Question

In a per-unit system, the base impedance ($Z_{\text{base}}$) is defined as:

• A. $V_{\text{base}} \times I_{\text{base}}$
• B. $V_{\text{base}} / I_{\text{base}}$
• C. $I_{\text{base}} / V_{\text{base}}$
• D. $V_{\text{base}}^2 \times P_{\text{base}}$

Hint:

Remember that base impedance always has the unit of Ohms, while the actual per-unit impedance is dimensionless.
Use the relation \(Z_{\text{base}} = \frac{(kV_{\text{base}})^2}{MVA_{\text{base}}}\) for quick numeric conversions in power system problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the fundamental definition of base impedance (\(Z_{\text{base}}\)) in terms of base voltage and base current within the per-unit system of power system analysis.

Step 2: Key Formula or Approach:
According to Ohm's Law, impedance is the ratio of voltage to current:
\[ Z = \frac{V}{I} \] In any per-unit system, the relationship between the chosen base quantities must satisfy the same fundamental physical laws. Therefore:
\[ Z_{\text{base}} = \frac{V_{\text{base}}}{I_{\text{base}}} \]

Step 3: Detailed Explanation:

• A per-unit system is used to simplify calculations in multi-voltage level power networks by normalizing quantities against reference values called bases.

• To establish a per-unit system, we typically select two independent base quantities: base voltage (\(V_{\text{base}}\)) and base power (\(S_{\text{base}}\) or \(P_{\text{base}}\)).

• The remaining base quantities are then derived from these two selected values.

• The base current is derived from base voltage and base power:
\[ I_{\text{base}} = \frac{S_{\text{base}}}{\sqrt{3} V_{\text{base}}} \quad \text{(for 3-phase systems)} \]
• Natively, using Ohm's law, the base impedance \(Z_{\text{base}}\) is the ratio of the base phase voltage to the base phase current:
\[ Z_{\text{base}} = \frac{V_{\text{base}}}{I_{\text{base}}} \]
• Substituting the current expression, this can also be expressed in terms of system voltage and power:
\[ Z_{\text{base}} = \frac{V_{\text{base}}^2}{S_{\text{base}}} \]
• Among the given choices, the direct ratio \(V_{\text{base}}/I_{\text{base}}\) represents this definition.

Step 4: Final Answer:
The base impedance is defined as \(V_{\text{base}} / I_{\text{base}}\).