+ Post New Thread
Results 1 to 18 of 18

17th November 2019, 02:11 #1
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
Hello All, we are looking at 5 pulse MPW for small inverters, 24VDC to 230Vac 50/60 Hz. ( unipolar for those tech savy in this area )
Is there a paper or person out there who has looked at the low order harmonics resulting from the 5 pulse approach and the spacing of the pulses and relative width at full power for lowest harmonic magnitude for the lower order harmonics?  particularly the 3rd, 5th, 7th, 11th, maybe the 15th
I guess I will be doing this from scratch from 1st principles to calc the harmonics resulting from the various arrangements possible  if someone has covered the ground before and zeroed in on the best relative spacing and relative widths I would be appreciative of some pointers in the right direction.
Most important is that the lowest harmonics have the lowest magnitude as, as you go up in freq the higher order are easier to filter.
Please no " guesses or 'helpful' suggestions " from those not au fait with fourier analysis or harmonic series mathematics or unipolar 5 pulse MPWM ( multiple pulse width modulation )
If some one has the ability to do this work  I would be happy to recompense for sound results
kind regards
   Updated   
additional info: the middle of the 5 pulses ( per half cycle ) is to be fixed, they are to vary in width to control Vout from no load ( skinny ) to full load ( maximum ideal width for min low order harmonics )  ta.

17th November 2019, 11:09 #2
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
1 members found this post helpful.

17th November 2019, 15:02 #3
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
A similar modulation scheme with harmonic cancellation is referred to as Magic Sinewaves, for some reason using an even number of pulses per half cycle. https://tinaja.com/glib/msinprop.pdf

Advertisement

17th November 2019, 19:03 #4
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
Hello FvM, yes your sketch is correct, the magic sine waves page does not quite cover what I am seeking ( 5 pulse unipolar ) I note that LT Spice will give me an FFT of a waveform  so I will begin there before I jump into the heavy maths for an analytic solution, kind regards,

17th November 2019, 23:28 #5
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
You can determine the optimal pulse timing for harmonic cancellation using fourier series and Excel solver. I'll send you an example tomorrow.
1 members found this post helpful.

18th November 2019, 04:16 #6
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter
Hello All, thought I would repost this here  as it essentially a mathematics problem.
Determine the placement and width of a 5 pulse multiple pulse width modulated (mpwm) system  unipolar on each half cycle
to get the least ( ideally zero ) lowest order harmonics for the 3rd, 5th, 7th, (9th) 11th, 15th
the lower the better for the lower orders as these are the hardest to filter ...
We are looking at 5 pulse MPW for small inverters, 24VDC to 230Vac 50/60 Hz. ( unipolar for those tech savy in this area )
Is there a paper or person out there who has looked at the low order harmonics resulting from the 5 pulse approach and the spacing of the pulses and relative width at full power for lowest harmonic magnitude for the lower order harmonics?  particularly the 3rd, 5th, 7th, 11th, maybe the 15th
I guess I will be doing this from scratch from 1st principles to calc the harmonics resulting from the various arrangements possible  if someone has covered the ground before and zeroed in on the best relative spacing and relative widths I would be appreciative of some pointers in the right direction.
Most important is that the lowest harmonics have the lowest magnitude as, as you go up in freq the higher order are easier to filter.
If some one has the ability to do this work  I would be happy to recompense for sound results
additional info: the middle of each of the 5 pulses ( per half cycle ) is to be fixed, they are to vary in width to control Vout from no load ( skinny ) to full load ( maximum ideal width for min low order harmonics )  ta.Last edited by FvM; 18th November 2019 at 12:38. Reason: Threads merged

18th November 2019, 08:42 #7
Awards:
 Join Date
 Apr 2014
 Posts
 16,022
 Helped
 3631 / 3631
 Points
 78,950
 Level
 68
Re: Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter
Hi,
I see your idea:
There are positive signals causung some overtones...and there is the same signal negative ...and you want it to cancel all the frequencies.
For sure they include the same frequencies and for sure the same amplitudes....but there is more than this: Phase. Phase or each frequency.
You can only calculate FFT if you have a signal with fully specified timing.
KlausPlease don´t contact me via PM, because there is no time to respond to them. No friend requests. Thank you.

