HOUSTON, May 30 (Reuters) - Luminant, the biggest electric generator in Texas restarted three North Texas coal-fired power plants in time for summer when power demand to run air conditioners traditionally soars, a spokesman said on Wednesday. The units are Monticello 2, a 583-megawatt coal plant in Titus County and two 800-MW coal units at the Oak Grove plant in Robertson County, the spokesman said. All three units restarted in the past few days, he said. Texas set a record for power use in May on Tuesday and the grid operator has warned the state is poised for a hotter-than-normal summer that will strain power resources. Earlier this month, Luminant executives disclosed that Monticello 2 had been shut since mid-December to address a main power transformer failure and that units at Oak Grove plant were shut in March and April to repair turbine bearing packing damage. Luminant is a unit of Energy Futures Holdings Co, which is owned by a group of private equity firms including Kohlberg Kravis Roberts and TPG Capital.