Thaddeus,
There are many variables that will affect your electric bill and it is a legitimate complaint from your tenant. It may not be proper for her to break her lease but if the electric bill is so high that it has changed the affordability ratio for her, you have a potential problem for non-payment! She is obviously a responsible person or she would not have asked you to change the lease terms. Here are my suggestions:
1) Ask your tenant about the difference in square footage between her last place and this. It should be easy to understand that a larger place uses more electric.
2) Ask about the size of her household, if there is a new baby or boyfriend, this will affect the electric usage. This is also easy to find.
3) Ask if she has any electric appliances that she did not have at the last place. New TV's, Computers, Printers, Entertainment systems all use electricity differently than she has done in the past.
4) Check the electric supplier and rate from her last home. If it is in the same city and a different supplier, have her change to the other supplier. If it is a different city and that supplier is not available or perhaps the same supplier but different negotiated rate with the city in your area, point this out. She should recognize that her move to be closer to work or whatever came with a price increase in electric that nobody knew about.
5) Check the usage of existing appliances and equipment. If someone in the house is mining Bitcoin for example and leaving the computer on 24 hours a day that will be more expensive. If she is using a washer dryer in your apartment but at her old place she had to go to the laundry room or laundromat, her costs may actually be less for the convenience and she doesn't recognize that. Check the age and function of the refrigerator. Sometimes these just use too much power. You may be able to borrow a gauge to measure the power consumption at your library or city hall or your local power company.
6) Check if she is now using more power supplies for devices. These buggers are power hogs!
7) Check with the power company to see if the bill is similar to the neighbors. If not, the problem is in your house.
8) Ask if the lights ever get suddenly brighter for a moment and then go back to normal or if the tenant notices that she must frequently replace bulbs. If yes, then you have a good indication of a loose neutral wire. Either way, check for a loose or resistive neutral wire in the house. This will drain power faster than you might imagine. The loose wire will periodically connect and then disconnect at unpredictable times perhaps even "connect" with a small gap that allows the power to flow but requires more of it to complete the connection. This is a dangerous fire and electrocution hazard and must be addressed immediately. Sometimes the only indication you have of this is the higher than normal bill. This was the problem in my home until my wife informed me that we were regularly paying double the rate the neighbors pay. The power company will check this likely at no charge. If you have one, the bill is higher because more voltage is required to run your devices due to a loss in the line.
Once you have identified the problem area, you can work on solutions. What follows are several solutions that are cheaper than finding a new qualified, responsible tenant.
1) Purchase, or have her do it, a supply of LED bulbs for every lamp and fixture in the house. The price of these devices has really come down and they are as affordable as the old carbon filament lamps once were. Some of these lights can last for 18+ years so they will still be there for your next tenant and they could possibly cut the electric bill by as much as half which, in your case would reduce the tenant back to her original power consumption level. If this saves the tenant, it is more than worth it.
2) Replace the offending appliance. If your refrigerator is sucking back power at pre-1970 levels, you need a new one anyway. Today's appliances are quiet and energy efficient. Any one appliance is cheaper than all the costs of getting a new tenant.
3) Get the power company to do an energy analysis and check the house for bad neutral connections as mentioned above.
4) Purchase a set-back thermostat for the house. These are big energy savers! Show the tenant how to use it, you can get one at the big box store or get a pro to install it for under $100 in most areas.
5) Buy some timers to control the power supplies on the tenant's devices. By midnight her phone and toothbrush are likely at full power and you can turn off the power to those outlets without interfering with the tenants' use of those devices. You can have the power come back on just before wake-up time just to be certain that the power is topped up. You can actually use these on all your electrical devices and appliances in the house. Turning off your equipment doesn't mean you cut the power, it only means you suspended the operation of it. If the equipment has a little red or green etc., led indicator on it, that is an indication that it is still using power to run your remote control and such.
6) Change the furnace filters and explain that the furnace/AC can use as much as 40% more with a dirty filter than with a clean one. That's a great way to get the tenant to commit to regularly changing them when she can see the difference in her pocket!
There are other things you can do besides this. Check with your power company or with the USA Federal Government. The government has got more stuff to work with than you could ever believe in all areas of your life and business. Check them out at https://www.usa.gov/
I hope this helps!
Holler if you heard me! I'm available to answer questions too.
Best regards,
Mark