This is a real mess and there is a lot you aren't saying.
First, if you install solar panels on a home that is partly your residence and partly a rental, you can only claim a partial credit. Specifically, if less than 80% of the property is personal use, you must reduce your credit.
Second, you say your tenants are paying a "small amount" toward utilities. Are you treating this as a rental on schedule E? Are you charging rent at or above fair market value (what a landlord would charge a stranger to rent a similar property in the same neighborhood) or is this a more casual arrangement among friends or relatives?
Generally, if you are renting to strangers at a fair market rate, all the money you receive is "rent", even if you consider that it covers different categories (use of kitchen, space in garage or parking lot, utilities, etc.) Then your expenses are whatever you pay to the utility company, mortgage, property taxes, property insurance, maintenance, etc.
If you are renting below market rate, especially to family or friends, then there are a number of limitations on deducting rental expenses. This type of use may also be considered "personal use", that further limits you as to reporting it as a rental.
The solar credit is completely separate from monthly utility bills. On your own residence, you claim the credit one time only, as of the date the system is installed. You claim the entire contracted price when the system is installed, even if you are paying over time. If more than 20% of the property (by square footage) is a rental or other kind of business use, then you must determine the percent of personal use and only claim that percent of the cost. In other words, if you rent 25% of the house, and 75% is your personal residence, and the system cost $20,000, then you can only claim the credit on $15,000 of installation costs. If business use is less than 20% and personal use is more than 80%, you can claim the entire amount.
There is a separate solar panel credit for business property (section 48, I believe) that I don't know much about. I think it is 10%, and you might be able to claim that on the business percentage that is not eligible for the 30% credit on the personal portion.
