3 phases - 3 wires, no neutral - power computation

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Greetings from Belgium !

I am currently installing an OpenEnergyMonitor on my main fusebox.
I live in Belgium, and my house is connected with 3phases - 3wires (no neutral, 220V between phases, 132V between phase & ground). Half of the country is wired like that, another half is wired with 1phase 220V, and industrial buildings with 3phases + N - 380v between phases

My “loads” are evenly spread between L1/L2, L1/L3 and L2/L3, but I also have 3-phases loads (motors for woodworking tools for example)

I am using the latest 3phases 4wires/3wires firmware, written by Robert.Wall (great work, thank you!) and followed the calibration procedure in the pdf

I have 3 ct and 1 voltage sensor pluged between L1/L2.
When putting all CT on the same wire with a resistive load (kettle of 2kW), I can adjust calibration values. Then, I set the sketch to 3-wire and each CT to the phase it will be used on in the sketch, leaving the c.t’s on the test load. I measure around 1.5x the load value and pf of 0.75. Great, like expected in the pdf.

But when I place the CTs on each phase at their final location (not all 3 on the load-test phase), I measure half the power (I have to change the orientation of all ct to get positive power)

I tested by moving the kettle around phases, and this is the output :
232.66 9.786 9.814 0.513 0.000 -1336.95 0.0 80.79 0.00 50.263 -0.2932 0.0 0.6774 0.0000 300.00 Pulses=0 PLL is locked
(power1+power2 = 1336W)
around 10A in ct1 & ct2 (what comes in, goes out)

234.31 0.283 10.262 10.141 0.000 -1345.16 0.0 2370.03 0.00 50.263 -0.5444 0.0 0.9974 0.0000 300.00 Pulses=0 PLL is locked
(Power3 give the correct result)
around 10A in ct2 & ct3

235.01 9.593 0.586 10.018 0.000 -1264.73 0.0 1136.12 0.00 50.292 -0.5287 0.0 0.4826 0.0000 300.00 Pulses=0 PLL is locked
power1+power2 = 1264W
power3 =1136W
around 10A in ct1 & ct3

any idea on what I need to modify in the sketch to make it compute the correct total power ?
Thank you

Welcome to the OEM forum, and thank you for your kind words.

What do you mean by

A fundamental principle of power measurement in a polyphase system is that you need one less wattmeter than the number of wires. That means, for a 3-wire system, you need two wattmeters. Or in the case of the emonTx, two c.t. inputs and two voltage inputs (which are the equivalent of two wattmeters). We don’t have two voltage inputs, so one has to suffice. So we pretend that the third phase is a neutral, and we delay the one voltage sample by 60° and pretend it is the second voltage, because the angle between the two phases measured from the third (which is pretending to be the neutral) is 60°.

Now this means that the total power in the system is the sum of the two powers that ct1 & ct2 measure. Individually, the powers from ct1 & ct2 have no physical meaning as soon as any load is connected L1 - L2. (There is a note in the comments in the sketch that explains this.)

I presume you have put ct3 on the wire that is in effect the neutral, so you should discount this when trying to calculate the total power.

Thank you Robert for your reply.

In my config, I don’t have neutral wire. Between all phases I have 220V, and between each phase & gnd I have 136V.
With a small schematic of my breakerbox :

(this installation configuration is very common in my country)

So the monophase load is connected between L1-L2 or L2-L3 or L3-L1 (with specific recommendations not to unbalance the system), and 3phase load are connected on the 3 phases.

If I remove the 3rd CT (on phase 3), I measure about 1300W for a 2000W load (which is the serialoutput given in the first post, if we only take into account the first power result)

In my configuration, is it possible to measure all the power consumption directly from the 3 main wires ? or do I have to treat it as a “multiple monophase” system ? (each L1-L2, L2-L3, L3-L1 treated as monophase, with 1ct on one of the two wires), which means I can only monitor a few circuits ?

I’ll come back to this later.

