Several aspects of power distribution systems are described. One aspect relates to apparatus for providing a direct current to a load comprising one or more light emitting diodes. The apparatus comprises: a rectifier operatively connectable to a secondary winding of a transformer whose primary winding is for carrying a high-frequency alternating current; a first capacitor operatively connectable to the secondary winding; and a second capacitor operatively connectable, at least partly via the rectifier, to the secondary winding. The first and second capacitors together provide a reactance referred to the primary winding which substantially compensates for the reactance of the primary winding.