On May 15, Hankyu revealed they are to decrease local trains on Takarazuka Line and semi-express trains on Kyoto Line during daytime in the case that KEPCO request them to save large amount of electricity. Hanshin also reviews to reduce express trains. How many trains will be reduced is subject to the amount of saving electricity request.
On estimation, local trains between Umeda and Hibarigaoka-Hanayashiki will run between Umeda and Toyonaka, and semi-express trains for Kawaramachi from Umeda will depart from Ibaraki-shi (from 11:30 to 15:30). semi-express trains from Kawaramachi for Umeda will be changed to local trains and will terminate at Takatsuki-shi (from 11:00 to 15:30).
Hanshin plans to reduce express trains between Umeda and Amagasaki or Nishinomiya.
Citation: http://www.asahi.com/travel/rail/news/OSK201205150149.html
Only two railway companies in Kansai revealed train reduction plan. I'm afraid that the other railway companies will reduce trains more boldly.