# Measuring three-phase power

*Last Modification: January 25, 2014*

When doing measurements on a three-phase power installation, the power in all three phases must be measured simultaneous to become the total power. For this there are three commonly used methods who are described in this article.

## One wattmeter method

It is very obvious to measure the power of only a single phase and to multiply this by three to become the total power of the installation:

[equ. 1]

This only works as long as the voltages between themselves and the loads from the three phases are exactly the same. It doesn't matter whether or not the neutral point of the load is connected to the "neutral" or that the load is delta configured.

The objection to this method is that without additional measurements one never can be sure that the three voltages are equal. And there is also a real change that the loads are also not equal. This all can cause measurement errors that would not normally be noticed. To determine this additional measurements would be necessary. Therefor this method isn't advisable.

## Three wattmeter method

To perform an accurate measurement to three-phase power installations the power of all three individual phases must be measured. Therefore three wattmeters are necessary who each measure the power of one phase. Each wattmeter is connected so that the phase voltage is measured in respect to the neutral and measures the current of the same phase. Figure 2 shows how the three wattmeters are connected.

The total power of the installation or machine can now be calculated by adding the readings of all three individual wattmeters:

[equ. 2]

## Two wattmeter method

If the neutral terminal isn't available and the load is only connected to the three phases, than the neutral can't be used to measure the line voltage. In these cases on of the phases can fulfill the task as "null" reference, and only the power has to be measured of the remaining two phases. So, only two wattmeters are needed and the total power is the sum of the two readings:

[equ. 3]

*Figure 3 shows the voltage sources and loads connected in star configuration. For the measurement this is of no importance and the circuit may also be in a delta configuration.*

### Caution!

Before this measurement is used, one must ensure that there are no (hidden) loads present between one of the phases and the neutral. If there is a current flowing through the neutral line, than this will cause false readings!

### Checksumming

To check if the two wattmeter method is valid a comparative calculation is done: This is done by randomly chosen instantaneous values for the voltage *v(t)* and current *i(t)*. The resulting instantaneous power *p(t)* must always be valid regardless the amplitude, phase and shape of the voltage and current. More information about this theory in the article Theory & Definitions.

Because the neutral isn't connected, the sum of the instantaneous current in L1, L2 en L3 must be zero by Kirchhoff's current law:

[equ. 4]

With this condition as fact, it can be demonstrated that the sum of the instantaneous powers of the three phases are equal to the instantaneous powers of two phases with the third phase (L2) as voltage reference:

[equ. 5]