- Medium Transmission Line Definition: A medium transmission line is defined as a transmission line with a length between 80 km (50 miles) and 250 km (150 miles).
- Importance of Shunt Capacitance: Shunt capacitance is significant in medium transmission lines and must be considered due to the line charging current.
- Nominal Π Model: he nominal Π model places the series impedance in the middle and the shunt admittances at both ends, forming a circuit resembling the symbol Π.
- Nominal T Model: In the nominal T model, the shunt admittance is in the middle, and the series impedance is split equally on either side, resembling the symbol T.
- ABCD Parameters: The ABCD parameters for medium transmission lines are calculated using the lumped shunt admittance and series impedance, crucial for analyzing and designing these lines.
What is Medium Transmission Line?
A medium transmission line is a transmission line model that includes shunt charging current but represents the parameters as lumped elements. Length from 80 km to 250 km is one teaching convention, not a universal boundary. A short transmission line may neglect shunt capacitance, while long transmission lines use distributed parameters. In the medium model, total shunt admittance is Y and series impedance is Z.
The ABCD parameters follow from the placement of lumped Y and Z. The frozen list gives three historical approximations:
- Nominal Π representation (nominal pi model)
- Nominal T representation (nominal T model)
- End Condenser Method
The following sections derive the nominal π and nominal T matrices from Kirchhoff’s laws, then describe the end-condenser approximation.
ABCD Parameters of Medium Transmission Line
Nominal Π Representation of a Medium Transmission Line
In the nominal Π representation, the full series impedance Z lies between the ports. The total shunt admittance Y is split equally, with Y ⁄ 2 connected at each end. The arrangement has the shape of the Greek letter pi.
The symbol Π gives this nominal network its name. The equivalent medium transmission line model is widely used in load flow studies.
VS and VR are the sending-end and receiving-end voltage. Is and IR are the corresponding terminal current values. I1 and I3 flow through the shunt halves, while I2 flows through series impedance Z.
Apply KCL at node P.
Apply KCL at node Q.
Substitute equation (2) into equation (1).
Then apply KVL around the series path.
Compare equations (4) and (5) with the standard ABCD equations.
This identifies the nominal-π values of A, B, C and D.
Nominal T Representation of a Medium Transmission Line
In the nominal T model, shunt admittance Y is at the midpoint. Series impedance Z is divided into two halves, one on each side. The circuit resembles a capital T.
Vs and Vr are the sending-end and receiving-end voltages.
Is is sending-end current.
Ir is receiving-end current.
Vm is the midpoint voltage at node M.
Apply KVL to the network.
The sending-end current is:
Substitute VM into equation (9).
Compare equations (8) and (10) with the standard ABCD equations.
The T network for a medium transmission line has these parameters:
End Condenser Method
The end-condenser method places all line capacitance at the receiving end. It is a rough historical approximation and can overstate the receiving-end charging effect, so nominal π or a more detailed model is normally preferred for study work.
