εo 8.854 10 12−⋅:=4.32

f 60:= d 1.51100

⋅:= cm D 0.5:= meter ω 2 π⋅ f⋅:=

Cn2 π⋅ εo⋅

lnDd

2

⎛⎜⎜⎝

⎞⎟⎟⎠

:= Cn 1.325 10 11−×= F/m to neutral

Yn j ω⋅ Cn⋅ 1000⋅:= Yn 4.994i 10 6−×= S/km to neutral

4.39

Deq3 8 8⋅ 16⋅:= Deq 10.079= meter

From Table A.4 (Cardinal) r1.1962

0.0254⋅:= r 0.01519= meter

C12 π⋅ εo⋅

lnDeqr

⎛⎜⎝

⎞⎟⎠

:= C1 8.562 10 12−×=

Y1 j ω⋅ C1⋅ 1000⋅:= Y1 3.228i 10 6−×= S/km

VL 230000:= VLNVL

3:=

For a 100 km line length: Ichg Y1 VLN⋅:=

Ichg 0.429= per phase

4.46 part a

Deq3 12 12⋅ 24⋅:= Deq 15.119= r

0.03282

:= r 0.0164=

C12 π⋅ εo⋅

lnDeqr

⎛⎜⎝

⎞⎟⎠

:= C1 8.149 10 12−×=

X'C1

ω C1⋅:= X'C 3.255 108×= ohm-meter

For 125 km L 125000:= XCX'CL

:= XC 2.604 103×=

4.46 part b

H1 40:= H2 H1:= H3 H1:= H12 402 122+:= H21 H12:= H12 41.761=

H31 402 242+:= H31 46.648= H23 H12:=

X'C 3.255 108×=X'C2.8660

109⋅ lnDeqr

⎛⎜⎝

⎞⎟⎠

13lnH12 H23⋅ H31⋅

H1 H2⋅ H3⋅

⎛⎜⎝

⎞⎟⎠

⋅−⎛⎜⎝

⎞⎟⎠

⋅:=

XCX'C125000

:= XC 2.573 103×=