I would suspect if you had done anything that would increase your power bill such as add a spa or swimming pool heater you would have expected the power bill to increase So being that you are here asking what the issue might be, I am sure that is not the case.
There are indeed several things that could make your power bill increase with the new heat pump.
1.You may have a refrigerant leak that is causing the outdoor unit to cycle off on low pressure and therefore causing the backup elements to heat the house.
2.Your heat pump could be operating in cool mode rather than heat also causing the elements to heat the house
3.Heating sequencer could be stuck causing elements to stay on.
4..Outdoor may not be coming on at all causing elements to run.
To the lay person who does not work on these units, the answer would be "since your unit is new, there is nothing to cause this". but to those of us in the field actually dealing with these issues, we know that many things can be wrong.
Some of these things you would need refrigerant gauges a volt meter and an amp meter to check. Some we can check visually.
My first suggestion is to call the installing contractor if you had a company install it as this is sure to be a warranty issue and they may even help with this high utility bill.
If this is something you want to troubleshoot, I will be happy to assist you. Just let me know if you have the meters and we will go from here.