Calculate the Maximum Power That Transmitted To the Load?

A 25 MW load at the 33 kV receiving-end busbar of a short 3-phase transmission line has a power factor of 0.8 lagging. The line impedance is 

Z = Z ∠ Ψ = R + jX = 5 + j20 Ω / phase

 a) Using a simplified algebraic expression for the voltage drop across the line:

ΔV = V_S - V_R ≈ RP + XQ / V_R

 Where P and Q are the real and reactive power delivered to the load. Find

i. The approximate MVAr to be provided by a shunt reactive power compensator at the receiving-end in order to maintain the voltage at both ends of the line at 33 kV. Indicate whether the compensator is supplying or consuming lagging VAr in this case.

ii. The overall power factor of the compensator- load combination.

b) Show that the maximum real power through such a line can be formulated as follows:

P_max = V_S. V_R / Z - V²_R cos Ψ

Applying this relationship, calculate the maximum power that can be transmitted to the load under the voltage conditions of part (a).