Generalized Formulation for Electromagnetic Forces on Current-Carrying Conductors

A completely general and rigorous approach to the determination of electromagnetic forces between any number of conductors, each of arbitrary shape and located in an arbitrary manner in space, is developed. Neither the simple Ampère's law of force nor the modifications attempted by other recent investigators are sufficient to predict accurately the effects of heavy load currents and damaging fault currents. This inadequacy is due to the fact that the conductors deviate significantly from the straight, parallel condition assumed in most analyses. The equations developed in this paper and the associated computer program can solve for the electromagnetic forces in literally any system of current-carrying conductors and include all known previous attempts as special cases. This approach has been applied to recent designs of bundled conductor systems for extra-high-voltage transmission.