Abstract: Electrically driven mobile compressor or pump, comprising at least one compressor element or pump element for supplying a pressurised fluid to a network of consumers of such pressurised fluid; an electric drive motor with a variable speed control coupled to the compressor element or pump element and a controller for the variable speed control of the electric drive motor as a function of the flow rate of compressed gas and/or pressure demanded by the network, and a connection for connection of the compressor or pump to an electricity supply source, and the controller is provided with an algorithm with which the electric current drawn from the supply source can be limited to a set or adjustable maximum value by controlling the speed.