On-board electrical system stabilization apparatus for a vehicle having a vehicle battery and an internal combustion engine, which comprises: - an electrical energy store for supplying electrical energy to an on-board electrical system of the vehicle; - a sensor device for detecting a voltage dip in the on-board electrical system; - and a controller which, when a voltage dip due to failure of the vehicle battery or disconnection of the vehicle battery from the on-board electrical system has been detected by the sensor device during an idle sailing state of the vehicle, in which state the on-board electrical system of the vehicle is fed by a generator, which is driven by the internal combustion engine, and the vehicle battery, and the power demanded by the on-board electrical system is greater than the power delivered by the generator, is designed to adjust a rotation speed of the internal combustion engine upward; wherein the on-board electrical system stabilization apparatus is also designed to feed energy from the electrical energy store into the on-board electrical system until the rotation speed of the internal combustion engine has been increased, wherein the energy store is designed to provide a reference voltage for controlling the generator. which comprises: - an electrical energy store for supplying electrical energy to an on-board electrical system of the vehicle; - a sensor device for detecting a voltage dip in the on-board electrical system; - and a controller which, when a voltage dip due to failure of the vehicle battery or disconnection of the vehicle battery from the on-board electrical system has been detected by the sensor device during an idle sailing state of the vehicle, in which state the on-board electrical system of the vehicle is fed by a generator, which is driven by the internal combustion engine, and the vehicle battery, and the power demanded by the on-board electrical system is greater than the power delivered by the generator, is designed to adjust a rotation speed of the internal combustion engine upward; - an electrical energy store for supplying electrical energy to an on-board electrical system of the vehicle; - a sensor device for detecting a voltage dip in the on-board electrical system; - and a controller which, when a voltage dip due to failure of the vehicle battery or disconnection of the vehicle battery from the on-board electrical system has been detected by the sensor device during an idle sailing state of the vehicle, in which state the on-board electrical system of the vehicle is fed by a generator, which is driven by the internal combustion engine, and the vehicle battery, and the power demanded by the on-board electrical system is greater than the power delivered by the generator, is designed to adjust a rotation speed of the internal combustion engine upward; wherein the on-board electrical system stabilization apparatus is also designed to feed energy from the electrical energy store into the on-board electrical system until the rotation speed of the internal combustion engine has been increased, wherein the energy store is designed to provide a reference voltage for controlling the generator.