- Short Transmission Line Definition: A short transmission line is defined as a transmission line less than 80 km (50 miles) long or with a voltage less than 69 kV.
- Negligible Shunt Capacitance: In a short transmission line, the shunt capacitance is ignored, simplifying calculations.
- Phasor Diagram: The phasor diagram uses the receiving end current as a reference for comparing voltages.
- Two-Port Network Representation: Short transmission lines can be modeled as two-port networks, using ABCD parameters for analysis.
- Performance Efficiency: The efficiency of a short transmission line is calculated similarly to other electrical devices, based on its electrical resistance.
What is Short Transmission Line?
A short transmission line is a transmission line model that neglects shunt capacitance because charging current has little effect on the required calculation. Length below 80 km or voltage below 69 kV are common teaching guides, not universal limits. medium transmission lines include lumped shunt admittance, while long transmission lines use distributed parameters.
The short-line approximation omits shunt capacitance and combines series electrical resistance with the reactance described on the inductor page. The equivalent circuit therefore has one series impedance. Its vector diagram uses receiving-end current Ir as the reference. Sending and receiving voltages then make angles φs and φr with that current.
With no shunt branch in the model, sending-end current equals receiving-end current.
The phasor diagram gives the following approximation for Vs:
Rearranging that relation gives:
The approximation uses the stated small-angle relation:
Under no load, the short-line model has zero current because it omits charging current. Its series-impedance drop is therefore zero, so receiving-end voltage equals sending-end voltage in this approximation.
Using the stated definition of voltage regulation for a power transmission line gives:
Here, Vr and Vx denote the in-phase and quadrature voltage-drop components used by the displayed approximation.
A transmission-line section has a sending port and a receiving port, so it can be represented as a two-port network. A 2 × 2 matrix relates the terminal voltages and currents.
This representation lets the short-line series impedance be combined with other network sections.
The 2 × 2 matrix uses ABCD parameters to map receiving-end voltage and current to sending-end voltage and current.
A, B, C and D are the chain constants of this network model.
Setting Ir = 0 in equation (1) represents an open receiving end and isolates A.
A is the sending-to-receiving voltage ratio with the receiving end open, so it is dimensionless. Setting Vr = 0 in equation (1) represents a short circuit and isolates B.
B, the sending-end voltage divided by short-circuit receiving-end current, is the transfer impedance in ohms.
C is sending-end current divided by receiving-end voltage with the receiving end open. It has units of admittance.
D, the sending-to-receiving current ratio under the stated short-circuit condition, is dimensionless.
The short-line equivalent circuit gives:
Comparison with equations (1) and (2) gives A = 1, B = Z, C = 0 and D = 1. For this reciprocal network, A, B, C and D satisfy:
AD − BC = 1Substitute A = 1, B = Z, C = 0 and D = 1.
⇒ 1.1 − Z.0 = 1The determinant is one, which is consistent with the reciprocal short-line model. Equation (1) then gives:
When Ir = 0, the receiving end is open. Equation (1) then gives the no-load receiving-end voltage for the stated sending-end condition.
Substitution in the transmission-line voltage-regulation definition gives:
Performance of Short Transmission Line
Short-line efficiency is receiving-end real power divided by sending-end real power. The difference is mainly the series I²R loss in this model:
R is the per-phase line resistance. The efficiency expression also depends on current, receiving-end voltage and load power factor as shown in the frozen formula.
