- Transmission Line Definition: A transmission line is a designed conductor that carries large volumes of electrical power across large distances at high voltages.
- Line Types and Lengths: Transmission lines are categorized by length; short lines are under 80 km, medium lines between 80 and 250 km, and long lines over 250 km.
- Efficiency Explained: Transmission line efficiency is the ratio of power received to power sent, indicating how much power reaches its destination versus how much is sent.
- Voltage Regulation: Voltage regulation of a transmission line shows how voltage levels vary from the source to the destination under different loads.
- Capacitance in Transmission Lines: In longer transmission lines, the effect of capacitance is significant and must be modeled correctly to ensure accuracy in power transmission.
What Is a Transmission Line?
A power transmission line carries electrical energy between substations or other grid nodes at a selected voltage. It may use overhead conductors or insulated cables. Some high-voltage overhead lines use bundled phase conductors, but bundling is not part of the definition.
Transmission-Line Models
Engineers calculate voltage drop, power loss, efficiency, regulation and reactive-power behaviour from the line parameters. Series impedance contains resistance R and inductive reactance from L. Shunt admittance contains conductance G and capacitive susceptance from C. Short, medium and long line categories identify common steady-state approximations rather than three different physical line types.
Short Transmission Line
A short transmission line model has these features:
- Less than about 80 km is a common teaching guideline for a 50 or 60 Hz overhead line.
- Voltage alone does not decide whether the approximation is accurate.
- Shunt capacitance is neglected when its charging current has little effect on the required result.
- The model retains series resistance and inductance but omits shunt capacitance.
Medium Transmission Line
A medium transmission line model commonly has these features:
- A length from about 80 km to 250 km is a common overhead-line guideline.
- Published voltage ranges are conventions, not a substitute for checking model error.
- Shunt capacitance is included because charging current affects terminal voltage and current.
- The nominal T and nominal pi approximations represent total shunt admittance with lumped elements rather than a continuous distribution.
Long Transmission Line
A long transmission line model commonly has these features:
- A length above about 250 km is the usual overhead-line teaching guideline.
- High operating voltage often accompanies a long line, but voltage is not the mathematical boundary.
- Series impedance and shunt admittance are treated as distributed along the line. The resulting hyperbolic equations can also be expressed as an exact equivalent-pi circuit for steady-state studies.
Transmission-Line Efficiency
Transmission efficiency is the ratio of real power received, PR, to real power sent, PS, expressed as a percentage. The difference includes conductor and other line losses under the stated operating condition.
cosθs is the sending-end power factor.
cosθR is the receiving-end power factor.
Vs is the sending-end voltage per phase.
VR is the receiving-end voltage per phase.
Transmission-Line Voltage Regulation
Voltage Regulation Defined: transmission-line voltage regulation compares the magnitude of receiving-end voltage at no load with its magnitude at a specified load. Hold the sending-end voltage constant, divide the difference by the loaded receiving-end voltage, and express the result as a percentage.
For a short line, the no-load receiving voltage equals the sending voltage. For a general line, the no-load value follows from the line’s ABCD constant A. Vs is the sending-end voltage per phase and VR is the loaded receiving-end voltage per phase in the displayed short-line approximation.
XL is the per-phase reactance.
R is the per-phase resistance.
cosθR is the receiving-end power factor.
The following expressions show the short-line approximation for two load power factors:
- For a lagging load
- For a leading load
These relationships give the following usual trends:
- A lagging or unity-power-factor load usually gives positive regulation because the receiving-end voltage falls as load is applied.
- A sufficiently leading Power factor can produce negative regulation, meaning the loaded receiving-end voltage exceeds the no-load value.
How Load Power Factor Affects Efficiency
The efficiency definition is:
For a short-line model, IR = IS = I.
For a balanced three-phase short line:
Therefore:
Power and Current Relationship: at fixed receiving-end real power and voltage, a lower receiving-end power factor requires more current. The higher current increases I-squared-R loss.
For medium and long lines, sending- and receiving-end currents also differ because shunt admittance draws charging current:
Power factor still affects current and loss, but efficiency is not simply proportional to power factor. Voltage, shunt current, resistance, compensation and operating point also matter.
End-Condenser Model for a Medium Transmission Line
The end-condenser model places all line capacitance at the receiving end. It is a historical lumped approximation and is generally less accurate than the nominal pi model because it does not split the shunt current between both ends.
Here IR is the receiving-end load current per phase,
R is the resistance per phase,
XL is the inductive reactance per phase,
C is the capacitance per phase,
cosΦR is the receiving-end lagging power factor,
VS is the sending-end voltage.
Use the displayed receiving-end voltage 
as the reference phasor:
The receiving-end load current is:
The capacitive current is:
The total line current is:
The sending-end voltage components then follow:
and
Nominal T Model for a Medium Transmission Line
In the nominal T method, total shunt admittance is concentrated at the midpoint. Half of the total series impedance is placed on each side.
Here:
IR is the receiving-end load current per phase,
R is the total resistance per phase,
XL is the total inductive reactance per phase,
C is the total line capacitance per phase,
cosΦR is the receiving-end lagging power factor,
VS is the sending-end voltage.
V1 is the midpoint voltage across the equivalent capacitor.
The midpoint voltage is:
The shunt capacitive current is:
The sending-end current is:
The sending-end voltage is:
Nominal π Model for a Medium Transmission Line
In the nominal pi method, total shunt admittance is divided equally between the sending and receiving ends. The total series impedance is placed between them. This arrangement is widely used in steady-state network studies.
Here IR is the receiving-end load current per phase,
R is the total resistance per phase,
XL is the total inductive reactance per phase,
C is the total capacitance per phase,
cosΦR is the receiving-end lagging power factor,
VS is the sending-end voltage.
Use the displayed receiving-end voltage as the reference phasor:
The receiving-end load current is:
The receiving-end shunt current is:
The series-branch current is:
The sending-end voltage is:
The sending-end shunt current is:
The sending-end current is:
Nominal T Model Summary
Nominal T Method Explained: the model places the whole shunt admittance at the midpoint and half of the line’s series impedance on each side. The current in the first series half includes the receiving-end load current and the full midpoint charging current.
