Computation of the Electromagnetic Coupling of Parallel Untransposed Power Lines

A correction current injection method for power flow analysis of unbalanced multiple-grounded 4-wire distribution networks

“…The main feature of this method is the inherent flexibility in how multiconductor network models and their associated effects are considered. Mutual coupling influences between phases, are computed through a method that was originally developed for calculating electromagnetic coupling of complex conductor geometries [15]. The use of such a multi-conductor approach facilitates accounting for any kind of interaction between phases meaning that any network shunt element connections can be considered in terms of the system's phase and reference potentials and with respect to specific grounding (earthing) options.…”

“…The so-called YBranch represents the relationship between currents (positive if entering) and voltages (with respect to a common zero-voltage reference) of the 2n ports of the branch element. The construction of the Z and Yt sub-matrices within the π-model is obtained using the classical Carson-Clem formulation for a n-phase branch as described in [15]. An approximation of the correction terms for the real and imaginary components of the external part of the self and mutual impedance with earth return, is also provided in [15].…”

“…The construction of the Z and Yt sub-matrices within the π-model is obtained using the classical Carson-Clem formulation for a n-phase branch as described in [15]. An approximation of the correction terms for the real and imaginary components of the external part of the self and mutual impedance with earth return, is also provided in [15]. It is important to note that in practical cases these correction terms could be the dominant impedance in the 4-wire model, especially when considering unbalanced operation.…”

Passive mitigation for magnetic coupling between HV power line and aerial pipeline using PSO algorithms optimization

“…In low frequencies, the self and mutual impedances with earth return of the conductors are obtained according to Carson-Clem's formulae [34,35]:…”

“…where, R i is the DC resistance per unit length of conductor in (Ω/km), R GM is the geometric mean radius of the conductor in (m); d ij is the distance between the conductor i and the conductor j. These Carson-Clem's simplified expressions are generally sufficiently accurate when the mutual distance d ij between conductors i and j is less than 15% of the equivalent earth return distance D e [35].…”