(Solved): Subject: Figure 1 shows the one-line diagram of a simple three-bus power system with generation at ...

Subject: Figure 1 shows the one-line diagram of a simple three-bus power system with generation at bus 1 . The voltage at bus 1 is \( V_{1}=1.0 \angle 0^{\circ} \) per unir. The scheduled loads on buses 2 and 3 are marked on the diagram. Line impedances are marked in per unit on a \( 100 \mathrm{MVA} \) base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected. To determine the phasor and magnitude values of the voltage at the buses 2 and 3 , the final solution using Ganss-Seidel method is: \[ \begin{array}{l} V_{2}=0.90-j 0.10=0.905554 \angle-6.34^{\circ} \quad \text { pu } \\ V_{3}=0.95-j 0.05=0.9513 \angle-3.0128^{\circ} \quad \text { pu } \end{array} \] 4) Active and reactive power of slack bus a Express the active and reactive power \( \mathrm{P1}-\mathrm{j} 1 \) with \( \mathrm{V} 1, \mathrm{~V} 2, \mathrm{~V} 3 \) and \( y \mathrm{j} \) ? \( P 1-j Q 1= \) \( \mathrm{b} / \) Calculate the per-unit value \( (\mathrm{P} 1-\mathrm{Q} 1) \) \( (\mathrm{Pl}-\mathrm{jQ1}) \mathrm{pu}= \) Deduce the value of \( \mathrm{P} 1 \) and \( \mathrm{Q1} \) \( \mathrm{Pl}(\mathrm{MW})= \) Q1(Mvas) \( = \) 5) Line currents a) According to the following figure, express the current lij with \( V_{i}, V_{j} \) and \( y_{i j} \) b/ With line charging capacitors neglected, find the line currents? 6) Line flows 7) Deduce the line losses 8) Complete the power flow diagram shown in figure.2 Figure. 2: Power flow diagram. (powers in MW and Mvar) 9) Give the advantages of Gauss-Seidel method? 10) Using LTspice software, plot the power flow diagram shown in figure. 2