The invention concerns an electrostatic precipitator comprising an ionisation stage, a collector stage and a power supply. The power supply comprises a first high-voltage power supply unit for applying a first DC high voltage to the ionization stage and a second high-voltage power supply unit for applying a second DC high voltage to the collector stage. The first high-voltage power supply unit is configured to operate the ionization stage current-controlled. A current sensor required for this is advantageously arranged in the return line carrying low voltage, for which purpose the first high-voltage power supply unit and the second high-voltage power supply unit are galvanically isolated from the mains connection and from each other.