I think I got the math on this problem

CT1 measures current on L1
CT2 on L2
CT3 on L3

current in the load1 = i12 between L1 & L2
load2 = i23 between L2&L3
load3 = i31 between L3&L1

so CT1 measures i12 + i31
CT2 = i12 + i23
CT3 = i31 + i23

CT1+CT2+CT3 = 2* (i12 + i23 + i31)

if I want load currents only :
(CT1+CT2+CT3)/2 - CT3 = i12
(CT1+CT2+CT3)/2 - CT1 = i23
(CT1+CT2+CT3)/2 - CT2 = i31
with matlab, everything matches (with sinus waves and delay for each phases)

and I can estimate the total power :
Ptot = V12 x i12 + V23 x i23 + V31 x i31

I’ll try to put that in sketch, then share it with the community if it works.

When you measure the line currents, I think my sketch as published will give you the total power in all your loads in power1 (the first data item sent by radio, see sendResults( ) for its position in other output formats), using the first two c.t’s for that, and therefore c.t’s 3 & 4 are free for individual circuits.

So your expression for Ptot is a very roundabout way of obtaining the total power.

It is never a good idea to subtract numbers that might be nearly equal, when the two nearly equal values will be subject to component tolerances. The difference will be subject to the sum of the errors in absolute terms, which might be a very large error in percentage terms.

Hello, I am from Belgium too :slight_smile:

I just bought the EmonTX Shield to monitor my power consumption with an Arduino. I am exactly in the same configuration as ‘pitouse’ [pierre jauniaux] (3phases - 3wires (no neutral, 220V between phases, 132V between phase & ground)). as I am in the early stages of the implementations, I tried to read a lot around to find a way to solve the readings for this configuration. So far, I am still a bit confused, and still do not know:

  • if I need 2 or 3 CT
  • how to modify your (Robert Wall) sketch, etc. (btw, congrats for the user guide attached with the code, it is quite exhaustive and already helps a lot!).

I was happy to find this thread, and if you can fill the above gaps, it would be wonderful.

Thanks a lot !

If you look at page 4 of the documentation, near the middle, you’ll see the setting WIRES explained…

If you change that in the sketch to

#define WIRES 3-WIRE

that changes everything so that the third phase is regarded as a neutral, the a.c. adapter is connected between phase 1 and phase 3, and phase 2 is 60° behind phase 1. Because phase 3 is regarded as the neutral, a c.t. on it will give you no additional information, so 2 c.t’s only are needed.

You can use CT3 & CT4 inputs for monitoring separate loads or groups of loads.

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Hi, thank you very much for your swift answer. This is perfect !

Best regards,

Hey Michel,
Keep me updated if it works “out of the box” in your case. In my understanding, we have to modify more deeply the sketch to make it work in our case. I didn’t have the time to modify the sketch yet and run some tests.

With our configuration, the system can be totally unbalanced in current. Phase 3 cannot be only considered as neutral and we need to measure it. Correct me if I am wrong please :slight_smile:

Hi Pierre, I will do some tests, I effectively have some concerns, because I fear that when a load is consuming power between Phase1 and Phase2, this will not appear in the measurement (both measures on L1 and L2 will be of same value and opposite sign thus the sum will be zero). We have in our configuration like 3 different Phase-Neutral networks (L1-L2, L2-L3, L3-L1, taking respectively L2, L3, L1 as Neutral for each network, depending on which Phase couple the load is connected).
Beware that I am no electrician (and my studies about that subjet are 35 years old and long gone :frowning: …) so those thoughts are only driven by my logic and maybe I am missing the understanding of electric power consumption theory.

Sorry, but you are wrong. If you study classical electrical engineering theory, then you can prove - and I have it in my University text books from 50 years ago (and I don’t think it’s changed since) and it is no doubt available on-line somewhere so I have no intention of copying it here - that you need one less wattmeter than wires when measuring power in a multi-phase system.

A wattmeter measures the power in a circuit by measuring the voltage and current and the phase relationship between them. (That latter point is most important: if voltage and current are 90° out of phase, then we all know that there is no nett power flow when averaged over one complete cycle of mains.)

The emonTx measures one voltage L1-L3, but internally it generates a copy of that delayed by 60° to use as the “estimated” voltage of L2-L3. So by measuring the L1 & L3 currents, it can perform exactly the same calculation as two wattmeters, and the total power measured is indeed the total power flowing in the three-phase system.

Can you explain to me why you think you need to measure the current in the third phase? Where does that current come from? If it is not the vector sum of the currents in the other two phases, then you have a fault to earth - it’s as simple as that.

