A 400KV 50Hz Cable is 6km long. If the cable capicitance is 326nF per phase per km what are;
i) the charging current in each phase
ii) the total reactive power generated by the cable
iii) by deriving the formula for the maximum current that can be transmitted at a power factor angle φ find the maximum active power that could be transmitted at a power factor of 0.85, if the rating of the cable is 1000MVA.
as for (i) i did the following
found Xc = 9764.11ohms(for 1km)
(for 6km) Xc = 58584.66ohms
Ic = 400kv/9764.11ohms = 40.966A(1km)
Ic = 400kv/(6*9764.11ohms) = 6.828A (6km)
(ii) Q = V^2/Xc = 2.731MVAR
(iii) For part 3 i derived the formula for maximum current
Imax = sin φ * Ic + (Ic^2*sin φ ^2 - Ic^2 + Irat^2)^1/2
after I used S = √ 3 * Vl * I max
getting a value for I max of 833.33A
and to find the power P = √ 3 * Vl * Imax * cos φ
However i cant understand the link, why has the formula been derived when you can use the equation of Power ?
Can someone guide me if I m working out this problem correctly ?
Thanks in advance
i) the charging current in each phase
ii) the total reactive power generated by the cable
iii) by deriving the formula for the maximum current that can be transmitted at a power factor angle φ find the maximum active power that could be transmitted at a power factor of 0.85, if the rating of the cable is 1000MVA.
as for (i) i did the following
found Xc = 9764.11ohms(for 1km)
(for 6km) Xc = 58584.66ohms
Ic = 400kv/9764.11ohms = 40.966A(1km)
Ic = 400kv/(6*9764.11ohms) = 6.828A (6km)
(ii) Q = V^2/Xc = 2.731MVAR
(iii) For part 3 i derived the formula for maximum current
Imax = sin φ * Ic + (Ic^2*sin φ ^2 - Ic^2 + Irat^2)^1/2
after I used S = √ 3 * Vl * I max
getting a value for I max of 833.33A
and to find the power P = √ 3 * Vl * Imax * cos φ
However i cant understand the link, why has the formula been derived when you can use the equation of Power ?
Can someone guide me if I m working out this problem correctly ?
Thanks in advance