Three-Phase Positive Sequence Voltage Basics

In a three-phase AC supply system, three distinct AC voltages are used. These voltages are balanced, meaning they share the same magnitude, and are phase-shifted from each other by 120 degrees.

A positive sequence signifies a particular order for these phases, conventionally A -> B -> C. This sequence establishes a fixed phase relationship between the voltages:

• The voltage of phase B (Vbn) lags behind the voltage of phase A (Van) by 120 degrees.
• The voltage of phase C (Vcn) lags behind the voltage of phase B (Vbn) by 120 degrees.
• This also means Vcn lags Van by 240 degrees, which is equivalent to leading by 120 degrees.

The relationship connecting consecutive phases in a positive sequence is expressed as:

Vcn = Vbn ∠ -120°

Positive Sequence Vcn Calculation

The problem provides the voltage for phase B:

Vbn = 110 ∠30° V

To determine the voltage for phase C (Vcn) under the assumption of a positive sequence, we apply the established relationship:

Vcn = Vbn ∠ -120°

Substitute the given value of Vbn into this equation:

Vcn = (110 ∠30°) ∠ -120° V

To compute the resultant phasor voltage, we sum the phase angles:

Vcn = 110 ∠(30° - 120°) V

Performing the angle subtraction:

Vcn = 110 ∠-90° V

Vcn Result Verification

The calculation yields 110 ∠-90° V for the phase voltage Vcn.

We now compare this result with the multiple-choice options provided:

The calculation confirms that 110 ∠-90° V is the correct voltage for Vcn when considering a positive sequence three-phase supply with the given Vbn.