Measuring 3-phase power. How to calculate?

Question

I'm designing AC power consumption meter device for apartment based on popular MCU and current/voltage transformers. Currently I successfully managed to measure current and voltage in each phase line individually. There're lots of mentioning 3-phase power formula, like this:

P (kW) = (I (Amps) × V (Volts) × PF × 1.732) ÷ 1,000

I even found that PF is basically phase shift between current and voltage sine.

The only thing I don't get is which current and voltage to use here - I have three of each. Is it average for three or some kind of RMS or what?

Will greately appreciate any advice here.

Answer 1

Measuring 3-phase power. How to calculate?

The simplest way is probably this; the two wattmeter method: -

Image from Two Wattmeter Method of Power Measurement and, I mention this because, it is a true 3-phase measurement of power into a 3-phase load. There is also the three wattmeter method: -

Image from Measurement of Three Phase Power: Three Wattmeter Method and, again I'm showing old fashioned wattmeter methods because, if you want accuracy despite non-linear loads or asymmetrical voltage supplies you have to look at what a wattmeter does.

A wattmeter is an analogue multiplier of the voltage and current waveforms. In other words, it's \$v \times i\$ with no worries about power factor. If you try and calculate power using power factor then you have to measure phase angle between \$v\$ and \$i\$ and, the massive problem with this, is that a typical load may be somewhat non-linear (i.e. not wholly resistive) therefore, using zero-crossing detectors (for example) for estimating phase angle, is a bit useless and, gives rise to significant errors.

In other words, your formula assumes a balanced and linear load with a voltage source that is balanced both in amplitude and 120° phase angles. It's folly to think you might be able to do this for practical loads except a kettle and, I don't think they make three phase kettles. Sure there are 3-phase heating elements and these'll be OK but, in the main, you'll be disappointed with V.I.Cos(φ).

But, if your supply is both amplitude and phase balanced and feeds a linear load then you can use that method.

Going back to \$v \times i\$, you can employ modern digital techniques and sample at around 20 times the line frequency as a minimum to avoid current waveform harmonics contributing too much of an error. If you sample and multiply at a higher rate then even better.

Then you accumulate the \$v \times i\$ sampled value over (say for instance) 1 second and divide by the samples per second. Use this method in the equivalent of a two or three wattmeter method.

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Answer 2

You can just purchase one of the many three phase wattmeter and power analyzer ICs and add the required external PTs and CTs, and interface it to a microcontroller to log and display the values. Or you can purchase dedicated power analyzers that display RMS voltage, current, power, power factor, phase angle, and total (and peak) watt-hours. Some even allow entry of cost/kWh to obtain total cost.

You can, of course, design something like this using a microcontroller with six simultaneous ADCs to compute instantaneous voltage and current, and multiply them to obtain power, and average the readings over a period of time for true-RMS and power, and you can compute power factor using W/VA, or phase angle by comparing zero crossings of voltage and current,

It is easiest and most accurate to read current in each phase and phase-to-neutral voltage, but you can derive the third voltage or current from two currents or two voltages, although it may be less accurate for unbalanced loads and distortion.