How do you calculate the total power in a three-phase system?

To calculate the total power in a three-phase system, the formula used is P_total = √3 × V × I × cos(θ). In this formula, P_total represents the total power, V signifies the line-to-line voltage, I is the line current, and cos(θ) is the power factor, which accounts for the phase difference between the voltage and the current.

This equation arises from the combination of three individual phase powers in a balanced system, where each phase contributes equally to the total power. The factor of √3 is crucial because it accounts for the geometric relationship between the line-to-neutral voltages and the line-to-line voltages in a three-phase system.

In contrast, the other formulas do not apply to three-phase power calculations. For instance, the formula involving V multiplied by I and sin(θ) pertains to reactive power rather than total real power. Additionally, the formulas involving V squared over R or I squared times R represent power in single-phase resistive circuits and do not accommodate the intricacies of multi-phase systems.