An important application of computers from the 1950s and onwards has been for designing and operating complex infrastructural systems like air traffic, telephony, railways, and electricity. This paper tells the story about how computers from the 1950s and onwards became an important tool for designing and operating the Swedish power grid. It describes two phases of this development. In the 1950s and 1960s, computers were used for making complicated calculations for designing power grids in a reliable way and optimizing the use of the different power plants. In a second phase starting in the late 1960s, computer systems were developed for real time monitoring supporting human control of the power grid. The paper analyzes by whom and for what purposes computers became tools for controlling electricity flows. In the conclusion, it also discusses the wider implications of computers for the development of the Swedish power system.