For the system in Figure 4 with given generation and load dispatch determine the voltages after two itterations of Gauss-Seidel method. Assume the initial voltage to be 1.01 at angle of 0◦ pu at bus 1, 1.015 at angle of 0◦ pu at bus 2, and 1.0 at angle of 0◦ pu at bus 3. All line impedances are in per unit on a common base, and charging is neglected. Take base power of 100 MVA.

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For the system in Figure 4 with given generation and load dispatch determine the voltages after two itterations of Gauss-Seidel method. Assume the initial voltage to be 1.01 at angle of 0 pu at bus 1, 1.015 at angle of 0pu at bus 2, and 1.0 at angle of 0 pu at bus 3. All line impedances are in per unit on a common base, and charging is neglected. Take base power of 100 MVA.

This diagram represents a three-bus power system network. Here's a detailed description of the components and parameters involved:

1. **Bus 1 (Slack Bus):**
   - Voltage \( V_1 = 1.01 \angle 0^\circ \).
   - Acts as a slack bus to balance the active and reactive power in the system.

2. **Bus 2:**
   - Voltage magnitude \( |V_2| = 1.015 \).
   - Active power \( P_2 = 180 \, \text{MW} \).

3. **Bus 3:**
   - Power flow out of this bus is \( 280 + j100 \, \text{MVA} \).

4. **Transmission Lines:**
   - Impedance between Bus 1 and Bus 2: \( z_{12} = j0.25 \).
   - Impedance between Bus 1 and Bus 3: \( z_{13} = j0.15 \).
   - Impedance between Bus 2 and Bus 3: \( z_{23} = j0.10 \).

The diagram illustrates a simple representation of a power system network where power flows between different buses through transmission lines with specified impedances. Bus 1 is designated as the slack bus, which means it compensates for the active and reactive power imbalances in the system. Bus 2 has specified active power output, while Bus 3 details the complex power being delivered. The impedances of each transmission line are purely reactive, denoted by "j" followed by the reactance value.
Transcribed Image Text:This diagram represents a three-bus power system network. Here's a detailed description of the components and parameters involved: 1. **Bus 1 (Slack Bus):** - Voltage \( V_1 = 1.01 \angle 0^\circ \). - Acts as a slack bus to balance the active and reactive power in the system. 2. **Bus 2:** - Voltage magnitude \( |V_2| = 1.015 \). - Active power \( P_2 = 180 \, \text{MW} \). 3. **Bus 3:** - Power flow out of this bus is \( 280 + j100 \, \text{MVA} \). 4. **Transmission Lines:** - Impedance between Bus 1 and Bus 2: \( z_{12} = j0.25 \). - Impedance between Bus 1 and Bus 3: \( z_{13} = j0.15 \). - Impedance between Bus 2 and Bus 3: \( z_{23} = j0.10 \). The diagram illustrates a simple representation of a power system network where power flows between different buses through transmission lines with specified impedances. Bus 1 is designated as the slack bus, which means it compensates for the active and reactive power imbalances in the system. Bus 2 has specified active power output, while Bus 3 details the complex power being delivered. The impedances of each transmission line are purely reactive, denoted by "j" followed by the reactance value.
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