Note that, if it's truly the
Equivalent Series Resistance, DF is included.
In general, ESR depends on frequency. Because well, it's an equivalent, eh?
Its power is V^2/R but only the V dropped across the ESR, which you can't measure externally*. I^2*R is more practical.
*I mean, you can, actually -- through the magic of complex numbers! But phase-sensitive voltmeters are unusual, and having an accurate enough phase null of the capacitive voltage is quite tricky indeed.
I take it, the voltage you want to regulate, is AC mains, and the regulation shall be with respect to source and load variations (the full meaning of "regulation")?
The simplest off-the-shelf (but probably second least efficient
) option is: the ferroresonant transformer. Sola is the famous brand here, but there are others I think. A transformer is wired as an inductor coupled to a resonant tank; the coupling is through a ferromagnetic core, operated on the threshold of saturation. If voltage rises, saturation rises, reducing the transformer's gain. If load rises, saturation falls, increasing gain. One downside: saturation depends on flux (the product of voltage and time, or equivalently, the ratio of voltage and frequency), so while this works nicely on mains (that is amazingly consistently 50.000 / 60.000 Hz), it won't help all that much on a genset for example. These are inefficient because the core loss at saturation is quite high; a 1kVA transformer may dissipate 100W under most any condition, giving a maximum efficiency of 90%. Other benefits are the strong filtering of the resonant tank (removes EMI and surges), and the prevention of inrush currents (the output short-circuit current isn't much higher than the nominal rating).
A variac with servo control is much more efficient, but slow, and, well, requires a servo controller, eh?
Impedance dividers aren't really relevant, because there is no regulation as such. If you have a means of varying the impedances, you can achieve active regulation. This is feasible at radio frequencies (varactor diode), but harder to do at line frequencies. There is once again, the saturable reactor, or magnetic amplifier, which can be used with reasonable efficiency to create such a system. These were common back in the day, but are much heavier than modern alternatives like phase control. (Like the ferroresonant transformer, they are very robust, and can be made to filter and protect; a ferroresonant transformer is essentially a conveniently integrated example.)
One of the "other" options you alluded to -- you can construct an AC/DC transformer with a buck or boost switching circuit. To handle AC, you need to use bidirectional switches, and the switching must be synchronous (you can't rely on catch diodes when switching off). The input and output filtering must use nonpolarized capacitors, and can only afford so many uF of them (without drawing too much reactive current at mains frequency). A typical case might be a 100kHz switching frequency, with the filters rolling off at say 10kHz, so the switching noise is well filtered while only requiring a few uF total. With MOSFETs, this can be made arbitrarily efficient, but some downsides are surge and inrush robustness, which semiconductors really just don't have, not by themselves. A typical solution would be, MOVs on the input and output, clamping surges to 1-1.5kV; switches using 1.2 or 1.7kV SiC MOSFETs; isolated gate drivers; and a current and voltage mode control, to limit inrush current to safe levels and achieve output voltage regulation.
Tim
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