A device for covering the peak load of an electrical consumer (VB) that is connected to an alternating current terminal of a public electricity network (ENT). A power inverter (WR) is fed from a direct current accumulator (BAT) and is connected in parallel at the output thereof to the electricity supply (EB) of the consumer (VB). A measuring device (Z1, Z2) is connected in the connection circuit (EN) of the consumer and a control device (STE). With the aid of the measuring device (Z1, Z2), the control device monitors the energy consumption of the consumer (VB), estimates from it a consumption quantity of electrical energy (E*(T)) up to the end (T) of a given time interval, for example via linear extrapolation, and in the event that the prognosis value obtained in this way exceeds a given threshold value (E.sub.max), puts the power inverter (WR) in operation in order to support the supply of the consumer.