Energy transfer on three-phase high-voltage lines: the strange behavior of the Poynting vector

The energy transfer along three-phase high-voltage power lines will be analyzed using the Poynting vector. The result is somewhat strange: From a single-phase line it is well known that the time averaged Poynting vector vanishes at each point of the space in case of a pure reactive load since in that case no active power is transmitted. But in contrast, for three-phase lines, it comes out that there are regions in space where the time averaged Poynting vector does not vanish, not even in case of pure reactive loads, except the loads are balanced and the geometry of the line system is complete symmetrical. In detail it is shown that for an asymmetric but besides pure reactive load there are areas in space around the lines where active power is permanently transmitted in the direction to the loads whereas in other areas active power is permanently transmitted from the loads, i.e. in the direction to the generator. The paper discusses this surprising behavior and tries to give an explanation in terms of physics.