1. FIGURE 52 shows the one-line diagram of a simple three-bus power system with generation at bus I. The voltage at bus l is V1 = 1.0L0° per unit. The scheduled loads on buses 2 and 3 are marked on the diagram. Line impedances are marked in per unit on a 100 MVA base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected a) Using Gauss-Seidel method and initial estimates of Va 0)-1.0+)0 and V o)- ( 1.0 +j0, determine V2 and V3. Perform two iterations (b) If after several iterations the bus voltages converge to V20.90-j0.10 pu 0.95-70.05 pu determine the line flows and line losses and the slack bus real and reactive power. 2 400 MW 320 Mvar Slack 0.0125 0.05 300 MW 270 Mvar FIGURE 52

Q2\ The one-line diagram of a simple power system is shown in figure below. All impedances are expressed in per unit (pu) on a common MVA base. All resistances and shunt capacitances are neglected. The generators are operating on no load at their rated voltage. A three-phase fault occurs at bus 1 through a fault impedance of Zf = j0.08 per unit. Using Thevenin's theorem obtain the impedance to the point of fault and the fault current in per unit. Determine the bus voltages and line currents of generators during fault. X₁ = = 0.1 XT-0.1 3 1 to ojo XL=0.2 2 040 X₁ = 0.1

Q31 Generator cost rate functions in $/hr for a three-unit system are given as follows: Fl=0.004(P1) +5.3(P1)+500, F2=0.006(P2)² + 5.5(P2) + 400, and F3-0.009(P3)°+ 5.8(P3)+ 200 These three generators must supply a total demand of 975 MW. (1) Conpute 2. (i) Determine the total cost rate.

A three-bus power system has generators at buses 1 and 2 with per unit subtransient reac- tances G1X"=0.1 and G2X"=0.08. The per unit branch reactances are X12=0.05, X13=0.10, X23=0.05, with 0.0540 0.0368 0.0425 Zbus = j 0.0368 0.0506 0.0460 0.0425 0.0460 0.0782 The pre-fault voltage magnitude is 1.02 per unit and the system is unloaded. Suppose a three-phase fault occurs at bus 3. (a) Calculate the fault current I" at the faulted bus. (b) Calculate the per unit generator terminal voltages (V1, V½) during the fault. (c) Calculate the per unit line currents feeding bus 3 (I13, I23) during the fault.