I'd suggest that you discuss your concern with your home training nurse. Ask how long the internal battery in your cycler lasts. If your power is off longer than that but for a relatively short time, your nurse should be able to tell you what you need to do to complete that treatment, assuming your schedule would allow that. If the power might be off longer, it would probably be a good idea to have some CAPD supplies at home so you can do manual exchanges. Your nurse can tell you how many exchanges to do to make up for the time you missed on the cycler. Ask your nurse or contact the company that makes your cycler what size uninterruptible power supply (UPS) or battery backup you would need to run the cycler. Office supply stores sell them for a variety of uses, mostly for computers. I suspect you'd need to only use it for the cycler because of the electrical power required to run it.
Finally, be sure your utility company knows that you use a dialysis machine at night while your sleep (essential medical equipment) so they put you on a priority list to get power restored. Your utility company may have a form for you to complete or your clinic may need to have your doctor write a letter to the utility company about this need.