One of the nice or nasty things about 150Hz, is that is looks the same on all 3 phases, so if the 3f zero crossing is say 10 degrees after the 50Hz one, on one phase it will also be on the other 2 phases. So if the loads on all 3 phases were exactly equal, the 3 F, 9F components etc would all cancel. However this does not mean that you need a neutral to have distortion to the line waveform that gives a 150Hz repeating feature. In fact the 3 phase/ 6 diode bridge does it depressingly well because in reality the 6 diodes are never quite equal. So the answer is that the 3 F current in any one phase is imperfectly cancelled by the nearly corresponding 3F currents in the other two, and when the 150Hz current is   is 5-10 percent of the 50Hz RMS current then that 3F component is  is 30-20 dB down and is about the sort of thing you get with no special precautions taken.  I would expect any 3F currents flowing in the CPC to be a lot lower.

Mike.

thanks for your response Mike.

forgive my ignorance, but does this depend on how things are connected, and specifically whether that PE is just a case earth? I imagine that this issue arises all the time with industrial motors and drives, which are generally 3-wire with a PE connection somewhere

does this depend on how things are connected ?

It does. Massively.

The main source of earth currents is RFI filters of designs where the 3 phase lines are decoupled by capacitors wired in star with the star point connected to the incoming supply CPC.

In most cases the CPC is great for blowing fuses, but too high an impedance at higher frequencies say above a MHz or so, to do much more than function as a long wire antenna that happens to be grounded so far away it does not much affect the radiation of high frequencies from it.

There is a lot to be said for filter designs that use a delta of RFI capacitors of large value, and then parallel in some smaller ones in star but a lot of the folk in the business do not really understand EMC and tend to do what they did last time to avoid risk.

left to its own devices the 3 cap star is pretty good, so long as all 3 caps are the same value, and the 3 phase voltages also, as the 50Hz currents then cancel, much as a 3 phase resistive star load needs no neutral.

Unfortunately when filtering is most needed, the waveforms on the 3 phases are generally not quite the same, and there are high frequency components that are not equal in magnitude or phase and that do not cancel.

Mike.

thanks, Mike

sorry, it's taken me a while to get my head round this. please let me run this back past you to see if I understand it yet

a six-pulse rectifier connects the load across each phase pair in turn. this drags a lumpy current down each phase, and we use the convenient fiction of harmonics to describe that lumpiness. triplen load currents don't combine in a common conductor because there isn't one - could we go so far as to say that a six-pulse rectifier is essentially a delta connection?

is the phenomenon of triplen currents combining in the neutral conductor associated with having many single-phase connections, where each single-phase rectifier connects its load between phase and neutral, so each such rectifier is pushing a lumpy current down the neutral? stretching my earlier point, might we call this a star connection rather than delta?

There's then another issue of spill current from any filtering where, in the real world, the current through the capacitors won't balance

how am I doing?

Dave

Absolutely fine, apart from the 'fiction' part - it is no more a fiction than the fiction that my bank balance total is the sum of all the transactions on the account since I opened it ;-) 

Any repeating waveform really is a sum of multiples of the repetition frequency combined with suitable amplitudes and phases to make up the total at all times. How you deduce those amplitudes and phases, when only given the 'total balance'  time domain information, I defer to our dear departed colleague Mr Fourier, who worked it all out in the margins while the French Army was actually paying him to design a better cannon. (and then in the 1960s Cooley and Tukey wrote a computer program to do it and avoid recalculating the same thing more than once- the FFT - and now the world cannot move anything it seems without a digital signal processor in it somewhere.) Before that  we used 'tuned circuits' to extract the frequency component or components that we wanted, and in the radio world we still do.....

The problem with 1 phase is as you say - imagine a diode or  bridge of them, feeding a capacitor (or battery). The cap charges on the rising edges to the peak of the AC, and then as the AC drops away, the cap stays full, maybe declining slowly with the load and the AC voltage falls away and reverses. The result is a current that only flows at the wave tops (and bottoms on a bridge) and not in between. As you put it a 'lumpy'  current. So peak current many times the RMS, and flat top voltage waveform as the line voltage drop is time dependent with the current.

 3 of those, one each phase to neutral gives 3 pulses per cycle in the neutral, and as they do not overlap in time they cannot cancel,- result that cable where the copper in the neutral has a funny petrol blue colour and complaints of a hot smell, but no fuses blown....

Now with the 6 diodes no neutral  it gets a bit more fun - now the current always flows in from one phase (whichever is most positive) and out into whichever one or other of the other two is most negative at that instant in time. And I agree if the world were in perfect balance, then while any one diode would see a lot of 3F, the lines would not. But of course the diodes are not in perfect balance, the line resistances are not in perfect balance, and so maybe more current flows from red to blue on the upstroke than flows from blue to red on the down or something. We may assume that Red to yellow and blue to yellow cancel for now, though generally cancellation will be imperfect.

and yes caps have a 10% or 20% tolerance over their manufacturing range and further drift with temperature and ageing so that is not perfect either.

