JR West announced "In the case of electric power shortage alert, we will reduce frequency of Special rapid service by half."
In railway companies in Kansai, JR West is the 1st company that announced how to deal with electric power shortage alert.
The alert will be announced around 6pm on the day before implementation, when surplus electric supply is expected to become lower than 3%. After this announcement, JR West will reduce frequency of Special rapid service from 4 trains per hour to 2 trains per hour between Maibara and Himeji. This teduction is from noon to 3pm.
Citation: http://www.asahi.com/travel/rail/news/OSK201206280124.html
I wish this wouldn't affect my schedule on the next Saturday.