Do 1,000 Volt electrolytics exist?

I don't think 1000V is feasible with electrolytics. So multiple in series is the only way. I built 4kV supplies that way from 250V capacitors.

Always place high value resistors in parallel with capacitors placed in series, 470k-1M is fine. Otherwise initial voltage distribution is determined by capacitance and longterm by leakage currents. And considering the huge tolerances, that could end very bad indeed.
 
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I haven't seen any above 700V either.
You can always put two in series to get the higher voltage rating but the capacitance is reduced.
Two 100 uF 700V in series will give you 50 uF at 1400V.
It's important to place a high-ohms, say, 1 meg, across each cap to ensure that the DC voltage divides up equally between the two 'lytics. If that caps have different leakage currents, the one with the lower leakage current could eventually end up in an over-voltage condition. The resistors need to swamp out the leakage current and impose an equal amount of voltage across both caps.
 
500V is the practical limit for aluminium oxide, the insulator in E-caps. Tantalum oxide has a lower practical limit, and I don't know about other alternatives like niobium.
There is probably no realistic option for higher voltages, since it would be a breakthrough for many present-day applications like electric vehicles, HV-DC links, etc. and would be highly prized.
Future developments are always possible of course
 
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It's important to place a high-ohms, say, 1 meg, across each cap to ensure that the DC voltage divides up equally between the two 'lytics. If that caps have different leakage currents, the one with the lower leakage current could eventually end up in an over-voltage condition. The resistors need to swamp out the leakage current and impose an equal amount of voltage across both caps.
Thanks for pointing out that important safety issue.
 
What is a typical leakage current on say a 100uF/450V?

Elsewhere I wrote, considering a 820uF 400V cap:

Connecting the caps in series can also work, but again, more connections and if one of the resistors gets disconnected the voltage balance over the caps is not assured. I also suspect that 470k are too small for equal voltage sharing - the current through the resistor must be (much) larger than the leaskage current of the caps. Caps with high capacity and voltage have quite a leakage. In the example below it is: I(uA) = 3*sqrt(C*V), so 3*sqert(820*400) = 1718uA, or almost 2mA. Say the bleeder must pass 5mA, each bleeding resistor must be around 80k. The whole string would produce about 10W of heat (2000V*5mA), which is never nice around caps.
https://www.chemi-con.co.jp/products/relatedfiles/capacitor/catalog/SMQN-e.PDF
 
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Someone on a Dutch audio forum claims that there is no need for parallel resistors, because the leakage current of the capacitor with the highest voltage will automatically increase and equalize the voltages. I think he claimed that series connections without parallel resistors are used in professional switch-mode power supplies. I never dared to put his theory to the test...

Besides, parallel resistors also work as bleeders and reduce the chance of electrocution somewhat.

Regarding leakage, the leakage of electrolytic capacitors typically gradually drops to decades below the specified value when they are kept under voltage for a long time. I wouldn't want to rely on that, though.
 
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It is indeed the parts "I never dared to put this theory to the test" and "I wouldn't want to rely on that" that stopped me from putting lots of similar components in series to achieve higher voltage ratings in a set of GM70 amplifiers I made. I went for 6kV diodes and 1300V caps, both at very reasonable prices when looking at the overall costs of such an amplifier. When doing uF/USD calculations using surplus HV electrolytics (from eg SMPS) - which I also like to use for lower voltage tube amplifiers - the math is different.

https://www.digikey.com/en/products/detail/epcos-tdk-electronics/B32320I1666K000/13914393
https://www.mouser.ch/ProductDetail/Diotec-Semiconductor/BY6?qs=OlC7AqGiEDngOM3wfJTVnw==&_gl=1*hwecbv*_ga*MjA5NDk3MjczNy4xNjkxOTExMzIw*_ga_15W4STQT4T*MTY5Njc1MjgwNS43LjEuMTY5Njc1MjgwNi41OS4wLjA.
 
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This putting lots of capacitors in series is done in industrial applications. We have capacitor boxes that are used for hybrid motors and they contain supercaps in series to have 350V working voltage. As a single supercap is 5V working voltage you need to put a lot of them in series. There is active equalisation however.
 
Someone on a Dutch audio forum claims that there is no need for parallel resistors, because the leakage current of the capacitor with the highest voltage will automatically increase and equalize the voltages.
Probably not worth the risk - for instance what happens when the caps discharge quickly and they have very unequal amounts of charge - one will go reverse-polarity. Over time this abuse will probably cause permanent damage. You also have this problem even with voltage balancing resistors as the variation in capacitance values is large with electrolytics. Certainly you should only put identical capacitors in series (same value, brand and batch number is good) - just like with batteries. I'd suggest adding diodes to prevent reverse-polarity to the capacitor/resistor chain, and maybe make those zener diodes. 400V zeners are expensive though.
 
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Not that anyone asked, but there is a nice way to actively balance series caps without much power dissipation. A two-series cap balancer is essentially the output stage of a class B amplifier with its input set to the mid point of the bus. This requires a small number of parts in order to work - not nearly as simple as a pair of resistors, but it uses very little power. I will post a few circuits if anyone is interested.
 
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Probably not worth the risk - for instance what happens when the caps discharge quickly and they have very unequal amounts of charge - one will go reverse-polarity. Over time this abuse will probably cause permanent damage. You also have this problem even with voltage balancing resistors as the variation in capacitance values is large with electrolytics. Certainly you should only put identical capacitors in series (same value, brand and batch number is good) - just like with batteries. I'd suggest adding diodes to prevent reverse-polarity to the capacitor/resistor chain, and maybe make those zener diodes. 400V zeners are expensive though.

Good that you mention tolerances. There are many applications where they never will be discharged quickly, but then you still have to take capacitance tolerances into account when you calculate the allowable voltage across the series connection.