The company said there had been a surge in thefts and attempted thefts of metal, with 1435 such incidents recorded at the company's substations since January 2011.
The firm said this had resulted in 140,000 homes put at increased risk of damage, 50,000 homes in Glasgow losing power for 30 minutes in November 2011 and the death of a 43-year-old man in July this year after an attempted theft from a substation in Lanarkshire.
Around 11,000 hours have been spent on repairs and reinforcements, ScottishPower said.
A new Copped It advertising campaign by ScottishPower Energy Networks highlights the potentially fatal consequences of thefts in and around substations and power lines. It is also offering a reward of up to £10,000 for anyone whose information leads to a conviction for stealing metal from ScottishPower.
Frank Mitchell, chief executive of ScottishPower Energy Networks, said: "As well as continuing to increase our own security and working closely with the police, we want to raise awareness of the threats posed by these kinds of thefts and we want to encourage people to report any suspicious behaviour they see beside our power lines and substations.
"We are happy to pay rewards for information that leads to criminal convictions"