The three-phase power is the total power delivered by the three phases of a balanced alternating system.
So far, to calculate power we have used
And well, more or less yes, but more or less no. The total power is indeed the sum of what each of the three phases contributes:
But normally we cannot measure what happens inside a coil (
We need a formula that uses the data we can actually measure.
The formula with √3
In a balanced system with sinusoidal waveforms, regardless of whether the load is connected in star or delta, the total active power calculated from line values is given by the same expression.
Where:
- P: Active Power (W).
: The factor 1.732 (derived from three-phase geometry). : Line Voltage (typically 400V). : Line Current. In a balanced system it has the same RMS value in all three conductors. : The motor’s Power Factor (usually found on the nameplate, e.g., 0.85).
Why does it always work?
The mathematical proof is elegant:
- In Star (Wye): The current is the same (
), but the voltage is divided ( ). - In Delta: The voltage is the same (
), but the current is divided ( ).
Substituting these relationships into
Practical example: a conveyor belt motor
Suppose you need to size the protections for a three-phase motor.
- You measure the voltage between phases: 400 V.
- You measure the current in a cable with a clamp meter: 10 A.
- The motor nameplate states:
.
How much power is it consuming?
Mental calculation trick:
For a standard 400V network, the product
The other powers: Q and S
The power triangle we saw in module 6 remains valid:
- Apparent power (S):
- Reactive power (Q):
