Guru
Joined: 09/08/2007
Location: AustraliaPosts: 4406
| Posted: 11:00pm 03 Jul 2018 |
There are two different resonant frequencies that we should be interested in here, and both are important if the whole thing is going to operate efficiently as a "system".
The first involves a parallel resonance of the transformer secondary and the deliberate tuning capacitor we place directly across it.
A second resonance will be a series resonance caused by the series choke in the primary, and the reflected capacitance across the primary.
That reflected capacitance back into the primary will be the actual secondary tuning capacitor value, multiplied by the turns ratio of the transformer squared.
Now lets think about all this, because getting it wrong can have some pretty unfortunate effects, and getting it right can result in a very sweetly running and efficient inverter that runs with a lower stress.
The transformer secondary resonance can generate some pretty fearsome circulating currents, and if it happens to fall on a harmonic, particularly an odd harmonic of 50HZ, then you will very likely see some wiggles in the output waveform, especially at light load.
Even without a secondary tuning capacitor, there will be stray capacitance between the secondary and the core, and between layers and turns and it will still have a natural resonance all by itself (somewhere) without any help from extra added capacitance.
The series choke in the primary will generate a second resonance, and this can be even more of a disaster because its a series resonance which presents a very low impedance to the mosfet bridge at some unknown frequency. If that unknown frequency coincides with the PWM switching frequency, or even comes close, its going to present a very nasty low impedance load to the bridge.
To avoid all these evils, we need to be very careful and go about things in an orderly manner. I will give the solution without going too deeply into the theory.
I will take the liberty of using Renewable Mark's inverter as an example.
Very first step is to resonate the transformer secondary to 1.5 times the output frequency. 75Hz in Australia (and 90Hz in the US.) The purpose of adding this capacitor is to provide a very high attenuation of the PWM switching frequency.
In theory the more capacitance the better the filtering, but as we get down closer to 50Hz we can get a strong resonant buildup of energy which can make voltage regulation very difficult at light load.
But the trick is to resonate the transformer at EXACTLY 1.5 times the output frequency, so that any gradual resonant buildup ends up being out of phase with the next cycle. It has a magic self damping effect, and its amazingly effective. But you need to be within one or two Hz to get the maximum benefit. Mark's transformer tuned to 76Hz with exactly 6uF across the secondary.
Now we come to the choke. This absolutely must be a non saturating choke with sufficient inductance to limit the peak current flow through the mosfet bridge.
The 6uF tuning capacitor across the secondary will reflect back into the primary with turns ratio squared. In this case I don't know the exact ratio of Marks transformer, but I am assuming its about 9:1. So the 6uF on the secondary looks like 81 x 6uF or about 486uF across the primary.
Now the choke Mark is using measured as 125uH, and that will be in series with that reflected 486uF creating a very strong series resonance at around 646Hz.
That frequency needs to be well above 50Hz (almost x13) and well below 23.5Khz (about 36 times lower) so its well out of the way, and will be harmless where it is.
The choke will therefore present a very high impedance to the bridge at the PWM switching frequency, and should work very well. In fact the ripple current at 23.5Khz works out to about 8 amps peak to peak which is fairly low for a full rated load current of 100 Amps.
Cheers, Tony.