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I noted that in video, but actually it was drawn wrong, it showed it as a choke rather than a transformer be it buck or auto they really do the same thing. I have used many auto transformers and they work exactly like an isolation transformer but without the isolation. So output 220 volt at 8 amp and input will be 240 volt at 7.4 amp the transformer clearly gets warm so must use some power so output may be 1760 watts but input likely 1780 watts there will be some losses.As pointed out in the video when this snake oil device is reducing the voltage to the appliance the meter is still using the un-reduced voltage in the calculation of power being used. Hence for some loads the meter will be recording a higher consumption than the actual consumption of the load.
I was working at Sizewell power station building and we had a maze of tunnels to put temporary lighting in. My boss decided it would be better to use a festoon of fluorescent lamps so we had a load of 110 volt fluorescent lamps which were really standard 240 volt with an auto transformer to step it up, the transformer was marked 110 - 0 - 127 volt and the supply was connected to the 110 volt tapping, quick calculations 60W 110 volt so two lamps per amp so 16A supply with a safety margin so 25 lamps per festoon. Within a couple of hours called to failed lamps, after the third call took clamp on ammeter and they were using 25A no wonder 16A trip was opening. So we at first swapped all to 127 volt tapping instead but end lamps were not starting so returned the last 5 to 110 volt tapping. Measured current and down to 16A or just below so that 17 volt actually reduced the power used by 9A. I after that took a lamp and experimented with it and realised removing the PF correction capacitor also made a huge difference. With input to 110 volt tapping and capacitor removed it was drawing over an amp nearly double it's rating.
So there is no question with standard ballast controlling the voltage and correcting the power factor if required a unit like the Vphase can save a lot of money. It is NOT snake oil they CAN work. But for them to work they need to be supplying items like the fluorescent fitting, and today the good LED lighting with PWM drivers built in will not allow the unit to save money. However how many LED lamps do have a PWM driver and how many use a simple capacitor as a dropper? If using a capacitor what will the power factor be? In fact how will the transformer in the Vphase alter the power factor and is the power factor corrected in the unit?
Don't get me wrong I would never fit a Vpower unit, however I have fitted power factor correction units and they did reduce the bill. They were clearly tested and they did show a saving, however the 5% was for a house with no electrical heating of any type and if there was it was corrected for, so we are looking at houses with rather low electric bills to start with. So at £1 per month it would take 9 years to pay for its self.