I don't think there are any independent studies, because these things are all a scam. On this site, there are multiple threads discussing this very subject and the overwhelming sense is that it is nothing short of a way to get money from your wallet.
In the USA, power companies that I know of only bill people for ?real power?, not ?apparent power? ? which has components of both real and reactive power (by the way, heat loss is real power, not reactive power). So this device may "save" energy but it certainly won?t save you any money.
Industrial users do correct their power factor with banks of large capacitors, but thats because they?re charged extra for loads that are too inductive and because they use a lot more energy.
These ?power saver devices? are essentially Power Factor correction devices. Correcting a poor power factor will have no effect on the real component of AC power, as measured in your electric meter (residential). So, while this device may indeed correct the power factor and reduce the reactive power component, the load (Real Power) as measured by your meter, will not show any change.
Again if these types of devices really produced the savings that are claimed then the utility companies would be promoting these ideas and technology, and installing them at no charge to the consumer to help reduce the demand on the utility grid.
The websites for products like these extol supposed testimonials from residential and commercial customers, who are simply looking at their bill month over month. I think that is a non-scientific way to evaluate whether the product works or not. Energy use from month to month can vary for all kinds of reasons. The only meaningful way to test one of these products is to clock the electric meter before and after the product is installed, with the same exact devices running in the house or commercial building. That would be the only certified test comparison I would accept.
I wonder why no independent controlled tests have not been performed and why the US Department of Energy doesn't recognize these types of devices?
Here are some similar product discussions:
http://www.nlcpr.com/Deceptions1.php
http://energystar.custhelp.com/cgi-bin/energystar.cfg/php/enduser/std_adp.php?p_faqid=4941&p_created=1204908170
Good Luck!