NO, not directly. Assuming this is a permanent type of installation that becomes "a physical part of" the property (i.e.; not a portable generator) the cost just gets added to the cost basis of your home. So you won't report this anywhere on your taxes until the tax year you sell or otherwise dispose of the property, or convert it to some type of business use, such as a rental property.
As far as I know, a generator doesn't qualify for any energy credits. See https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit for details.
No, in general, a home generator does not qualify as a tax deduction or as a home energy credit improvement.
However, if you are either renting a part of your home or you have a qualified home office, then the cost of the home generator could be included as a 'whole home' expense or a 'whole home' asset to be depreciated.
Also, the generator may qualify as a medical expense if it is required to run medical equipment deemed necessary by a doctor.