[ I_sc^2 \cdot t = \kappa^2 \cdot S^2 \cdot \ln\left(\frac\theta_f + \beta\theta_i + \beta\right) ]
:
[ \boxedS = \max\left( S_ampacity, S_V_d, S_short-circuit \right) ] cable calc formula
…but that’s only the beginning. The steady-state ampacity of a cable is derived from the heat balance equation: [ I_sc^2 \cdot t = \kappa^2 \cdot S^2
(185 mm² Cu, R=0.106 Ω/km, X=0.078 Ω/km): [ V_d = \sqrt3 \cdot 340 \cdot 0.250 \cdot (0.106\cdot0.85 + 0.078\cdot0.527) \approx 12.9V ] Drop % = (12.9/400 = 3.2%) — within typical 5% limit. cable calc formula