What is the formula for three-phase reactive power?

In three-phase systems, reactive power is an important concept used to describe the power oscillating between the source and the load due to inductive or capacitive elements in the circuit. The correct formula for three-phase reactive power involves the use of the square root of three, which arises from the geometry of the three-phase system.

For a balanced three-phase load, the reactive power (Q) can be calculated using the formula Q = √3 * I * V * sin(φ), where I is the line current, V is the line-to-line voltage, and φ is the phase angle between the current and voltage. The presence of the factor √3 comes from the relationship between line current and phase current, as well as the conversion from line-to-line voltage to line-to-neutral voltage in a three-phase system.

This formula captures the essence of reactive power in three-phase systems, providing insight into how it relates to the overall power factor and the behavior of loads that may not consume power efficiently. Reactive power is critical for maintaining voltage levels and ensuring efficient operation in electrical power systems.

While the other options present variations of this formula, they either omit the essential factor of √3 or misrepresent the relationship between current, voltage, and the sine function