Locating source of excessive energy use
Since you say your backup heat is electric, I'd say that's what is using all the power. It could be that the weather is unseasonably cold and that the backup emergency heat is kicking in often.
Your Nest Thermostat could be switching to AUX heat more often than your old thermostat would have.
Since you say your nest thermostat is new (last summer), It is likely that it is responsible for kicking on the aux (emergency) electric heat more often than your old thermostat. There are settings to change how often this happens described below.
Your Nest thermostat may calling for aux heat more often than your old one would have. This can be configured with Heat Pump Balance which you might try changing to Max Savings or balanced. Note that the link below states that Max Comfort, the most expensive option, is selected by default. This is probably the issue. If changing this doesn't help, then I'd call an HVAC specialist.


Because auxiliary heat is so expensive, running the heat pump longer is still cheaper than using AUX heat. Heat Pump Balance automatically turns the heat on early to reduce AUX heat use as much as possible and get to your target temperature on time. It can turn on the heat up to 5 hours before a scheduled temperature if necessary. So if your schedule says 70ºF/20ºC at 7pm, Heat Pump Balance can use Early-On technology to start heating as early as 2pm.
Heat Pump Balance gives you four options to choose from:

Max Savings - This is the best setting for saving energy. In Max Savings mode, the Nest thermostat gives the heat pump more time to get to your target temperature before turning on AUX and sets a lower AUX lockout temp.

Balanced - This setting will give the heat pump more time to work, but will still turn AUX on quickly if it looks like it won't get you to your target temperature on time. Balanced has an AUX lockout temp somewhere between Max Comfort and Max Savings.

Max Comfort - When you choose Max Comfort, the Nest thermostat will make sure you'll get to the temperature you want, even if it means using auxiliary heat. Max Comfort is the default setting for Heat Pump Balance and generally gives you a higher AUX lockout temp.

Off - You can also turn Heat Pump Balance off entirely and adjust your AUX lockout temperature yourself. The AUX lockout temperature can be changed in SETTINGS &gt; EQUIPMENT &gt; HEAT PUMP.



There might be something wrong with your heat pump.
It could also be that there is something wrong with your heat pump. IE, it is running and using some energy but not generating any heat. Eventually, this will lead to the thermostat switching on the emergency electric heat and that will use even more power. Call an hvac specialist and have it inspected.