A hybrid electrical power supply system for an aircraft for supplying current to a load, the hybrid electrical power supply system comprising: an AC power source, wherein the AC power source comprises an electrical generator; an AC bus; first switching means arranged to switchably couple AC power from the AC power source to the AC bus; an HVDC power source, wherein the HVDC power source comprises a battery; an active voltage controller configured to generate a control signal representing a magnitude of a HVDC bus reference voltage; an active rectifier unit comprising an active rectifier configured to convert AC power to HVDC power and a controller configured to control the active rectifier to adjust an HVDC bus voltage in dependence on the control signal received from the active voltage controller; second switching means arranged to switchably couple AC power from the AC bus to the active rectifier unit; an HVDC bus coupled to receive DC power from one or both of the HVDC power source and active rectifier unit in dependence on the HVDC bus voltage from the active rectifier unit; an HVDC load coupled to receive HVDC power from the HVDC bus; and a flight power management controller configured to send power flow management commands to the active voltage controller to optimize overall energy usage and reduce fuel burn, wherein the flight power management controller is configured to perform operations comprising: determining what is a current phase of the flight of the aircraft; determining a battery state of charge; determining a fuel level; adjusting a battery usage profile in dependence on the flight phase, battery state of charge and fuel level; setting a battery discharging or charging current in accordance with the adjusted battery usage profile; and commanding the active voltage controller to cause the battery to be discharged or charged in accordance with the set battery discharging or charging current. an AC power source, wherein the AC power source comprises an electrical generator; an AC bus; first switching means arranged to switchably couple AC power from the AC power source to the AC bus; an HVDC power source, wherein the HVDC power source comprises a battery; an active voltage controller configured to generate a control signal representing a magnitude of a HVDC bus reference voltage; an active rectifier unit comprising an active rectifier configured to convert AC power to HVDC power and a controller configured to control the active rectifier to adjust an HVDC bus voltage in dependence on the control signal received from the active voltage controller; second switching means arranged to switchably couple AC power from the AC bus to the active rectifier unit; an HVDC bus coupled to receive DC power from one or both of the HVDC power source and active rectifier unit in dependence on the HVDC bus voltage from the active rectifier unit; an HVDC load coupled to receive HVDC power from the HVDC bus; and a flight power management controller configured to send power flow management commands to the active voltage controller to optimize overall energy usage and reduce fuel burn, wherein the flight power management controller is configured to perform operations comprising: determining what is a current phase of the flight of the aircraft; determining a battery state of charge; determining a fuel level; adjusting a battery usage profile in dependence on the flight phase, battery state of charge and fuel level; setting a battery discharging or charging current in accordance with the adjusted battery usage profile; and commanding the active voltage controller to cause the battery to be discharged or charged in accordance with the set battery discharging or charging current. determining what is a current phase of the flight of the aircraft; determining a battery state of charge; determining a fuel level; adjusting a battery usage profile in dependence on the flight phase, battery state of charge and fuel level; setting a battery discharging or charging current in accordance with the adjusted battery usage profile; and commanding the active voltage controller to cause the battery to be discharged or charged in accordance with the set battery discharging or charging current.