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How to calculate the power of three-phase AC motor?

Date:2023-10-08   Author:XINDA MOTOR
I believe anyone who has attended junior high school should know the formula P=UI for calculating electrical power.

But this most basic formula generally only applies to DC circuits and AC pure resistance circuits. A pure resistance circuit is a circuit that completely converts electrical energy into other energy, such as incandescent lamps, electric stoves, electric ovens, etc.

So, how to calculate the power of a three-phase AC motor that uses electromagnetic effects?

First of all, we need to understand that the power calculation formula of a sinusoidal AC circuit is P=UIcosφ (cosφ is the power factor).

φ is the phase difference between voltage and current. For a pure resistance circuit, φ=0. According to the trigonometric function, cos0°=sin90°=1. Therefore, this formula can be simplified to P=UI.

Secondly, for inductive loads and capacitive loads, there is a phase difference between voltage and current. (For pure inductive loads, the voltage leads the current by 90 degrees, and for pure capacitive loads, the current leads the voltage by 90 degrees.) φ is not 0, and cosφ is not equal to 1. Therefore, it cannot be calculated according to P=UI.

Below, give an example to explain in detail!

For a 3000-watt three-phase motor, current = power/voltage = 3000/380 = 7.89A. Is it calculated like this?
This involves the calculation of three-phase power. P=UIcosφ is the calculation of single-phase power. The three-phase power calculation formula is: P=3U phase I phase cosφ. The voltage and current in this formula refer to the phase voltage and phase current.

But what we usually call rated voltage and rated current refer to line voltage and line current.

This depends on the connection method of the three-phase AC motor:

1. When the load is a symmetrical star connection:

Line voltage = √3 phase voltage, line current = phase current;

2. When the load is a symmetrical delta connection:

Line voltage = phase voltage, line current = √3 phase current.

Therefore, regardless of whether the symmetrical load is star connection or delta connection, P=3U phase I phase cosφ can evolve into P=√3U line I line cosφ, and then the line voltage and line current can be calculated through this formula.

For the calculation of the power of a three-phase asynchronous motor, the efficiency of the motor must also be considered, so the formula is: P=√3×U×I×COSΦ×η. For example, to calculate the current of a 3000-watt three-phase motor, (the power factor is 0.86, and the efficiency is 0.88) can be substituted into the formula, 3000=√3×380×I×0.86×0.88, I=6.02A.