Nonlinear loads and neutral current

[synchro]

Look at it like this: "balanced" nonlinear loads on each phase to neutral will produce current, and that current will appear on the primary neutral in proportion to the transformer's voltage ratio.

Now, take those same loads and place them in delta. What happens? Does current appear on the primary neutral?

Obviously there will be essentially no current on a secondary side neutral of a wye-wye with only line-to-line loads, whether they are nonlinear or not.

If the wye-wye is made up of individual single-phase transformers I believe the neutral current on the primary side should also be negligible. For each line-to-line load, all of the current flowing through one phase winding connected to the load will flow back through the other phase winding, resulting in no current from their common neutral on the secondary side. The individual single phase transformers will reflect these same conditions to the primary side, resulting in negligible primary neutral current.

Now if the 3-phase transformer has common cores between phase windings (eg. 3, 4, 5 legs) then there is some coupling between the magnetic flux in the different legs of the cores. And even more so in the 3-leg variety because it's the least symmetrical for magnetic paths. So if there's a line-to-line load between two of the phases there will be some magnetic flux coupled into the core leg for the third phase. This would then cause some current to flow through the primary winding for the third phase, and therefore through the primary neutral. This effect would apply not only to currents at the fundamental 60 Hz frequency but also to harmonics. I don't know what level of neutral current this would cause, and it would obviously depend on the details of transformer construction.

 

[winnie]

What if it wasn't balanced? Still connected phase to phase, but just various nonlinear loads drawing current in various magnitudes. Would the still be no current on the primary neutral?

I don't know. I'm going to have to ponder this for a while

But think about what happens if you had a single phase L-L load with 3rd harmonic currents flowing. This would _have_ to flow through the transformer coils, and thus add on the neutral. But I'm not sure if you could actually _get_ 3rd harmonic currents flowing in this case.

An example of this is the use of '3rd harmonic boost' in VFD output. The PWM is intentionally modified to combine fundamental and 3rd harmonic. This boosts the fundamental component that the VFD can synthesize, and the 3rd harmonic doesn't enter the motor.

LIke I said, I will need to ponder this for a while.

-Jon

 

[synchro]

An example of this is the use of '3rd harmonic boost' in VFD output. The PWM is intentionally modified to combine fundamental and 3rd harmonic. This boosts the fundamental component that the VFD can synthesize, and the 3rd harmonic doesn't enter the motor.

-Jon

Right, the peak value of the fundamental frequency component of a square wave is higher than the peak of a square wave by about 27% ( actually 4/ pi ). Approximating a square wave by just adding the third harmonic of the Fourier series gets you most of the way there. So as Jon describes, the peak fundamental output of the VFD can be made to exceed the DC bus voltage.

 

[mbrooke]

Obviously there will be essentially no current on a secondary side neutral of a wye-wye with only line-to-line loads, whether they are nonlinear or not.

If the wye-wye is made up of individual single-phase transformers I believe the neutral current on the primary side should also be negligible. For each line-to-line load, all of the current flowing through one phase winding connected to the load will flow back through the other phase winding, resulting in no current from their common neutral on the secondary side. The individual single phase transformers will reflect these same conditions to the primary side, resulting in negligible primary neutral current.

Now if the 3-phase transformer has common cores between phase windings (eg. 3, 4, 5 legs) then there is some coupling between the magnetic flux in the different legs of the cores. And even more so in the 3-leg variety because it's the least symmetrical for magnetic paths. So if there's a line-to-line load between two of the phases there will be some magnetic flux coupled into the core leg for the third phase. This would then cause some current to flow through the primary winding for the third phase, and therefore through the primary neutral. This effect would apply not only to currents at the fundamental 60 Hz frequency but also to harmonics. I don't know what level of neutral current this would cause, and it would obviously depend on the details of transformer construction.

Did not know that.

So would line-line nonlinear loads cause primary neutral current and to what degree?

 

[mbrooke]

I don't know. I'm going to have to ponder this for a while

But think about what happens if you had a single phase L-L load with 3rd harmonic currents flowing. This would _have_ to flow through the transformer coils, and thus add on the neutral. But I'm not sure if you could actually _get_ 3rd harmonic currents flowing in this case.

An example of this is the use of '3rd harmonic boost' in VFD output. The PWM is intentionally modified to combine fundamental and 3rd harmonic. This boosts the fundamental component that the VFD can synthesize, and the 3rd harmonic doesn't enter the motor.

