Find the magnitude of the current in per unit through each transformer and the MVA output of each transformer. What problem do you detect? Show that the problem can b (b) From the point of view of load sharing are the values of transformer reactances given above ideal? Justify your answer. ) Draw an impedance diagram for the system. Show all impedance values in pu. Use a common MVA base of 100 MVA and a voltage base of 138 kV for the transmission lines. (b) Calculate the MVA supplied by each synchronous machine, if there is a three phase shortcircuit fault at bus C. Assume one per-unit prefault voltages and zero prefault currents throughout the system. [15 marks] (c) During the fault defined in part (b) the voltages at bus A and bus B will both drop. Which voltage do you think will drop more and why? (No calculation needed). (a) A 50 Hz three-phase transmission line is 400 km long. It has a total series impedance of 30 + j 140 Ω and a shunt admittance of 10 –3 90° S. It delivers 60 MVA at 275 kV, with 0.8 power factor lagging. Find the voltage at the sending end by (i) the short-line method (ii) the nominal – T approximation and (iii) the long-line equation. [25 marks] (b) Suggest an explanation for the difference in the magnitude of the sending end voltage that you found in part (a) (i) and the one you found in part (a) (ii). (a) Construct the admittance matrix for the network. (b) Using the Kron Reduction method, obtain a 4 × 4 admittance matrix by eliminating node 2 . [10 marks] (c) Use the Y – Δ (see page 22 of your textbook) to eliminate node 2 of the network and construct an admittance matrix for the reduced network. Compare this matrix with your answer to part (b). [10 marks] (d) The sum of values in row 2 (and column 2) of the matrix in part (a) should be zero, whereas the sum of values in row 4 (or column 4) should be –j1. Explain why? (a) Zbus by direct formulation (show all calculation steps); [10 marks] (b) the voltage at each bus using Zbus. (c) the current drawn by a capacitor of 4.0 per unit reactance connected between bus ground. (Use an appropriate Thevenin Equivalent circuit). 3 and [5 marks] (d) In practice what would be the purpose of the capacitor in part (c). Use your answer from part (c) to justify your answer. [The MATLAB file psa9p12.m should be used for this question. Draw the positive, negative, and zero sequence networks for the system. Include all impedance values. (b) A three phase fault occurs on line 1 at a point equidistant between bus 1 and bus 2. Calculate the following currents (in amperes): Fault current Line current for Generator 1 Line current for Generator 2 [10 marks] (c) Assume that a single line to ground fault at bus 2. Using the networks from (b), calculate (in ampere) the resulting fault current. [10 marks] (d) Thomas does not believe that the fault in part (c) will cause currents to flow in the delta winding of the 3-winding transformer. His reason is that the delta winding is not physically connected to anything. Provide a diagram and a few words to convince Thomas that he is wrong. A small electrical power system has four on-line generators. Incremental generation costs and power limits are given below. Draw a graph of the system incremental cost against system load ranging from 250 MW to 1200 MW. Neglect system losses. [20 marks] If the system load is 900 MW, deduce the optimum incremental cost and the corresponding power distribution among the generators. Do problem 13.17 in your textbook with a short term purchase request of 200 MW. In other words, all conditions remain unchanged except the load during the second interval is 1600 MW. (Please note that there are errors in table 13.6 of your textbook. You should perform your own calculations rather than rely on values given in that table.)