Due to the parallel alignment of phase conductors and shield wires, and the ground connections at each overhead tower, circulating currents in these ground loops are setup from magnetic induction. The true losses as a result of this current loop induction are not well described, and further modeling of this is desired, which could include mathematical modeling and electromagnetic simulations.
The mathematical approach should take into account all the mutual reactances of the three phases and the shield wire(s), and possibly also any electrostatic couplings (capacitive effects), by development of impedance coupling matrices, in order to precisely estimate shield wire current flows and voltage buildups, taking into consideration the length between ground points (span lengths), ground resistance, and phase and ground conductor spatial locations.
The outcome of the mathematical approach should be compared to simulated results from FEM models (COMSOL) simulating the magnetic and electric influences on shield wire(s) in vicinity of a three-phased system, and/or EMTP software (e.g. PSCAD) allowing for the setup of advanced electrical circuit models.
The results should be used to recommend optimal phase conductor and ground wire installation placements to reduce power losses from the induced current flows, and possible transposition schemes.