Hi everyone, this is Min and I am writing about "Medium and short line approximations analysis" for the transmission line. This is regarded as a basic step before analyzing the long-distance transmission line and this is relatively easy to calculate for the transmission system. Let's delve into the content now.
Medium and short line approximations are simplified models of transmission lines that are used to calculate voltage and current at different points along the line. These approximations are less accurate than more complex models, but they are much easier to use and are sufficiently accurate for many applications.
Medium line approximation
The medium line approximation is used for transmission lines with lengths between 80 km and 250 km. In this approximation, the shunt capacitance of the line is divided into two equal parts, each placed at the sending and receiving ends of the line. This is called the nominal pi circuit model.
The following equations can be used to calculate voltage and current at the receiving end of a medium line:
V_R = V_S * cosh(γl)
I_R = I_S * cosh(γl)
where:
- and are the voltage and current at the sending end of the line
- and are the voltage and current at the receiving end of the line
- is the length of the line
- is the propagation constant of the line
Short line approximation
The short line approximation is used for transmission lines with lengths less than 80 km. In this approximation, the shunt capacitance of the line is neglected. This is because the effect of the shunt capacitance is negligible for short lines.
The following equations can be used to calculate voltage and current at the receiving end of a short line:
V_R = V_S - I_S * Z_L
I_R = I_S
where:
- and are the voltage and current at the sending end of the line
- and are the voltage and current at the receiving end of the line
- is the series impedance of the line
Accuracy of the approximations
The accuracy of the medium and short line approximations depends on the length of the line and the operating conditions. The approximations are more accurate for shorter lines and for lines that are operating at lower voltages.
The following table shows the typical error in the voltage calculation for the medium and short line approximations:
| 80 km | < 1% | < 5% |
| 160 km | < 5% | < 10% |
| 240 km | < 10% | < 15% |
Applications
The medium and short line approximations are used in a variety of power system applications, including:
- Load flow analysis
- Voltage stability analysis
- Short circuit analysis
- Transient analysis
Conclusion
The medium and short line approximations are useful tools for calculating voltage and current in transmission lines. They are easy to use and are sufficiently accurate for many applications. However, it is important to be aware of the limitations of the approximations and to use them carefully for longer lines or for lines that are operating at higher voltages.
I hope this content will help you for improving your knowledge.
Min,P.E.
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