I think you have it, but this sort of mental gym is my bread and butter so I know I can accidentally  leave out the essential 'obvious' steps when explaining, so if things make no sense, do come back and I'll be very happy to have another go.

^

How 150Hz can give either crest  peaks or flat tops depending on the phase relation of the 3F to the fundamental

Also note that you could fill in those residual wiggles in the tops with a bit of 9th the right way up ;-)

Mike.

Dave Miller said:

and we use the convenient fiction of harmonics to describe that lumpiness

I'm not quite sure it's like that. The waveform exists, and it's possible to demonstrate that the harmonics in the waveform 'exist' by filtering out frequencies above and below them.

A little thought experiment tells us that, if we take for granted that a waveform can be made of of multiple frequencies of waves of different frequencies interfering with each other, then a regularly-repeating waveform can only be made up of harmonics (waveforms with integer multiples of the frequency) of the fundamental - so a 50 Hz square wave really does contain a 50 Hz sine wave, along with other harmonics - e.g. see https://pages.uoregon.edu/emi/14.php. This is the basis of Fourier Analysis, and its use in understanding the response of circuits when waveforms with harmonic contents are applied as voltages or currents relies on a principle of Superposition.

The response of circuits to waveforms that don't regularly repeat, can also be analysed based on harmonic content plus a set of transient functions (step, exponential rise and decay, etc.), and that is what Fourier Transforms are about ... this is definitely a step into abstract thinking and perhaps much more deserving of the moniker of 'fiction to describe' (I think mathematicians would prefer 'another paradigm' ... perhaps in the same way as Phasors are to dealing with reactance in AC circuits?).

Greetings all,

So the original question "with no neutral, where does the current arising from the third harmonic content of the line current flow? I’m trying to prevent unwanted tripping of the upstream 30mA RCD device."

The third harmonic content of the line current can create a residual current that may trip the device. However, if your EV charge point is a 3-phase 4-wire system that comprises of no neutral then the third harmonic current will not flow through the protective conductor (PE), but instead through the line conductors. This will create heat in the conductors due to the circulation of the third harmonic. The problem can be overcome with Third Harmonic Filter (THF) that eliminate up to 95% of third harmonics.

AMK said:

The third harmonic content of the line current can create a residual current that may trip the device. However, if your EV charge point is a 3-phase 4-wire system that comprises of no neutral then the third harmonic current will not flow through the protective conductor (PE), but instead through the line conductors. This will create heat in the conductors due to the circulation of the third harmonic. The problem can be overcome with Third Harmonic Filter (THF) that eliminate up to 95% of third harmonics.

The original question is perhaps a little mis-guided, in that it can't be a 4-wire system with no Neutral conductor. It would be a 3-phase 3-wire system by definition? There may be a neutral point in a 3-wire system but it doesn't have to be distributed, only earthed. That would be 3-phase 3-wire U₀/U 230/400. The alternative is a 3-phase 3-wire (delta) with one line conductor earthed, which is U₀/U 400/400

This is an important differentiation to answer the question you asked.

As Mike says in earlier posts, if it's 3-phase 3-wire 230/400 V, then some of the harmonics may travel back through PE, but some will still cause heating in the transformer.

However, if it's 3-phase 3-wire 400/400 V, then the harmonics pretty much all cause heating in the supply transformer.

Whichever, harmonics in general are bad for transformer efficiency and temperature, but triple-n harmonics cause additional problems for the neutral in 4-wire systems.

In the UK there are limits on harmonic distortion for equipment (EMC product standards) and installations as a whole (ENA EREC G5). Larger installations will require a harmonic study where equipment with power converters are used.

Hi Mike, Im glad you know a lot about the topic of 150Hz harmonics and how they affect the 3-phase system. You’ve explained how the 3F, 9F, and other odd multiples of 3F harmonics are made by the 3-phase/6-diode bridge and how they’re partly cancelled by the other phases. You’ve also said that the 3F currents in the CPC are likely to be much lower than the line currents. I have a few things to ask and say if you don’t mind:
• You said that the 150Hz current is 5-10 percent of the 50Hz RMS current, but how did you get that number? Is that a normal or a bad case? How does that change with different kinds and sizes of loads?
• You said that the 3F component is 30-20 dB down, but what does that mean for the power and voltage distortion? How does that change the power quality and efficiency of the system? How can you measure and reduce this distortion?
• You said that you’d expect any 3F currents in the CPC to be a lot lower, but how low is low enough? Is there a limit or a rule for how much harmonic currents you can have in the CPC? What are the risks or problems of having too much harmonic currents in the CPC? Cheers