Can transformers be used to adjust capacitors?

Question

It seems capacitors are subject to a "quality triangle", where we can only pick two out of three desirable traits:

• High voltage rating
• High capacitance
• Cheap

For example, a high-voltage high-capacitance capacitor is not likely to be cheap.

But, can we get around that by adding a step-up transformer with a cheap high-voltage low-capacitance capacitor on the secondary? Since

$$Z_{reflected} = \left(\frac{N_P}{N_S}\right)^2 Z_{secondary}$$

then that low-capacitance capacitor will reflect a much greater $$ \frac{1}{j\omega C_{reflected}} = \left(\frac{N_P}{N_S}\right)^2\frac{1}{j\omega C} \Rightarrow C_{reflected} = \left(\frac{N_S}{N_P}\right)^2 C $$

Not sure if this is a common practice or not (or, if the cost of getting a properly-rated transformer would exceed that of just getting the more expensive, high-voltage, high-capacitance capacitor in the first place!)

Answer 1

Yes you can Place the cap bank on the end of a transformer or even an auto transformer .Remember that the windings must handle the leading reactive capacitor current .So if your Cap bank is rated for say 100KVAr then 100KW is your required transformer rating .This at power frequencies looks expensive .I have not seen this done .I have seen tertiery windings on an existing transformer at 60Hz allowing for cheaper low value high voltage film caps and have done this on a resonant mode powersupply at 150 KHz .I do not think that the economics will stack up for your job .

Answer 2

The short answer is "no." A capacitor is, fundamentally, an energy storage device. The energy density (joules per liter) of a particular kind of capacitor (film, electrolytic, whatever) is roughly constant, whether a particular module is optimized for high voltage/low capacitance or for high capacitance/low voltage. Transformers let us trade voltage for current, but the energy entering the low voltage side is still the same energy coming out the high voltage side. So the same volume of capacitance (and thus the same approximate materials and cost) will be needed to do the same job, regardless of which side of the transformer the capacitor is installed on.

More broadly, you may be interested in the concept of a Pareto Frontier. The phenomenon you describe of being unable to optimize multiple qualities simultaneously, and thus having to make tradeoffs among them, is pretty much universal.