On the basis of length, transmission lines are often classified into three groups.
|Short transmission line||Up to 80 km (Up to 50 miles)|
|Medium transmission line||80 – 240 km (50 – 150 mile)|
|Long transmission line||Above 240 km (> 150 miles)|
The classification of lines into different groups simplifies the process of modeling. Each group of lines is modeled based on the different parameters. The entire process is made simple by considering a distributed circuit.
A distributed constant circuit has a uniform distribution of resistance, capacitance, inductance, and leakage conductance along its length. The figure below illustrates this:
R = Resistance
XL = Inductive reactance of conductor (ohms)
C = Capacitance from line conductor to neutral
G = Leakage conductance per unit length
Short transmission lines
The mathematical modeling of short transmission lines is simplest. The capacitance is too small to prevail and it is simply ignored. Shunt admittance is also ignored due to the same current flowing through the line.
The line can be through as simple lumped having impedance Z that can be mathematically expressed by:
Z = R + j XL
If Vs and VR are sending and receiving end voltage, the circuit diagram for short lines is:
As the length increases above 80 km, the capacitive effects become quite significant. At this point ignoring capacitance and admittance introduces large errors ultimately leading to incorrect approximations. The shunt admittance and capacitance are now lumped and are modeled using Nominal T or Nominal Pi Methods.
Nominal T circuit:
Nominal Pi Circuit:
Long Transmission lines
The lumped analysis of line yields useful results for lines up to 240 km. However, the results are not veracious for longer spans. For modeling longer spans, the parameters are considered to be uniformly distributed across the line.
The Rigorous methods is used for solving longer spans.