We have 3-phase electric network. How to determine phase sequence (L123 or L132) from 2 line-to-line voltages U12 and U32? I prefer computationally simple solutions. Is it possible to determine phase sequence without computing phase voltages (which seems to me to complicated if searching generally valid solution for assymetric systems).

The solution looked for needs to be a mathematical algorithm. I am not searching circuit design. I need to write computer program for this. Lets say we know amplitudes and phases of vectors U12 and U32:

\$U_{12} = |U_{12}| \exp \left[j \left(\omega t + \phi_{12}\right)\right]\$

\$U_{32} = |U_{32}| \exp \left[j \left(\omega t + \phi_{32}\right)\right]\$

  • \$\begingroup\$ If you can choose the time between samples, then it's trivial. If not, are you at least given this information? \$\endgroup\$
    – Adam Davis
    Commented Apr 18, 2014 at 22:08

6 Answers 6


Maybe something like this?

    phi_a < phi_b 
    (phi_a + 180) > phi_b

You can ignore amplitude or replace it with 1, you don't need this for determining phase order. Phases are always 120 deg (unless you power network from seriously damaged inverter). Amplitude assymetry does not matter at all.


Here is a circuit design that displays correct 3 phase order. It uses the SCR to store the memory of state B-C sequence and the polarity of A for each cycle. No neutral is required here.

enter image description here

If you wanted to detect a missing phase, one would need a neutral reference and trigger a one-shot for each phase.

  • \$\begingroup\$ Does this circuit work on european 400 V lines? And what about using a capacitor to drop some voltage instead of those huge resistors? \$\endgroup\$
    – Al Kepp
    Commented Dec 26, 2012 at 17:47
  • \$\begingroup\$ Where you got that schematics? \$\endgroup\$
    – Kamil
    Commented Apr 18, 2014 at 18:30
  • \$\begingroup\$ @AlKepp Capacitor used instead of huge R1 resistor will never discharge, notice the thyristor. \$\endgroup\$
    – Kamil
    Commented Apr 18, 2014 at 18:36

An interesting problem, with a simple solution, with a catch...


Convert \$\phi_{\Delta}\$ to the range \$-\pi\$ to \$\pi\$

Check if the result is positive or negative.

Now, the catch. This will tell you the effective rotation for a delta load on this system. You only have two relative measurements so it can not tell you the absolute rotation.

The absolute rotation is only consistent if ground is inside the triangle bounded by \$A, B, C\$.


Sorry I misunderstood your post. I see you have access to all three phase wires.

Quadrature decoding;
Using line 2 as a reference, the next line to go high identifies direction.

A resistor in series with a Zener diode, should furnish a square wave.
A “D/Q” flip flop should turn Q or /Q high indicating direction.

D/Q Circuit explanation;
If “D” is high when “Clock” latches, “Q” can light a LED.
Indicating the line triggering the “Clock” is the next in phase.


To determine the phase offset of otherwise equal signals (here: two or three sine waves) you can use the cross-correlation. The discrete cross correlation could be used with actual samples from an ADC on a micro controller or as a simulation on a PC.

I'm not sure which of the two you want. Will update my answer when you clarified your question. simulation or circuit?, To which signals you have access to?

  • \$\begingroup\$ I am reading the properties of signals (amplitude, phase) from digital power meter through RS-232 interface. I have not access to signal samples. \$\endgroup\$ Commented Jul 28, 2013 at 16:43
  • \$\begingroup\$ @truthseeker I don't get it. If you know the phase of the signals how can you not know the phase sequence? \$\endgroup\$
    – Alexander
    Commented Jul 29, 2013 at 10:08
  • \$\begingroup\$ Thats the question. Because there are many options how the vector are oriented one to another. There can be assymetric systems where U12 and U32 are largely different in absolute value. And secondly - I don't know phase voltages and phase phases, just line-to-line voltages and line-to-line phases. Its impossible on the first sight to say what the phase sequence is. Even if it would - how to tell it to computer through some programmic language? I need an algorithm, mathematical algorithm. \$\endgroup\$ Commented Jul 31, 2013 at 20:18
  • \$\begingroup\$ When the electrical 3-phase network is balanced it is sufficient to measure just 2 line-to-line voltages and 2 phase currents and we can tell what the electric power is. We can save one current clamp (with associated measuring circuits) and one voltmeter / AD converter. \$\endgroup\$ Commented Jul 31, 2013 at 20:21

Put a capacitor and resistor in series across each line. Measure voltage from each cap to the other line. The line with the lowest voltage is lagging the other line.

But if @optionparty is right that you only have two wires, there is no way. Maybe you mean two lines, and the neutral?


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