The line in Problem 5.14 has three ACSR 1113 kcmil conductors per  phase. Calculate the theoretical maximum real power that this line can  deliver and compare with the thermal limit of the line. Assume VS= VR = 1.0 per unit and unity power factor at the receiving end. Problem 5.14 is the following in the picture.

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The line in Problem 5.14 has three ACSR 1113 kcmil conductors per 
phase. Calculate the theoretical maximum real power that this line can 
deliver and compare with the thermal limit of the line. Assume VS= VR =
1.0 per unit and unity power factor at the receiving end. Problem 5.14 is the following in the picture.

 

### Problem Statement (5.14):
A 500-km, 500-kV, 60-Hz, uncompensated three-phase line has a positive-sequence series impedance \( z = 0.03 + j0.35 \) \(\Omega/km\) and a positive-sequence shunt admittance \( y = j4.4 \times 10^{-6} \) S/km. Calculate:

(a) \( Z_{oc} \)

(b) \( \gamma l \)

(c) The exact ABCD parameters for this line.

### Explanation:
- **Positive-sequence series impedance (\(z\))**: This is the impedance per unit length of the transmission line, which affects the phase voltage and current along the line. Here, \( z = 0.03 + j0.35 \) \(\Omega/km\).

- **Positive-sequence shunt admittance (\(y\))**: This is the admittance per unit length, representing line susceptance affecting reactive power. In this problem, \( y = j4.4 \times 10^{-6} \) S/km.

- **Transmission line parameters to be calculated**:
  - **\( Z_{oc} \)**: The open-circuit impedance of the line.
  - **\( \gamma l \)**: The propagation constant times the length of the line, where \(\gamma\) is the propagation constant.
  - **ABCD parameters**: These parameters represent the relationship between the sending end and receiving end voltages and currents in the transmission line. 

### Diagrams and Graphs:
None provided with the problem statement. 

### Notes:
- The properties provided are specific to the positive sequence components, which are standard in analyzing balanced three-phase lines.
- The propagation constant (\(\gamma\)) and characteristic impedance are critical in determining the performance and design of long transmission lines.

This problem appears in the context of electrical engineering, specifically in power system analysis, and is essential for understanding the behavior of power transmission lines. The calculations derived from the provided data are crucial for line design and performance evaluation in electrical power systems.
Transcribed Image Text:### Problem Statement (5.14): A 500-km, 500-kV, 60-Hz, uncompensated three-phase line has a positive-sequence series impedance \( z = 0.03 + j0.35 \) \(\Omega/km\) and a positive-sequence shunt admittance \( y = j4.4 \times 10^{-6} \) S/km. Calculate: (a) \( Z_{oc} \) (b) \( \gamma l \) (c) The exact ABCD parameters for this line. ### Explanation: - **Positive-sequence series impedance (\(z\))**: This is the impedance per unit length of the transmission line, which affects the phase voltage and current along the line. Here, \( z = 0.03 + j0.35 \) \(\Omega/km\). - **Positive-sequence shunt admittance (\(y\))**: This is the admittance per unit length, representing line susceptance affecting reactive power. In this problem, \( y = j4.4 \times 10^{-6} \) S/km. - **Transmission line parameters to be calculated**: - **\( Z_{oc} \)**: The open-circuit impedance of the line. - **\( \gamma l \)**: The propagation constant times the length of the line, where \(\gamma\) is the propagation constant. - **ABCD parameters**: These parameters represent the relationship between the sending end and receiving end voltages and currents in the transmission line. ### Diagrams and Graphs: None provided with the problem statement. ### Notes: - The properties provided are specific to the positive sequence components, which are standard in analyzing balanced three-phase lines. - The propagation constant (\(\gamma\)) and characteristic impedance are critical in determining the performance and design of long transmission lines. This problem appears in the context of electrical engineering, specifically in power system analysis, and is essential for understanding the behavior of power transmission lines. The calculations derived from the provided data are crucial for line design and performance evaluation in electrical power systems.
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