AC Capacitor current not smooth on scope

[Bob773]

I work in the power industry (standby generators) and have been playing with a scope recently.  Learning a lot by visualizing current phase shift, reactive power, etc.  I am using some motor run capacitors across 120v 60hz mains to look at the current phase shift and visualizing power factor correction.  The capacitor current shows up squiggly and not a smooth sine wave?  I have tried several different current clamps, different scale settings, and also a 10x line splitter.  The current for a resistive load or induction motor shows up very nice smooth sine wave as expected.  When I combine the inductive and capacitive loads on 1 circuit I get power factor correction like expected but the resultant combined current is also squiggly.  What causes this?  Please see picture, yellow is voltage, blue is current.  Thanks

[bdunham7]

If you look at the points where there is a kink or squiggle in your current trace and then go vertically to the corresponding point in time on your yellow voltage trace, you'll see a much smaller kink or squiggle, some may be barely noticeable or perhaps not really visible at all.  What happens with a capacitor is that it has a certain reactive impedance at 60Hz and the overall current will be approximately 120(V) divided by this impedance (ohms).  However, when there are harmonics present--and there is significant harmonic distortion in your voltage waveform--then the reactive impedance of the capacitor to those harmonics is lower and thus more current flow is sensed from them. 

Some of that distortion looks like it might be at the 13th or 15th harmonic, so even if that level of that harmonic was quite low, the current resulting from it would be 13X or 15X as much as for the same voltage at the fundamental.  IOW, if you had a 15th harmonic at 1% (voltage) of the fundamental, that would only be 0.01% of the power in a resistive load but across a capacitor it would result in a current of 15% of the fundamental.

[The Electrician]

I work in the power industry (standby generators) and have been playing with a scope recently.  Learning a lot by visualizing current phase shift, reactive power, etc.  I am using some motor run capacitors across 120v 60hz mains to look at the current phase shift and visualizing power factor correction.  The capacitor current shows up squiggly and not a smooth sine wave?  I have tried several different current clamps, different scale settings, and also a 10x line splitter.  The current for a resistive load or induction motor shows up very nice smooth sine wave as expected.  When I combine the inductive and capacitive loads on 1 circuit I get power factor correction like expected but the resultant combined current is also squiggly.  What causes this?  Please see picture, yellow is voltage, blue is current.  Thanks

The current through a capacitor is proportional to the derivative of the voltage applied to it.  Look in the math menu of your scope and see if it has a derivative function.  Set it up to display the derivative of your voltage waveform, and you should see the derivative waveform looking just like the capacitor's current waveform.

[Bob773]

Thanks for your response.  So I assume this harmonic distortion is “normal” for residential mains?  I am not sure if an isolation transformer will filter that?  Or I might try a stand-alone generator of sufficient size.  very interesting indeed.

[The Electrician]

The only way the capacitor current will look like a sine wave is if the voltage applied to it is essentially a perfect sine wave.  Since you have access to generators, try this experiment on the output voltage from a generator.  Only a generator that has an inverter in it generating the actual output voltage will have an output waveform that is anywhere near enough to a perfect sine wave to produce a clean sine waveform of capacitor current.

Just looking at the yellow waveform in your scope capture, you can see that it's not a perfect sine wave.  It has flat tops, and other distortions.

Does your scope have a derivative function? Try my suggestion to look at the derivative of your voltage.

[The Electrician]

Thanks for your response.  So I assume this harmonic distortion is “normal” for residential mains?  I am not sure if an isolation transformer will filter that?  Or I might try a stand-alone generator of sufficient size.  very interesting indeed.

Here's a capture of the grid waveform at my house.  The yellow waveform is the grid voltage, the blue is the current through a capacitor connected to the grid, and the (sort of) pink waveform is the derivative of the yellow waveform.

[bdunham7]

Thanks for your response.  So I assume this harmonic distortion is “normal” for residential mains?  I am not sure if an isolation transformer will filter that?  Or I might try a stand-alone generator of sufficient size.  very interesting indeed.

Yes, some harmonic distortion is normal and yours doesn't look particularly awful.  An isolation transformer wouldn't filter that out, a transformer would filter out lower frequencies and DC--but will pass harmonics at least up to a few kHz.  A generator is not likely to be much of an improvement on that unless you get a good quality inverter-style genset and only have 'nice' loads on it--and you'll still have subharmonics.

[Bob773]

Thanks again both.
The Electrician, I tried the diff math function but didn’t get very good results.  A quick search on the forum and it appears this is a pretty weak feature in my Rigol.  But the concept makes very good sense, the definition of how a capacitor works is essentially the derivative, never thought of it that way.  I spent 3 years in college for EE 15 years ago and after playing with a scope for several months I can finally really understand a lot of what I “learned” back then.  The scope takes all the mystery out of it.

[The Electrician]

When you get a chance, connect the cap to the output of some of the generators you have access to and scope the cap current.  It would be interesting to see what kind of results a modern generator would give.

And, or course, we'll all be waiting to see what you get!

[EPAIII]

Bdunham7 and The Electrician, thanks for what are probably two points of view on the same answer. It explains some mysterious waveforms I have seen over the years and never had time to really investigate. I need to read both answers again after some sleep.

And yes, modern scopes, particularly the DSOs are a real marvel.

[Terry Bites]

Hmm https://www.pscad.com/webhelp/Master_Library_Models/Passive/Filters/Passive_Filter_Design.htm

[eugene]

I tried the diff math function but didn’t get very good results.  A quick search on the forum and it appears this is a pretty weak feature in my Rigol. 

You might also try the FFT function. If the distortion in your voltage is harmonic distortion then you should (might) see the harmonics. But distortion is not always well characterized by harmonics.

And be glad your power doesn't look like The Electricians. That waveform might look fairly smooth, but it also looks very far from a sine wave. I would expect an FFT of that to include a decaying series of odd harmonics.

[The Electrician]

I tried the diff math function but didn’t get very good results.  A quick search on the forum and it appears this is a pretty weak feature in my Rigol. 

And be glad your power doesn't look like The Electricians. That waveform might look fairly smooth, but it also looks very far from a sine wave. I would expect an FFT of that to include a decaying series of odd harmonics.

My grid waveform is not all that bad.

Check these out: https://www.eevblog.com/forum/projects/show-us-your-mains-waveform!/

[Bob773]

So here is an older 15kw 3 phase diesel generator reconnected in zig-zag configuration for 120/240 single phase.  Running with no load.  I tried it line to neutral (120v) on both sides and they looked very similar.  Then I connected it 240v line to line, the capacitor current is somewhat smoother on 240v, but obviously still quite distorted. 2 screenshots

[Bob773]

And now for the inverter generator… I thought this might get interesting.  This is a tiny little Honda EU1000.  I didn’t think it would handle the 45uF cap so I connected 3 of them in series.  Kind of a strange AM looking wave.  But if you zoom in enough the current does look nice at the carrier frequency!