07. How can I calculate electromechanical forces between conductors?

Example short circuit waveform (42kA_RMS-SYMM, 111.8kA_PEAK)

The Lorentz Force Law may be used to calculate the electromechanical force between conductors, as follows:

F/l = μ₀ * i₁ * i₂ / 2πs

Where:

F/l = Distributed force between conductors
F = Electromechanical force
l = Lineal spacing between cable restraints
μ₀ = Magnetic permeability constant
i₁ = Instantaneous current magnitude in conductor #1
i₂ = Instantaneous current magnitude in conductor #2
π = pi (mathematical constant representing the ratio of a circle’s circumference to its diameter)
s = Spacing between conductor centers

Most alternating current short circuit waveforms involve asymmetry due to transient and subtransient reactance, as well as unidirectional current contribution (i.e. dc offset).  As such, the most appropriate calculation for short circuit electromechanical forces between two conductors is the Lorentz Force Law.  Since the Lorentz Force Law considers two conductors, basic mathematical techniques may be utilized to solve for three or more conductors.

CAUTION: Equations that are based on the RMS or peak current magnitude in only one conductor are erroneous and should not be used for calculating forces between cables during an alternating current short circuit (i.e. where the short circuit includes asymmetrical current).  IEC 61914:2015 warns readers of this severe limitation.  Talon Products is pleased to assist with your cable force calculations utilizing our proprietary cable force calculation software.