Question

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is an infinite bus having a voltage of magnitude \(|V_3| = 1.0 \, \text{p.u.}\) and angle of \(-15^\circ\). A variable current source, \(|I|\angle \phi\) is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, \(\phi = \theta \pm \tfrac{\pi}{2}\), where \(\theta\) is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as: \begin{center} \includegraphics[width=0.65\textwidth]{19.jpeg} \end{center}

• A. Bus 1: Slack bus, Bus 2: \(P - |V|\) bus, Bus 3: \(P - Q\) bus
• B. Bus 1: \(P - |V|\) bus, Bus 2: \(P - |V|\) bus, Bus 3: Slack bus
• C. Bus 1: \(P - Q\) bus, Bus 2: \(P - Q\) bus, Bus 3: Slack bus
• D. Bus 1: \(P - |V|\) bus, Bus 2: \(P - Q\) bus, Bus 3: Slack bus

Hint:

In load flow studies: - Slack bus: voltage magnitude and angle specified. - PV bus: real power and voltage magnitude specified. - PQ bus: real and reactive powers specified.

Answer 1

The Correct Option is D

Step 1: Identify bus 3 (infinite bus).
Bus 3 is given as an infinite bus with fixed voltage magnitude (\(1.0 \, \text{p.u.}\)) and fixed angle (\(-15^\circ\)). - An infinite bus is always treated as the slack bus.

Step 2: Identify bus 2 (alternator bus).
Bus 2 supplies active and reactive power: \[ P_2 = 200 \, \text{MW}, Q_2 = 40 \, \text{MVAr} \] Thus, at bus 2 both \(P\) and \(Q\) are specified. Hence, bus 2 is a \(P - Q\) bus (load bus).

Step 3: Identify bus 1 (controlled current source bus).
At bus 1, the magnitude of the voltage is maintained at 1.05 p.u., but the phase angle of current is controlled (\(\phi = \theta \pm \pi/2\)). This implies: - Voltage magnitude \(|V|\) is specified. - Active power \(P\) is controlled by the current injection. Thus, bus 1 is a \(P - |V|\) bus (generator bus / PV bus).

Step 4: Categorize.
\[ \text{Bus 1: } P - |V| \, \text{bus}, \text{Bus 2: } P - Q \, \text{bus}, \text{Bus 3: Slack bus} \]

Final Answer:
\[ \boxed{\text{Bus 1: \(P - |V|\) bus, Bus 2: \(P - Q\) bus, Bus 3: Slack bus}} \]