What is the frequency of the oscillation you observe?
If it is relatively low frequency, then the drop is probably caused just by energizing the TPS61222 output cap and inductor. You could fix that by adding more hysteresis on the comparator. Seems unlikely to me, however, because the super cap is so large.
If it is highish frequency, it could be caused by inductive and resistive drops in the path between the supercap and the input to the TPS61222 (including the internal resistance of the supercap itself, which is likely considerable). Again, adding more hysteresis on the comparator will help fix it. You can also improve the situation by using a bulk input capacitor right next to the inductor to hold the input to the TPS61222 in the face of the relatively large currents you will see at startup - this will work if you take Simon's recommendation and drive the EN pin of the boost converter instead of a load switch. That recommendation is likely a good one anyways, since it saves you a part.
Note that if you are running a load at the output of the boost, you may observe some sort of "oscillation" any time your load power exceeds the input power from the cell. The solar cell will charge up the super cap until the boost turns on, at which point the power drawn from the SC exceeds that going in and the voltage starts to drop. It continues dropping until the TPS61222 turns off / gets disconnected, and then the process starts over.
Let's say your "inverter" works just like a battery backed up UPS, and that it has a pretty wide margin on its storage voltage, going from 14V down to 7V before it taps out.
That means your main capacitor in case of the low voltage option can only drop 7V.
The voltage drop across a capacitor is an integral over time of the current signal taken from it, which becomes a very nice fiddly bit of magic concerning systems of differential equations once you add in a 10W constant load and a variable converter efficiency, so I'm going to roughly ball-park it, because I'm lazy and it's evening and I have a million things to do.
(( Ref: Wikipedia page jumped to the spot where the voltage current relation of a capacitor is given ))
How will I do this?
- Coursely take 80% efficiency for a converter going from 12VDC to 120VAC (which may be seriously overestimating it in a DIY scenario, to be honest).
- Estimate the current draw to be constant, calculated at a capacitor voltage of 9.5V, rather than the exact average, which voltage I drew from my large hat of "that'll probably do". If you want to do other use cases, you can take the average, since a constant current assumption will be off any ways.
- Simplify the integral for constant current, which then becomes a simple linear equation: V = (I*t) / C.
So, the current from the capacitor will be:
I = (10W / 0.8 [=efficiency]) / 9.5V =~ 1.32A
Which then can be put into the simplified linear equation for the assumption of constant current (be aware, this is a very broad and lazy assumption):
V =~ (1.32A * t) / C
Let's say you want only ten seconds of power, with the known voltage drop of 7V across the capacitor, that becomes:
7V ~= (1.32A * 10s) / C
Which becomes:
C =~ 13.2As / 7V =~ 1.88F
Let's quickly do that for 120VDC as well:
Same assumptions, but the voltage range will be 80V to 120V, probably, so a drop of 40V is allowable, estimating the constance of current at the 90V point:
I = 10W / 0.8 / 90V =~ 139mA
with t=10s:
40V =~ 1.39As / C
C =~ 1.39As / 40V =~ 35mF --> Charged up to 120V = very, very lethal.
So, you see, I've already used a lot of assumptions about all the stuff you're not giving us about your project, and how you will personally be able to complete the electronics and it's still a lot of calculation, even though I made a very bad and broad assumption of constant current
The final choice will depend on fixing all the parameters and some will intertwine. There's no solution to that and that's what makes electronics design a difficult field.
This is just your very first, very broad ball park. But to be honest, re: "very, very lethal", if you are asking this question I don't really think you should be considering anything above 30VDC to store energy the likes of this.
Best Answer
You are wasting your time and money using supercaps because each tiny 18650 Li Ion cell has over 10 thousand Farads and you can use all of its Ah capacitance over a small voltage range of 3.7 to 3.0V unlike caps which must be up- converted to use all of its stored energy down to 0V. If you wanted more Jerk for about 100 milliseconds which won’t give you must acceleration boost averaged over 10 seconds.
But imagine baby elephant solution with costly power electronics to satisfy a super wide input Voltage range (>2:1 is wide, 10:1 is super-wide 100:1 is never a good idea, so think again. It’s a great idea to start snowmobiles for << 1s but not drain an e-bike for 10s with a heavy, expensive “white elephant” solution.
But hold this thought for another 10 years and maybe Maxwell will have a super corrosive solution with C60 electrodes that packs more energy/kg.
Also when using higher voltage batteries, you can expect higher ESR from series connections but enjoy less conduction losses for the same power demand since it uses less current.