Maybe, but it's not something you'd do individually. IF the power company has been overcharging everyone, then it's a viable class-action suit. If the power company has just been overcharging you, you're probably better off just asking them for a refund.
Typically the state regulatory authority (such as a Public Utility Commission) requires electric power providers to have a bill dispute resolution procedure. I would start by determining what their process is and get a copy of the rules governing their bill dispute procedure and follow the rules for initiating a billing dispute. To do this, you will want to call their "consumer services" or "customer services" division.
You also might want to see if you can get the billing history on this property and compare it to the period prior to when you moved in to determine if there are really any material differences in what is being billed.
Also, find out their meter reading procedures. Are they doing it manually or do they use some sort of remote or electronic meter reading in your area? Knowing how that works may bring you closer to an understanding of the possible sources of the problem with the recordation of your meter readings. Request that the meter itself be checked for proper operation.
Sometimes the issue can be in the billing process itself where a digit gets added erroneously to your consumption, mixup of addresses, etc Initiating the billing dispute through their consumer services division and obtaining the information described above will at least get you started toward getting some answers. Best of luck to you.