And I’m afraid you too are forgetting that real power is being measured, so the power in L1 and L2 is being measured with respect to the voltages L1-L3 and L2-L3, and there’s a 60° phase difference between them.

Maybe you both would be reassured if you looked at my profile and checked my credentials?

If you’re still not happy, you can of course write your own sketches, or use somebody else’s.

Sorry if I offended you, it was certainly not my intention. As I wrote, my thoughts were exactly that: thoughts, based on (clearly wrong) attempt to visualise what is going on in the wires.
I trust you 100%, do not worry.
I guess the important thing to take into account is that we are facing a 3 vectors situation, with each wire being dephased from the others and not 3 parallels wires with the same phase; that is the hard part to visualise when you are not in the current theories knowledge (my case).

Some questions:

  • for NUMSAMPLES, you suggest in our case (3-WIRES / 50 Hz) to use 45, correct (I ask because the default 36 value is a multiple of 6 as well, which is required for a 3-Wire installation).
  • I guess the location of the vectors is important: how to determine what is L1, L2, L3 (with respect to the angles between each phase vector). Or the only important matter is to have the AC-AC Volts measure between one wire part of the CT measure and the third wire not part of the CT measure ?

There is no problem with using less than the recommended number of samples, other than you risk alias effects and so not reading high order harmonics correctly. But in any case, the EU standards should mean that there’s minimal power at those frequencies anyway. If you are using the 4th c.t., you probably need to use 36 samples. If it does not achieve phase lock, that will be the likely reason.

The important thing is Phase Sequence. You must identify the correct sequence of the three phases, and follow that accurately. Which phase you regard as Phase 1 does not matter (it could be brown, black or grey, whichever pair is most convenient for your a.c. adapter), the only important thing is to get the two c.t’s on the correct wires relative to that.

OK, I checked on the official mains meter, and the cables colours seems to follow HD308 norm (Brown = L1 - Black = L2 - Gray = L3) see page 5, “3 conducteurs”).
Obviously, my electrician clearly did not respect phase rotation order (Black-Gray-Brown in the cabling cupboard which I wrongly took as being L1-L2-L3) so maybe this is the root cause of the issues we see with the calculations. I will let you know as soon as I succeed to fix my setup.

(I have a power point socket on real L3 (Gray)-L2 (Black), therefore I guess I can threat my L3 as the L1 of your sketch, my L1 as your L2, and my L2 as your L3).

Hi Robert,
I understood why emonTX was unable to correctly calculate the total power of my setup.
I used L1-L2 as voltage reference, and measured i1 and I2

I thus moved the voltage measure to L3-L1, and kept CT1 and CT2 on L1 and L2. This works and correctly correspond to the 2watt-meter approach for measuring 3 phases systems.

At least I got back into my books to read again the 3 phases theory that was in my attic ! :smiley:

Thanks Robert.

The sequence is correct, it’s just that it is rotated by one. That has happened before. It won’t matter for most loads, but if you connect a 3-phase motor and the sequence is wrong, it will rotate in the wrong direction. (There is an old electrician’s joke: If you connect a motor and goes in the right direction first time, immediately go out and buy a lottery ticket, because luck is on your side :smiley: )
Sequence does matter with the 3-phase sketch too, because it must synthesize the second (and usually the third) phase voltages internally, and those must agree with the c.t. placement on the cables.

There is a procedure in the installation instructions to help you identify the phases correctly.

Yes, that’s fine. There is no such thing as absolute phase - everything is relative. It is only the sequence that matters.

This is just perfect now:

For instance, lighting a 150 W halogen lamp (I have reduced the output because I do not use CT4, TEMP, so I cut out all the temps and “4” values etc…):

17:31:23.295 -> 275.26 3.950 3.996 0.000 -1332.49 0.0 -0.06 50.032 -0.6092 0.0 0.0000 PLL is locked
17:31:28.277 -> 275.08 4.266 3.993 0.000 -1481.02 0.0 0.21 50.027 -0.6519 0.0 0.0000 PLL is locked

1332.49 + 150 => 1481.02 W

I tried several plugs in the house (to be sure to cover all combinations L1/L2/L3 regarding calibration) => always correct results !

Thank you a lot for your sketch and all your explanations (and your patience :slight_smile: ) !


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