Question

A. Consider a simplified model of a transmission line with resistance and capacitance neglected. a. Show that the sending end real and reactive power are given by the equations respectively. Vs is the voltage magnitude at the sending end, Vr is the voltagemagnitude at the receiving end, is phase angle between the sending and receiving end voltages, and is the series reactance. When we use this or the more general formulas we say the voltage magnitudes are close to normal so the maximum real power that can be transferred is Pmax=VsVrX B. Assuming nominal values for voltage, calculate the real and reactive power at each end of the line using the simplified formulas, above, as wel as the exact formulas for -40 deg. 75 deg and 90 deg. Comment on the reactive power requirement; who supplies this reactive power? What are we assuming when we say Vs and Vr are nominal values? Next, let us look at voltage stability limits. C. In one of the Lectures, we derived an analytical solution for VL given Vs, Z and SL. A power factor correction capacitor was included. Re-derive and plot the solutions neglecting the resistance in the line impedance Z and omitting the capacitor