(Solved): 6. The figure shows the one-line diagram of a simple three-bus power system with generation at bus ...

6. The figure shows the one-line diagram of a simple three-bus power system with generation at buses 1 and 2. The voltage at bus 1 is V? = 120° per unit. Voltage magnitude at bus 2 is fixed at 1.05 pu with a real power generation of 400 MW. A load consisting of 500 MW and 400 MVAR is taken from bus 3. Line admittances are marked in per unit on a 100 MVA base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected. 913-20 Slack Bus V?1.0/0° P? P? 312 = -j40 3- 500 MW Y23 = -j20 400 Mvan 2 P?= 400 MW |V?|= 1.05 Determine: (a) (5 points) Show that the expression for the real power at bus 2 and real and reactive power at bus 3 are = 40|V?||V?|cos(90° - 8? +61) +20|V?||V3|cos(90° - 82 +83) = 20|V3||V?|cos(90° - 83 +61) +20|V3||V?|cos(90°- 83 +82) Q3-20|V3||V?|sin(90° — 83 +8?) +20|V3||V?|sin (90° - 83 +8?) +40|V3|² (b) (10 points) Using Newton Raphson method, start with the initial estimate of V(0) = 1.0 + 50 and V?0) = 1.0+ j0, and keep |V?| = 1.05 pu, determine the phasor values of V? and V?. Perform two iterations. (c) (10 points) Obtain the power flow solution using the fast decoupled algorithm. Find B. B" matrices. Perform one iteration. (1) (2) (3)