A superconducting electrical power distribution system comprising: a superconducting bus bar; one or more bus bar thermal conductor lines extending in thermal proximity along the bus bar to receive heat from the bus bar over the length of the bus bar; a plurality of superconducting cables electrically connected to the bus bar at respective electrical joints distributed along the bus bar; a cryogenic cooling sub-system; and a network comprising first and second thermal conductor lines, each line (203, 207) comprising a cold end which is cooled by the cryogenic cooling sub-system, and an opposite hot end, whereby heat received by each line (203, 207) is conducted along the line (203, 207) in a direction that is, during normal unquenched operation of system, from its hot end to its cold end; wherein each first thermal conductor line extends in thermal proximity along a respective one of the superconducting cables to connect at its hot end to the one or more bus bar thermal conductor lines adjacent the electrical joint of its respective superconducting cable, each first thermal conductor line thereby receiving heat from and cooling its respective superconducting cable over the length of the superconducting cable; and, the second thermal conductor lines connect at their hot ends to the one or more bus bar thermal conductor lines adjacent respective of the electrical joints, the second thermal conductor lines being in thermal communication with the first thermal conductor lines via their connections to the bus bar thermal conductor lines but otherwise thermally insulated from the superconducting cables; whereby, during a quench event at a location along one of the superconducting cables leading to local heating thereof, the or each second thermal conductor line connected at its hot end to the one or more bus bar thermal conductor lines adjacent the electrical joint of the quenched superconducting cable withdraws heat from the quenched superconductor cable via the hot end of the or each first thermal conductor line of the quenched superconducting cable, the withdrawn heat flowing along the or each first thermal conductor line of the quenched superconducting cable from the location of the quench event to its hot end. a superconducting bus bar; one or more bus bar thermal conductor lines extending in thermal proximity along the bus bar to receive heat from the bus bar over the length of the bus bar; a plurality of superconducting cables electrically connected to the bus bar at respective electrical joints distributed along the bus bar; a cryogenic cooling sub-system; and a network comprising first and second thermal conductor lines, each line (203, 207) comprising a cold end which is cooled by the cryogenic cooling sub-system, and an opposite hot end, whereby heat received by each line (203, 207) is conducted along the line (203, 207) in a direction that is, during normal unquenched operation of system, from its hot end to its cold end; wherein each first thermal conductor line extends in thermal proximity along a respective one of the superconducting cables to connect at its hot end to the one or more bus bar thermal conductor lines adjacent the electrical joint of its respective superconducting cable, each first thermal conductor line thereby receiving heat from and cooling its respective superconducting cable over the length of the superconducting cable; and, the second thermal conductor lines connect at their hot ends to the one or more bus bar thermal conductor lines adjacent respective of the electrical joints, the second thermal conductor lines being in thermal communication with the first thermal conductor lines via their connections to the bus bar thermal conductor lines but otherwise thermally insulated from the superconducting cables; whereby, during a quench event at a location along one of the superconducting cables leading to local heating thereof, the or each second thermal conductor line connected at its hot end to the one or more bus bar thermal conductor lines adjacent the electrical joint of the quenched superconducting cable withdraws heat from the quenched superconductor cable via the hot end of the or each first thermal conductor line of the quenched superconducting cable, the withdrawn heat flowing along the or each first thermal conductor line of the quenched superconducting cable from the location of the quench event to its hot end.