ECE470 POWER SYSTEMS I Homework Set 8 1. A 13.2 kV, 60 Hz, 42 MVA, Y-connected, eight-pole, salient-pole generator supplies a lagging rated load of 33.6 MW at rated voltage. Neglect armature resistance, Xd = 7.5 Ω, Xq = 5 Ω. Determine: (a) |Ef| and δ, (b) Reactive power developed, (c) Driving Torque and Overall Efficiency if the rotational losses are 1.25 MW, and the exciter draws a load of 0.5 MW. 2. In the system whose one-line diagram is shown below, the impedances are in pu on a base of 200 MVA, 69 kV. Both generators have 0.1 pu sub-transient reactance. Ignore the effect of any loads. a) Convert the generators to their Norton equivalent and draw the admittance diagram. b) Derive the [Ybus] matrix of the system. c) Determine the nominal symmetrical 3φ fault currents (kA) at each bus. d) Determine the current (kA) flowing from bus 3 to bus 4 when bus 2 is faulted. 3. In a system similar (but different) to the previous question generator 1 has an excitation of 124.2 kV, while generator 3 has an excitation of 138 kV. Both generators have 1.5 pu synchronous reactance. Loads are placed at busses 2 and 4, both loads are rated at: S = 0.9 pu, 0.75 lag pf (i.e., they are 0.9 pu when their voltages are 1 pu). Assume the answer to part (b) of Q2 is: (This is not the answer to part b of question2) a) Derive the [Ibus] matrix of the system. b) Determine all bus voltages (kV). −−−−−−−−−=7030040306130003050204002061j]Y[bus4. a) Load Flow analysis was performed on the system shown below and the base-case results are presented in tables 1 & 2. Determine: i) the current (A or kA) received at bus 4 from bus 2, ii) the current (A or kA) flowing into load 3, and iii) the power factor of load 4. b) Another load flow was run with one line removed for maintenance; the results are shown in table 3. If losses cost $175/MWh and the outage lasts for twelve weeks, how much is the increase in losses costing the utility? (Assume the loads are constant). c) It was decided to install capacitors at bus 4 during the outage. The results of a load flow are shown in table 4. Determine: i) The MVAR rating of the capacitor bank. ii) The capacitance/phase for wye-connected capacitors. iii) The saving in cost of losses achieved by installing the capacitors for the outage period, compared to not installing them during the outage.Table 1 MAG ANGLE PG QG PL QL ------------------------------------------------------------------------- BUS# pu degrees pu pu pu pu -------------------------------------------------------------------------------- 1 1.050 0.000 2.550 1.950 0.600 0.400 2 1.050 2.040 1.750 0.750 1.300 0.900 3 0.985 - 2.213 0.000 0.000 1.250 0.700 4 0.975 - 3.141 0.000 0.000 0.950 0.600 ----------------------------------------------- TOTAL 4.300 2.700 4.100 2.600 Table 2 LINE # BUS TO BUS P Q S ----------------------------------------------------------------------- 1 1 2 0.797 1.047 1.316 2 1 -0.705 -0.636 0.950 2 1 3 0.695 0.892 1.131 3 1 -0.601 -0.219 0.640 3 1 4 0.554 0.014 0.554 4 1 -0.334 0.080 0.343 4 2 4 1.005 0.386 1.077 4 2 -0.761 -0.865 1.152 5 3 4 -0.399 -0.381 0.552 4 3 0.295 0.285 0.410 Table 3 MAG ANGLE PG QG PL QL ---------------------------------------------------------------------------- BUS# pu degrees pu pu pu pu ----------------------------------------------------------------------------------- 1 1.050 0.000 2.750 2.003 0.600 0.400 2 1.050 -4.797 1.750 0.900 1.300 0.900 3 0.933 -8.945 0.000 0.000 1.250 0.700 4 0.953 -6.193 0.000 0.000 0.950 0.600 ------------------------------------------------ TOTAL 4.500 2.903 4.100 2.600 Table 4 MAG ANGLE PG QG PL QL ------------------------------------------------------------------------ BUS# pu degrees pu pu pu pu ----------------------------------------------------------------------------------- 1 1.050 0.000 2.450 1.600 0.600 0.400 2 1.050 -3.775 1.750 0.810 1.300 0.900 3 0.964 -13.073 0.000 0.000 1.250 0.700 4 0.980 -16.862 0.000 0.421 0.950 0.600 ------------------------------------------------ TOTAL 4.200 2.871 4.100