Problem $4(25$pts$)$:

For the shown HVDC terminal station, assume that the voltage at the AC filter terminal is equal to the rated voltage. AC frequency is $50$ Hz $.$ The filter is between the. AC network and the transformer.

$C_{11}=0\mathrm{.}834{10}^{-6}F$

$L_{11}=0\mathrm{.}100H$

$R_{11}=6\mathrm{.}91$

$Q_{11}=50$

$C_{13}=0\mathrm{.}834{?}^{1N6}$

$1q,$ D$...-$ o$$

$..--$

b$)$ Calculate the $50$ Hz reactive power delivered by each branch of the filter circuit.

c$)$ Assume now that the filter consists of only one branch per phase which is tuned to the eleventh harmonic, but delivering the same amount of $50$ Hz total reactive power which as furnished by the two filters in the original case. Find the branch inductance and resistance assuming the same value of quality factor.