A domestic combined heat and power (dchp) unit includes a Stirling engine (1) to provide heat for a domestic dwelling along with a source of electrical power. Under normal operation, the dchp is supplied with power from the national grid. When there is an interruption in the mains power from the grid, the dchp switches into a grid independent mode wherein power is generated by the dchp and is supplied to a controller (26) and to a water pump so as to maintain integrity of heat supply to the dwelling; the remaining power after that is supplied to selected domestic electrically powered equipment such as lights or television sets. The invention also discloses methods for black start of the dchp during a mains power loss, and also modification of the operating voltage on start up of electrical equipment during a power loss, to prevent the Stirling engine stalling.