In three-phase power calculation, what does S stand for, and how is S computed?

In three-phase power calculation, what does S stand for, and how is S computed?

• A. Real power; P = 3 × V_L × I_L
• B. Reactive power; Q = √3 × V_L × I_L
• C. Apparent power; S = √3 × V_L × I_L
• D. Apparent power; S = V_L × I_L

Answer: (C)

Apparent power measures the total power flow in a circuit, combining real power (doing work) and reactive power (storing energy). In a balanced three-phase system, the apparent power is S = √3 V_L I_L, where V_L is the line-to-line voltage and I_L is the line current. This reflects how three phases contribute to the total power compared to a single-phase expression. Real power is P = √3 V_L I_L cosφ, and reactive power is Q = √3 V_L I_L sinφ, with φ being the angle between voltage and current (power factor angle). The relationship S^2 = P^2 + Q^2 holds, and S can also be written using phase quantities as S = 3 V_phase I_phase. The alternative S = V_L I_L misses the √3 factor needed for three phases, so it does not describe the total three-phase apparent power.

Apparent power measures the total power flow in a circuit, combining real power (doing work) and reactive power (storing energy). In a balanced three-phase system, the apparent power is S = √3 V_L I_L, where V_L is the line-to-line voltage and I_L is the line current. This reflects how three phases contribute to the total power compared to a single-phase expression.

Real power is P = √3 V_L I_L cosφ, and reactive power is Q = √3 V_L I_L sinφ, with φ being the angle between voltage and current (power factor angle). The relationship S^2 = P^2 + Q^2 holds, and S can also be written using phase quantities as S = 3 V_phase I_phase.

The alternative S = V_L I_L misses the √3 factor needed for three phases, so it does not describe the total three-phase apparent power.