A modular system comprising electrical consuming units and an electrical connection unit. The connection unit has a contact plug for plugging into a power outlet and for electrical connection with a particular cable connecting an electrical terminal and distribution strip as well as one connecting the terminal and distribution strip to the contact plug. The consuming units have first connection elements for mechanical and electrical connecting to second connection elements on the terminal and distribution strip. The first connection elements are geometrically different depending on a maximum electrical power consumption of the respective consuming unit. The second connection elements are likewise geometrically different such that selected first connection elements cannot be connected to selected second connection elements. The type and number of second connection elements are determined such that a total maximum electrical power consumption of all electrical consuming units connected simultaneously is limited to a predefined maximum value.