MODULE 3 — Line Parameters
3.1 Line Parameters: R, L, C
Resistance
$$ R = \frac{\rho l}{A} $$
Inductance (3-ph)
$$ L = 2 \times 10^{-7} \ln\left(\frac{D_{eq}}{r'}\right)
$$
Capacitance (3-ph)
$$ C = \frac{2\pi\varepsilon_0}{\ln(D_{eq}/r)} $$
3.2 Skin Effect
$$ \delta_{skin} = \sqrt{\frac{\rho}{\pi f \mu}} $$
$$ R_{AC} > R_{DC} $$
AC:
Skin Depth = Moderate
3.2 Ferranti Effect
$$ V_R > V_S \quad \text{(No Load)} $$
$$ V_R = \frac{V_S}{\cos(\beta l)} $$
3.3 Transposition of Conductors
Balanced Inductance
$$ L_a = L_b = L_c $$
GMD Equivalent
$$ D_{eq} = \sqrt[3]{D_{12} \times D_{23} \times D_{31}} $$