A $$275$$ $$kV,$$ $$3$$-phase, $$50$$ $$Hz,$$ $$400$$ $$km$$ lossless line has following parameters:
$$x=0.05$$ $$ohms/km,$$ line charging susceptance $$y=3.0$$ micro-Siemens/k.

(a) Calculate the receiving end voltage on open circuit using justifiable assumptions.

(b) What load at the receiving end will result in a flat voltage profile on the line?

(c) If the flat voltage profile is to be achieved at $$1.2$$ times the loading in (b), what will be the nature and quantum of uniformly distributed compensation required?

A 66 kV, 3-phase, 50 Hz, 150 km long overhead transmission line is open circuited at the receiving end. Each conductor has a resistance of 0.25$$\Omega $$/km, an inductive reactance of 0.5$$\Omega $$/km and a capacitive admittance to neutral of 0.04 $$ \times $$ 10^-4 S/km.

(a) Draw the nominal π-equivalent circuit and indicate the value of each parameter.
(b) Calculate the receiving end voltage if the sending end voltage is 66 kV.

A 6.6 kV, 50 Hz single core lead sheathed cable has the following data:
Conductor diameter: 1.5 cm, length: 4 km. Internal diameter of the sheath : 3 cm
Resistivity of insulation : 1.3 $$ \times $$ 1012 $$\Omega $$-m. Relative permittivity of insulation : 3.5 Calculate

(a) the insulation resistance
(b) the capacitance and
(c) the maximum electric stress in the insulation

Each conductor of a $$33$$ $$kV,$$ $$3$$ phase system is suspended by a string of three similar insulators. The ratio of shunt capacitance to mutual capacitance is $$0.1.$$ Calculate the voltage across each insulator, and the string efficiency.