In three-phase systems, what does S = √3 V_L I_L represent?

In three-phase systems, what does S = √3 V_L I_L represent?

• A. The total real power in a three-phase system.
• B. The phase angle between voltage and current.
• C. The line current in a wye-connected system.
• D. The three-phase apparent power using line values.

Answer: (D)

In a balanced three-phase system, S represents apparent power—the combined effect of real power (P) and reactive power (Q). When you express this using line values, the total apparent power equals S = √3 V_L I_L, where V_L is the line-to-line voltage and I_L is the line current. The √3 factor comes from how the three phase voltages are spaced 120 degrees apart and how their powers add up in a three-phase system. This form makes it convenient to calculate apparent power from measurements at the system’s terminals. This isn’t the real power (that would be P = √3 V_L I_L cosφ) and it isn’t a phase angle or just the line current by itself. It’s also specifically about using line values for a balanced system; for unbalanced conditions you’d sum the individual phase powers.

In a balanced three-phase system, S represents apparent power—the combined effect of real power (P) and reactive power (Q). When you express this using line values, the total apparent power equals S = √3 V_L I_L, where V_L is the line-to-line voltage and I_L is the line current. The √3 factor comes from how the three phase voltages are spaced 120 degrees apart and how their powers add up in a three-phase system. This form makes it convenient to calculate apparent power from measurements at the system’s terminals.

This isn’t the real power (that would be P = √3 V_L I_L cosφ) and it isn’t a phase angle or just the line current by itself. It’s also specifically about using line values for a balanced system; for unbalanced conditions you’d sum the individual phase powers.