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You can try suing your landlord in small claims court for the increased electrical bill. These claims are difficult to prove (I think you at least have a "colorable claim" - meaning the basic elements necessary to create a cause of action - the landlord has failed to maintain the unit in a workable state, and caused you damages, namely the increased electrical cost, this is not a speculative damage, and is clearly identified), but small claims takes time and at least some money - usually about 4-8 months minimum.
You can find information about small claims here: https://www.depts.ttu.edu/sls/forms/How-to-Sue-in-Small-Claims-Court.pdf
Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.