kVA base change.