ScottishPower Energy Networks said the substation in Cambuslang, South Lanarkshire, was completely destroyed in Monday night's blaze.
The cost of the damage is estimated at £50,000, while the fire caused a power cut affecting around 2,500 homes and businesses.
The company is offering a £5,000 reward for information leading to the conviction of those who struck on Burns Terrace just after 6.30pm.
Guy Jefferson, customer service director, said: "This was an extremely dangerous act and whoever was behind this vandalism clearly doesn't care about the consequences.
"The location of the fire is in a residential area and close to a number of homes.
"Given the time of day this incident happened, there could also have been children playing nearby.
"It beggars belief that anyone could risk the lives of local people in this way."
Anyone with information should contact SP Energy Networks on 0800 092 9290.