As far I am aware they don’t. They shift power between real and inductive/capacitive, but unless you have a contract that reflects those (big power consumers like factories so) it won’t change your bill at all.
So it’s basically a scam, because a multimeter will show lower currents, but the electric company counts the actual power you consumed and not the current a multimeter shows.
The total power is dependant on Voltage, Current and Phase power factor (how simultanous Voltage and Current are). The device increases the power factor, reducing the current, but not your bill.
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