18th November 2019, 09:25 #8
 Join Date
 Apr 2011
 Location
 Minneapolis, Minnesota, USA
 Posts
 13,006
 Helped
 2587 / 2587
 Points
 53,201
 Level
 56
Re: Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter
I assume the filter is an inductor or transformer? The tendency is that voltage falls immediately after a pulse ends. I think the aim is to add a few brief pulses, to slow the drop.
My simulation makes each pulse adjustable as to length and when it occurs in the cycle. Diodes steer them to a joint output. The load gets the positive portion of a sinelike waveform. The inductor value was selected so as to slow the upward transition of the long pulse so it resembles the rise of a sine wave.
It may work just as well to make pulse #2 the long pulse. It leaves more remaining pulses which can be more finely spaced.

Advertisement

18th November 2019, 10:03 #9
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter
As mentioned before, the fundamental and harmonic magnitudes can be best calculated and optimized using Fourier series.
You can superimpose 5 instances of the elementary double pulse with alternating sign to model the unipolar 5pulse pattern.
See the below appended Excel table. Excel solver must be installed to perform the optimization.

18th November 2019, 11:53 #10
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Re: Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter
as it is symmetric about pi/2 ( 90 deg ) this helps in the maths

18th November 2019, 12:14 #11
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Fourier analysis of 5 pulse MPWM ( multiple pulse width modulation ) for inverter

18th November 2019, 19:49 #12
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
great work FvM, unfortunately it is a bit hard to see what you have presented, the middle pulse should be the major one  as per your sketch, the next outer pulses should be about half the width of the middle one and the outer pulses should be about half again in width  this will get near to low order cancellation ( <30dB ).
I have been reconstructing a "filtered" "sine wave" output by putting the 1st, 3rd, 5th, 7th, 9th, 11th, 13, 15, 17, 19, 21 back together after seeing what they are from the MPWM, this gives me good optics on the progress, and the effect of each harmonic. LT spice seems to be good for this  generating the harmonic amplitudes from the MPWM, and for adding the harmonic sine waves in various harmonics and phases ....

18th November 2019, 23:58 #13
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
The emphasis of the presented results is on the feasibility of harmonic cancellation over a certain magnitude range. I'm assuming that this solution, if achievable, is also unique.
Because the magnitude of higher harmonics isn't represented in the error function, the solution isn't necessarily optimal according to more general criteria, e.g. meeting power quality standards with or without lowpass filter.
Alternatively you can include higher harmonics in the error function and optionally apply weighting. Lowest four harmonics won't be exactly cancelled, but total T.H.D. or some weighted error function can be minimized.

19th November 2019, 01:02 #14
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
Hello FvM, thank you for your kind remarks, can you please explain what r1, f1 is in the above? and the ratio or exact width of the 3 pulses in the above also ( middle, outer, next outer )  from inspection and from common sense 5 pulses ( in total ) will be able to greatly reduce the 3rd, 5th, 7th, and one other ( 9th or 11th  whichever gives the lowest overall THD )  however none of that is easily viewable in your presentation.
kind regards,

19th November 2019, 09:25 #15
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics

19th November 2019, 10:02 #16
 Join Date
 Aug 2015
 Location
 Melbourne
 Posts
 1,946
 Helped
 711 / 711
 Points
 11,899
 Level
 26
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
that is impressive  are the rise & fall times in radians?

Advertisement

19th November 2019, 11:00 #17
 Join Date
 Apr 2011
 Location
 Minneapolis, Minnesota, USA
 Posts
 13,006
 Helped
 2587 / 2587
 Points
 53,201
 Level
 56
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
By definition the output which closely resembles a sinewave has the least harmonic content. Or from another viewpoint, the less filtering needed, the better.
Here is my simulation which puts the first pulse as the widest. The first upwardgoing transistion is slowed by the inline inductor. The remaining pulses are timed to allow a gradual drop in amplitude. (And not the typical sharp drop). The result is sinelike. A sinewave serves as reference.
A switching arrangement unfolds the output polarity, so that the load receives bipolar AC.

19th November 2019, 13:13 #18
 Join Date
 Jan 2008
 Location
 Bochum, Germany
 Posts
 45,764
 Helped
 13912 / 13912
 Points
 261,871
 Level
 100
Re: Multiple pulse width ( 5 pulses ) inverter and lowest low order harmonics
are the rise & fall times in radians?
+ Post New Thread
Please login