A 500-kV, 300-km, 60-Hz three-phase overhead transmission line, assumed to be loss-less, has a series inductance of 0.97 mH/km per phase and a shunt capacitance Zc, 0.0115HF/km per phase. (1) Determine the phase constant ẞ, the surge impedance Zc, velocity of propagation v, and the wavelength λ of the line. (2) Determine the voltage, current, real and reactive power at the sending end, and the percent voltage regulation of the line if the receiving end load is 800MW at 0.8 power factor lagging and at 500kV. (3) What will the load be to maintain [VS] = |VR with zero reactive power loss along the transmission line? (4) What is the maximum amount of real power that can be transferred to the load at unity power factor if the required load voltage should always be greater than 0.9 per unit (Vs = 500kV)? (5) How can we increase the maximum real power that can be transferred by this line to 1500MW for a unity power factor load if the required load voltage should always be greater than 0.9 per unit (|Vs] = 500kV)? (6) What will happen if the load is 800MW at 0.8 power factor lagging (Vs] = 500kV)? What is VR if the load is 400MW at 0.8 power factor lagging (Vs 500kV)? What could possibly be done to improve both power factor and receiving end voltage VR at the same time? What is the compensation will be if power factor should be between 0.9 lagging and 0.95 leading, and meanwhile 0.9 p. u. VR≤ 1.1 p. u?( here will be a region for the compensation. Please show the boundaries.) (7) If the load drops to one third of that during the day time (daytime load: 800MW at unity power factor), what will happen to the receiving end voltage (|Vs] = 500kV)? What can we do to maintain 0.9 p. u.≤ VR| ≤ 1.06 p. u.? show compensation values for both |VR = 0.9 p. u. and [VR] = 1.06 p. u.)