LIke I said, I will need to ponder this for a while.

-Jon

Is there any program that could simulate this for us?

What you said about 3 phase transformers is fascinating- and if there is neutral current on the primary how it differs between 3 leg, 4 leg, 5 leg, 6 leg and individual single phase units.

 

[gar]

190930-0811 EDT

mbrooke:

Assume 3 identical ideal single phase transformers connected wye to wye. Under steady state conditions no DC current flows, primary voltage is a precise replication of secondary voltage, and primary current is an exact replication of secondary current.

The secondary wye center point has no current flow anywhere external to it because there is no wire connected to it. At this point the sum of the three nonlinear currents of each secondary has to equal zero.

If the primary wye center point is connected to nothing, then there is no neutral external current there.

Now suppose that primary side is fed from a wye source with its center point grounded so that we have a reference point.

I would suggest that we may have an instantaneously varying voltage difference between the two primary side wye center points. If we connected those two center points together, then we may have a neutral current.

But now if there is no external current flow on the secondary side from its center point, then how can there be any on the primary side because of the exact replication of current from secondary to primary?

.

 

[mbrooke]

The original post is asking what happens when you have only L-L loads but fed from a wye:wye transformer. I think that this combination leads to some unexpected results.

1) When we talk about nonlinear loads, we are talking about loads where the current flowing through the load does not vary in a linear fashion with the applied voltage. This introduces harmonic currents to a system even when the applied voltage is perfectly sinusoidal.

I agree.

2) In the normal situation with nonlinear L-N loads on a 3 phase system, we care about the 'triplen' harmonics, because these are the ones that _add_ on the neutral instead of balancing. In a normal 'MWBC' you supply the different legs from different phases so that the neutral currents will tend to balance out. But even supplied from different phases the 'triplen' harmonics add, as if the MWBC were supplied from the same phase.

Correct, I agree

3) I would need to do more analysis, but my _guess_ is that if you had balanced 3 phase L-L loads, supplied by a wye secondary, that load induced triplen current would circulate through the loads, and _not_ couple to the transformer at all.

How would it circulate through the loads though? Wouldn't the load impedance "block" them?

4) If you have a wye:wye transformer any triplen current that does flow through the secondary would show up as triplen current on the primary.

-Jon

I agree.

 

[gar]

191001-0901 EDT

Now I see why I misunderstood the original post. It is written as "wye grounded wye grounded transformer". I did not read that as "wye grounded primary and wye grounded secondary transformer" but as a typo of "wye grounded transformer". Meaning the secondary was a wye configuration, and the secondary grounded.

.

 

[mbrooke]

191001-0901 EDT

Now I see why I misunderstood the original post. It is written as "wye grounded wye grounded transformer". I did not read that as "wye grounded primary and wye grounded secondary transformer" but as a typo of "wye grounded transformer". Meaning the secondary was a wye configuration, and the secondary grounded.

.

:blink:

I always thought wye grounded wye grounded was equal to wye grounded primary wye grounded secondary.

 

[winnie]

How would it circulate through the loads though? Wouldn't the load impedance "block" them?

Here is my thinking: imagine that you have a single phase load which, when you apply a sinusoidal voltage, both fundamental and 3rd harmonic currents flow.

Connect three of these loads in delta to a wye secondary. The applied sinusoidal voltages to the three separate loads are 120 degrees apart. Each load sees this sinusoidal voltage and both fundamental and 3rd harmonic current flows. But for the three loads the 3rd harmonic currents are _in phase_.

The load connected A-B has 3rd harmonic current flowing into the B node that will (in the balanced state) perfectly match the 3rd harmonic current flowing out of the B node into the B-C load. The B-C load will have 3rd harmonic current flowing into the C node that matches the 3rd harmonic current flowing out of the C node into the C-A load. Thus none of the 3rd harmonic current in this particular case actually couples to the wye.

Discussing this might actually be better on a live chat with a shared whiteboard

-Jon

 

[Carultch]

1

 

[synchro]

A somewhat practical example of a nonlinear load that could be put line-to-line across each pair of phases on a wye-wye secondary is a 4 diode full-wave bridge feeding a shunt capacitor and shunt resistor. This would be similar to many of the single-phase nonlinear loads that rectify the AC to provide DC for many applications including computers, lighting, etc.
Such a nonlinear load would draw current when the voltage across two phases V_L-L is near its peak value, but no current when |V_L-L| is less than |V_C|, where V_C is the voltage across the capacitor (and resistor). Therefore, there would not be any overlap between the time intervals when each of the three line-to-line loads conducts current. And when they do conduct, all of the current will that flows through each phase winding connected to a load will flow back through the other phase winding that's connected to the same load. Therefore no current will flow into the common neutral connection on the secondary because of any of the these line-to-line loads.

