Definition of a per-unit quantity

The per-unit system expresses a quantity relative to a selected reference or base value of the same physical quantity. It is defined as:

x_pu = x_actual/x_base

Voltage is divided by base voltage, current by base current, and impedance by base impedance. Both values must be expressed in the same units before division. Their units then cancel, leaving a dimensionless ratio.

Example with unit conversion

Step 1: Choose the actual and base values. Suppose the actual voltage is 5,500 V and the selected base voltage is 11 kV.

Step 2: Express both in the same unit. Convert the base voltage: 11 kV = 11,000 V.

Step 3: Divide actual value by base value. The normalized voltage is:

V_pu = 5,500/11,000 = 0.5 pu

Percentage value = 100 × 0.5 = 50%

A value of 1 pu means actual equals base, 0.5 pu means half the base, and 1.1 pu means 10% above the base. The same actual quantity can have different per-unit values on different bases, so the chosen base must be stated when interpreting or comparing results. This definition directly matches option C .

Quick Trick

PU = Actual / Base, same quantity, same units.

Why Other Options Are Wrong

A says ‘any units’ for both numerator and denominator without requiring consistency, so units may not cancel. B and D invert the required ratio. C correctly states actual/base in the same units.

Common Mistake

Mixing units such as volts and kilovolts without converting them consistently before forming the ratio.

Definition of a per-unit quantity

The per-unit system expresses a quantity relative to a selected reference or base value of the same physical quantity. It is defined as:

x_pu = x_actual/x_base

Voltage is divided by base voltage, current by base current, and impedance by base impedance. Both values must be expressed in the same units before division. Their units then cancel, leaving a dimensionless ratio.

Example with unit conversion

Step 1: Choose the actual and base values. Suppose the actual voltage is 5,500 V and the selected base voltage is 11 kV.

Step 2: Express both in the same unit. Convert the base voltage: 11 kV = 11,000 V.

Step 3: Divide actual value by base value. The normalized voltage is:

V_pu = 5,500/11,000 = 0.5 pu

Percentage value = 100 × 0.5 = 50%

A value of 1 pu means actual equals base, 0.5 pu means half the base, and 1.1 pu means 10% above the base. The same actual quantity can have different per-unit values on different bases, so the chosen base must be stated when interpreting or comparing results. This definition directly matches option C .

Quick Trick

PU = Actual / Base, same quantity, same units.

Why Other Options Are Wrong

A says ‘any units’ for both numerator and denominator without requiring consistency, so units may not cancel. B and D invert the required ratio. C correctly states actual/base in the same units.

Common Mistake

Mixing units such as volts and kilovolts without converting them consistently before forming the ratio.

Definition of a per-unit quantity

The per-unit system expresses a quantity relative to a selected reference or base value of the same physical quantity. It is defined as:

x_pu = x_actual/x_base

Voltage is divided by base voltage, current by base current, and impedance by base impedance. Both values must be expressed in the same units before division. Their units then cancel, leaving a dimensionless ratio.

Example with unit conversion

Step 1: Choose the actual and base values. Suppose the actual voltage is 5,500 V and the selected base voltage is 11 kV.

Step 2: Express both in the same unit. Convert the base voltage: 11 kV = 11,000 V.

Step 3: Divide actual value by base value. The normalized voltage is:

V_pu = 5,500/11,000 = 0.5 pu

Percentage value = 100 × 0.5 = 50%

A value of 1 pu means actual equals base, 0.5 pu means half the base, and 1.1 pu means 10% above the base. The same actual quantity can have different per-unit values on different bases, so the chosen base must be stated when interpreting or comparing results. This definition directly matches option C .

Quick Trick

PU = Actual / Base, same quantity, same units.

Why Other Options Are Wrong

A says ‘any units’ for both numerator and denominator without requiring consistency, so units may not cancel. B and D invert the required ratio. C correctly states actual/base in the same units.

Common Mistake

Mixing units such as volts and kilovolts without converting them consistently before forming the ratio.