Energy Academy
Level 1/Electrical Science Refresher
Three-Phase Systems6 / 10

Power in Three-Phase Systems

How to calculate power, and the advantages over single-phase.

9 min read

Three-phase power calculations are straightforward if you remember the formula. It's the same concept as single-phase, just distributed across three lines.

The formula revisited

P = โˆš3 ร— V_line ร— I_line ร— cos(ฯ†)

Where:

  • โˆš3 โ‰ˆ 1.73
  • V_line is the voltage between two phase lines (400 V in UK)
  • I_line is the current in each line
  • cos(ฯ†) is the power factor

If you measure two of these, you can find the third.

Example calculations

Example 1: A motor on 400 V three-phase drawing 20 A per phase, PF 0.9. P = 1.73 ร— 400 ร— 20 ร— 0.9 = 12,456 W โ‰ˆ 12.5 kW

Example 2: You have a 30 kW motor on 400 V, PF 0.85. What current? I = P / (โˆš3 ร— V ร— PF) = 30,000 / (1.73 ร— 400 ร— 0.85) โ‰ˆ 51 A per phase

Balanced vs unbalanced loads

In a balanced system, all three phases have the same current. Power is smooth and you can use the simple formula.

In an unbalanced system (common in buildings where single-phase loads are split unevenly across phases), one phase carries more than others. This causes:

  • Neutral current (even though it should be zero)
  • Harmonic distortion
  • Heating in the neutral wire
  • Inefficiency

Most commercial buildings are reasonably balanced because they have many small loads spread across phases.

Energy from three-phase

Energy (kWh) = Power (kW) ร— Time (hours), same as single-phase.

A 10 kW three-phase motor running 8 hours uses 80 kWh.