The per unit impedance of a circuit element is 0.30. If the base kV and base MVA are halved, then the new value of the per unit impedance of the circuit element will be: 

Explanation:

Per Unit Impedance in Power Systems

Definition: The per unit (p.u.) system is a method used in power systems to normalize system quantities (impedance, voltage, current, power) to a common base. It simplifies calculations and comparisons by expressing system values as fractions or multiples of base values. The per unit impedance is given by the formula:

Z_pu = Z_actual × (Base MVA / Base Voltage²)

Where:

• Z_actual = Actual impedance in ohms.
• Base MVA = Power base in MVA.
• Base Voltage = Voltage base in kV.

Given Data:

• Initial per unit impedance (Z_{pu, initial}): 0.30
• Base kV and Base MVA are halved.

We need to calculate the new per unit impedance (Z_{pu, new}) after the base values are halved.

Step-by-Step Solution:

Step 1: Relationship between per unit impedance and base values

The per unit impedance is inversely proportional to the square of the base voltage and directly proportional to the base MVA. Mathematically:

Z_pu ∝ Base MVA / (Base Voltage)²

Let the initial base values be:

• Base MVA = S_{base, initial}
• Base Voltage = V_{base, initial}

And the new base values after halving are:

• Base MVA = S_{base, new} = S_{base, initial} / 2
• Base Voltage = V_{base, new} = V_{base, initial} / 2

Step 2: Express the new per unit impedance in terms of the initial impedance

The ratio of the new per unit impedance to the initial per unit impedance is given by:

Z_{pu, new} / Z_{pu, initial} = (S_{base, new} / S_{base, initial}) × (V_{base, initial}² / V_{base, new}²)

Substitute the new base values:

• S_{base, new} = S_{base, initial} / 2
• V_{base, new} = V_{base, initial} / 2

Z_{pu, new} / Z_{pu, initial} = [(S_{base, initial} / 2) / S_{base, initial}] × [V_{base, initial}² / (V_{base, initial} / 2)²]

Simplify the terms:

Z_{pu, new} / Z_{pu, initial} = (1 / 2) × (V_{base, initial}² / [V_{base, initial}² / 4])

Z_{pu, new} / Z_{pu, initial} = (1 / 2) × 4

Z_{pu, new} / Z_{pu, initial} = 2

Therefore:

Z_{pu, new} = 2 × Z_{pu, initial}

Step 3: Calculate the new per unit impedance

Substitute the given initial per unit impedance (Z_{pu, initial} = 0.30):

Z_{pu, new} = 2 × 0.30 = 0.60

Thus, the new per unit impedance is 0.60.

Correct Option: Option 2 (0.6)

Additional Information

To further understand the analysis, let’s evaluate the incorrect options:

Option 1: 0.3

This option assumes that the per unit impedance remains unchanged even after the base values are altered. However, per unit impedance is dependent on the base values, as shown in the formula. When the base kV and base MVA are halved, the per unit impedance changes accordingly. Therefore, this option is incorrect.

Option 3: 0.003

This option represents a drastic reduction in the per unit impedance, which is not possible given the relationship between base values and per unit impedance. Halving the base MVA and base kV results in a doubling of the per unit impedance, not a reduction to such a small value. Hence, this option is incorrect.

Option 4: 0.006

Similar to option 3, this value is unrealistically small and does not align with the mathematical relationship between per unit impedance and the base values. The correct calculation shows that the per unit impedance doubles, not decreases. Thus, this option is also incorrect.

Option 5: (No option provided)

Since no value is specified for this option, it cannot be considered as a valid choice.

Conclusion:

The correct answer is Option 2 (0.6). When the base kV and base MVA are halved, the per unit impedance doubles, as derived using the formula for per unit impedance and its dependence on base values. Understanding the relationship between system quantities and base values in the per unit system is crucial for analyzing and simplifying power system calculations.