A3. Transmission line equivalent circuit Due Tuesday, February 22 via Canvas Consider again the three phase transmission line from A2, Problem 1. The correct values (hopefully you got that from A2) for the series impedance and the shunt admittance per unit of length are: z = 0.13562+ 0.84869i y = 4.94335ix 106 Problem 1 1.1) 1.2) 1.3) 1.4) ohm / mi Compute the propagation constant and the characteristic impedance of the transmission line. Build the transmission matrix as a function of the transmission line length Assume the line is feeding a 161kV, 70MW/10MVAr load. Plot the efficiency of the line (in %) as function of the length of the line. What happens to the line efficiency as the length of the line increases? Problem 2 siemens / mi Assume now that z is purely imaginary. Repeat 1.3). What's the source of the losses on the transmission line? Problem 3 Assume now the transmission line is connected to a constant voltage source of 161 kV at the sending end and it is open (nothing connected to it) at the receiving end. Using the transmission matrix, plot the magnitude of the receiving end voltage as a function of the length of the line. What's going on here? (Hint: google Ferranti effect) Consider now the exact II equivalent circuit for the transmission line and assume the line is 100 mi long. 3.1) Compute Zs and Y. 3.2) Assume |V₁|=|V2|=161kV and 012-8°. Compute from the equivalent circuit the complex power at the sending end, receiving end and the dissipation of complex in each element. Check the conservation of complex power theorem. Problem 4 Consider the transmission line shown in the figure below. As can be seen, the series impedance is purely imaginary ( Z =jX) and the shunt impedance has been neglected. V₁/0■ P, Q V₁=1 per unit V₂=1 per unit X= 0.6 per unit 0=5⁰ jX 4.1) Develop an analytical expression for P and Q as a function of V₁, V2, 0 and X. 4.2) Typical values (in per unit) for V₁, V2, 0 and X are the following: V₂/0 Problem 1: 20 points Problem 2: 20 points Problem 3: 20 points Problem 4: 20 points Professionalism: 20 points ӘРӘ ӘР aQ Compute for the values specified above. What can you say about 9 9 2 ᎧᎾ Ꮎ ᎧᏙ , ' Ꮩ the sensitivity of P and Q with respect to 0 and V₁?