Mains harmonic current levels with a five step "stairstep" current - Page 1
Forum section: electronics / projects

author: ocset
author_rank: Super Contributor
timestamp: August 27, 2017, 07:14:45 pm
content: Rearding Class C regulatory limits for mains harmonic currents (EN61000-3-2)…..is it possible for a mains input current to a ~150W offline product to pass Class C regulations when it has no more than five steps in a “stairstep” mains input current waveform?Attached is the LTspice simulation of a “product” which produces a five stage “stairstep” mains input current waveform. If you run the FFT on the input current waveform, you will see that it fails Class C regulations for Mains harmonic current levels.(The excel doc shows that it fails)What I am asking is…… is it ever possible for a five step “stairstep” mains current to ever pass Class C harmonic regulations?Page 7 of the following shows the Class C mains harmonic current limits….http://www.epsma.org/PFCver100406_b.pdf(EN61000-3-2)

author: jbb
author_rank: Super Contributor
timestamp: August 27, 2017, 08:01:37 pm
content: Maybe - I'm not sure. Glancing at Table 2, it seems the Type C limits are quite broad (>20% 3rd harmonic allowed!). If you have variable power demand (e.g. dimming) you should also carefully check the standard to see what limits apply when at less than full load.This sort of multilevel staircase trick has been deployed in large (MW+) power electronics equipment for a while now, so there is a good chunk of research. Academic papers discussing 'Selective Harmonic Elimination' might be useful.Note that there (sorry, sorry, I can't remember the citation) is always a similar amount of harmonic distortion energy (?) coming out of your switching stage, which is determined by the number of levels. Changes to switching frequency or switching pattern (aka modulation scheme) can change the frequency distribution of this energy such that it becomes easier to filter out. (I.e. high switching frequency pushes the harmonic distortion to high frequency region, where smaller filters are required to stop it.)LTSpice does have a built in FFT analysis, which could be helpful when you start fiddling with things. The 'industrial' method that universities & large companies (ABB, Alstom, GE, Siemens etc.) will use involves heavy numerical optimisation using Matlab or similar.Also, remember you'll almost certainly need some filtering for EMI reasons.

author: fourtytwo42
author_rank: Super Contributor
timestamp: August 27, 2017, 08:09:26 pm
content: Quote from: treez on August 27, 2017, 07:14:45 pmOf course it is, simply apply passive LC filtering to the basic modulator!The cost and size of the passive LC is inversely proportional to the cost and complexity of the modulator, i.e. the more sophisticated (and expensive) the modulator the simpler and cheaper the passive filterThe trick is finding the sweetspot, lowest system cost.

author: ocset
author_rank: Super Contributor
timestamp: August 27, 2017, 09:28:42 pm
content: QuoteThanks, though Mains Harmonics are from 150Hz to 2.05kHz, so the filter will be very large.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 28, 2017, 01:23:14 am
content: Yes. Maybe. Maybe not. But it can be proven.Set up the Fourier series for a waveform of that type. I assume the voltage levels are fixed (quantized) because of the architecture, so that leaves each step timing as a degree of freedom.Evaluate the Fourier series, using a few trig tricks (you only need to consider 1/4 wave, as long as the adjacent 1/4 wave is flipped 180 from it, and similarly for the other 1/2 wave). You will obtain a system of polynomials in \$\cos n\alpha\$, where each equation gives the amplitude of a given harmonic, as a function of the voltage levels and switching times. Now it's a minimization or root-finding problem.If each quarter wave is one-to-one (rising monotonically), then there may not exist a solution, and you'll need to add more steps. If this restriction is removed (i.e., you allow that the output can dither between steps), then for an arbitrary number of transitions and an arbitrarily low distortion level (in terms of any harmonics you wish to minimize), there will always be a solution. (That is, it reduces to PWM -- just add more transitions until it looks right.)This is very nearly the domain ofmagic sinewaves, except those are done with binary levels (so, a tri-level inverter, for AC purposes). You use the same approach, in any case.This is easily solved with, say, a bit of Mathematica, or MATLAB, or a bit of code, or even with spreadsheets if you're feeling masochistic.I don't see what relevance this has with LED lighting solutions, though (to draw a rather abrupt conclusion, on the off chance it happens to be correct). Continuous level PFCis easier, and market availability reflects that.Tim