Power System Transients, 2nd Edition

346 Power System Transients

In the frequency domain (FD), Maxwell’s equations are expressed as

() ()∇× =−

Er Brj

ω

(5.5)

() () ()∇× =+

Hr Jr Drj

ω

(5.6)

∇⋅ =

Dr r

() ()ρ

(5.7)

∇⋅ =Br() 0

(5.8)

where

j is the imaginary unit

ω is the angular frequency

The relations between the electric- and magnetic-ux densities and the

electric and magnetic elds are given as

Dr Er Er() () ()==εεε

r 0

(5.9)

Br Hr Hr() () ()==µµµ

r 0

(5.10)

where

ε

0

is the permittivity of the vacuum (8.854 × 10

−12

F/m)

μ

0

is the permeability of the vacuum (4π × 10

−7

H/m)

ε

r

is the relative permittivity of the medium

μ

r

is the relative permeability of the medium

ε is the permittivity of the medium

μ is the permeability of the medium

In a conductive medium, the following relation between the elect