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Your bill should itemize, showing exactly how much per KwH you are being charged, and you can consult previous bills for comparison. You can also make sure that one month's end reading is the same as the next month's beginning reading.
The smart meter should actually result in a lower flat service charge, since it no longer requires human meter readers, which is why the utility company is using them in the first place. If they do something that reduces their cost, but then charge you more, they DO have some 'splainin' to do. Which they will 'splain by saying other costs have gone up.