 

[mbrooke]

Discussing this might actually be better on a live chat with a shared whiteboard

-Jon

Can we make this happen? I think a Youtube video may suffice.

 

[winnie]

Is there any program that could simulate this for us?

What you said about 3 phase transformers is fascinating- and if there is neutral current on the primary how it differs between 3 leg, 4 leg, 5 leg, 6 leg and individual single phase units.

It could probably be simulated in any of the 'SPICE' programs...but you can almost do this in Excel. Use a sine function to calculate 3 sine waves every few 10 microseconds for your 3 phases. Subtract to get phase to phase voltage. Calculate phase to phase current through various load functions. Then calculate instantaneous current at each node.

Shouldn't be too hard.

-Jon

 

[mbrooke]

It could probably be simulated in any of the 'SPICE' programs...but you can almost do this in Excel. Use a sine function to calculate 3 sine waves every few 10 microseconds for your 3 phases. Subtract to get phase to phase voltage. Calculate phase to phase current through various load functions. Then calculate instantaneous current at each node.

Shouldn't be too hard.

-Jon

Need assistance

 

[winnie]

1

 

[mbrooke]

Well I gave it a shot in 'Open Office', and came up with the below graph. The blue line is the square term current similar to what Carlutch used. I calculated 3 phases worth and then calculated the 'sum' current seen by the wye supply. Notice the very pronounced harmonic content in the load (blue) relative to what the supply is feeding (red).

I'll see if I can send you the spreadsheet.

-Jon

Sent you an Email.

 

[gar]

191002-1256 EDT

If I take a DC power supply (transformer, full wave rectifier, large filter capacitor, and not fully loaded, but with substantial load) the output reads 17 VDC with about 0.04 V AC ripple, and the input has a large current pulse about 1.6 mS wide out ot 8.3 mS. The current pulse looks somewhat sinusoidal as would be expected, but of a higher frequency. The transformer magnetizing current is visible, probably not more than 10% of the load pulse. This load current pulse as seen at the transformer input would widen somewhat and get larger with a heavier output DC load.

The magnetizing current peaks at the trailing input voltage zero crossing, and the load pulse peaks at approximately the input voltage peak, 4 mS before the trailing voltage zero crossing. In other words somewhat following the peak voltage. Both as expected.

From an FFT the 1st, 3rd, and 5th harmonics are about the same magnitude. Then 7th, 9th, and 11th drop off. 13th and above are not distinguishable. FFT is not real good on the scope, but provides some idea of what happens. Some of the FFT is a result of the magnetizing current.

.

 

[mbrooke]

191002-1256 EDT

If I take a DC power supply (transformer, full wave rectifier, large filter capacitor, and not fully loaded, but with substantial load) the output reads 17 VDC with about 0.04 V AC ripple, and the input has a large current pulse about 1.6 mS wide out ot 8.3 mS. The current pulse looks somewhat sinusoidal as would be expected, but of a higher frequency. The transformer magnetizing current is visible, probably not more than 10% of the load pulse. This load current pulse as seen at the transformer input would widen somewhat and get larger with a heavier output DC load.

The magnetizing current peaks at the trailing input voltage zero crossing, and the load pulse peaks at approximately the input voltage peak, 4 mS before the trailing voltage zero crossing. In other words somewhat following the peak voltage. Both as expected.

From an FFT the 1st, 3rd, and 5th harmonics are about the same magnitude. Then 7th, 9th, and 11th drop off. 13th and above are not distinguishable. FFT is not real good on the scope, but provides some idea of what happens. Some of the FFT is a result of the magnetizing current.

.

I see. I still can't decide if the are reflected on the primary.

 

[gar]

191003-0811 EDT

mbrooke:

Assuming ideal transformers, then the current at the input of the transformer is a replication of the output current, but scaled by the turns ratio.

If on the output side the wye mid point only has internal current flow, that is, no outward neutral current (all currents balance at the midpoint), then on the input side there will be no external midpoint current flow because of the scaled replication of the currents. Whatever balancing was necessary for this to occur took place on the secondary side.

In the real world this won't be true because of magnetizing current, and slight differences in the transformers.

.

.