In the article the review of using the supercapacitor energy storage systems in frequency-controlled alternating current electric drives for various purposes are given. The article discusses various variants for connecting the electric energy storage devices based on batteries and supercapacitors to electric drive systems. The structures of the power part of combined (hybrid) power supplies for electric drives of vehicles (hybrid electric vehicles and urban transport), general industrial electric drives (cranes, freight and passenger elevators) are given. The review focuses attention on the problems, that are typical for traditional solutions for the power part of electric drive systems, as well as on the effect, which can be obtained, when supercapacitor energy storage systems are used in frequency-controlled electric drives.