A transmission line is the path used to transfer electrical power from a generating station or sending-end substation to a receiving-end substation and, ultimately, to the load centre. Transmission lines are designed for different power levels, distances and operating conditions. Their classification helps engineers select a suitable arrangement and mathematical model for analysing voltage, current, power loss, efficiency and voltage regulation.
Transmission lines can first be grouped according to the type of current used: AC transmission lines and DC transmission lines. In conventional AC transmission-line analysis, the line is further classified according to its length as a short, medium or long transmission line.
1. How Are Transmission Lines Classified?
There are two useful ways to classify transmission lines in this topic:
- According to the type of transmission: AC transmission and DC transmission.
- According to the length of an AC line: short, medium and long transmission lines.
The length-based classification is mainly used to decide how the electrical parameters should be represented in calculations. The exact length boundaries are conventional and can differ slightly between textbooks.
2. AC Transmission Line
An AC (alternating-current) transmission line transfers electrical power using alternating voltage and current. The magnitude and direction of AC vary periodically with time. AC transmission is widely used in interconnected power systems because voltage can be changed efficiently using transformers.
The electrical behaviour of an AC transmission line depends on the line parameters, the connected load and the operating frequency. These factors influence the sending-end voltage and current, power factor, power loss, efficiency, voltage regulation and the amount of power that can be transferred safely.
3. Four Electrical Parameters of an AC Transmission Line
A practical AC transmission line has four basic parameters: resistance, inductance, capacitance and leakage conductance. They are often represented by the letters \(R\), \(L\), \(C\) and \(G\).
3.1 Resistance (R)
Resistance is the opposition offered by the conductor to the flow of current. It causes heat loss in the conductor. This is commonly called copper loss or conductor loss, even when the conductor is made of aluminium.
Here, \(I\) is the current through the conductor and \(R\) is its resistance. For a three-phase balanced line, if \(R\) is the resistance of one phase conductor and \(I\) is the line current, the total three-phase conductor loss is:
3.2 Inductance (L)
Inductance is associated with the magnetic field produced around a conductor when current flows through it. Inductance produces inductive reactance, which affects the voltage drop and power factor of an AC line.
Here, \(X_L\) is inductive reactance in ohms, \(f\) is frequency in hertz and \(L\) is inductance in henries.
3.3 Capacitance (C)
Capacitance exists because an electric field is formed between conductors and between conductors and earth. A transmission line therefore draws a charging current even when its receiving-end load is very small or disconnected.
This is the magnitude relation for a capacitor supplied by an AC voltage \(V\), with \(C\) representing the capacitance concerned. In a three-phase line calculation, use the appropriate per-phase voltage and per-phase capacitance.
3.4 Shunt or Leakage Conductance (G)
Conductance represents leakage current through the insulation and surrounding medium between conductors and earth. It is the reciprocal of resistance for the corresponding leakage path. In many simplified overhead-line calculations, leakage conductance is small and is neglected, but it is one of the four general line parameters.
3.5 Series impedance and shunt admittance
Resistance and inductance together form the series impedance. Capacitance and leakage conductance together form the shunt admittance.
Here, \(j=\sqrt{-1}\), \(\omega=2\pi f\), \(X\) is inductive reactance and \(B\) is the capacitive susceptance in this convention. For long-line equations, lowercase \(z\) and \(y\) commonly mean series impedance and shunt admittance per unit length.
4. What Does Transmission-Line Performance Mean?
Transmission-line performance describes how the line behaves while transferring power. Important performance quantities include:
- Sending-end voltage (\(V_S\)): Voltage at the end from which power is supplied to the line.
- Sending-end current (\(I_S\)): Current entering the transmission line at the sending end.
- Receiving-end voltage (\(V_R\)): Voltage at the load or receiving end.
- Receiving-end current (\(I_R\)): Current delivered by the line to the receiving-end load.
- Power factor: Indicates the phase relationship between voltage and current.
- Power loss: Power dissipated mainly as heat in the line resistance.
- Efficiency: Ratio of receiving-end real power to sending-end real power.
- Voltage regulation: Change in receiving-end voltage between no-load and full-load conditions, with sending-end voltage held constant.
In the efficiency formula, \(P_R\) is receiving-end real power and \(P_S\) is sending-end real power. In the voltage-regulation formula, the magnitudes of receiving-end voltage are compared at no load and full load for the same sending-end voltage. Some books use slightly different sign conventions, so follow the definition specified in a particular problem.
5. Short Transmission Line
A short transmission line is one for which the effect of shunt capacitance is small enough to be neglected in the conventional simplified model. A commonly used textbook boundary is a line length below approximately 80 km. Some traditional classifications also associate short lines with lower transmission-voltage levels, often around 66 kV and below, but voltage is not a substitute for checking the actual line length and modelling assumptions.
5.1 Why is capacitance neglected?
For a relatively short overhead line, the total line capacitance is small. Its charging current is therefore usually small compared with the load current. For simplified performance calculations, the shunt capacitance is omitted, while resistance and inductance are retained.
5.2 Equivalent circuit of a short line
\(Z=R+jX\)Receiving end
The shunt capacitance branch is omitted in this approximation.
The per-phase voltage relation is:
For a short line, the current entering the line is approximately the receiving-end load current:
The short-line ABCD constants are:
These are phasor equations. Voltage and current must be added as phasors, not simply as ordinary scalar values, when the load has a phase angle.
6. Medium Transmission Line
A medium transmission line is long enough that its capacitance cannot normally be neglected, but it is still convenient to represent the capacitance as one or more lumped elements. The pasted reference uses the approximate range 80 km to 240 km. Other textbooks use a nearby upper boundary, such as about 250 km. These are approximate teaching limits, not universal physical boundaries.
Two standard equivalent circuits are used:
- Nominal-π model: Half of the total shunt admittance is placed at each end.
- Nominal-T model: The total shunt admittance is placed at the centre, while the series impedance is divided into two equal halves.
7. Nominal-π Model of a Medium Transmission Line
In the nominal-π model, the total series impedance \(Z\) is placed in the middle. The total shunt admittance \(Y\) is divided into two equal parts, \(Y/2\), one at the sending end and one at the receiving end. The arrangement resembles the Greek letter pi (\(\pi\)).
\(Y/2\)Series
\(Z\)Shunt
\(Y/2\)R
S = sending end; R = receiving end. Each shunt branch is connected across the line and the reference return.
For the nominal-π model, the ABCD constants are:
These constants come from cascading the sending-end shunt branch, the series impedance and the receiving-end shunt branch. They are useful for calculating sending-end voltage and current from receiving-end conditions.
8. Nominal-T Model of a Medium Transmission Line
In the nominal-T model, the total shunt admittance \(Y\) is concentrated at the centre of the line. The total series impedance \(Z\) is divided into two equal parts, \(Z/2\), placed on either side of the shunt branch. The arrangement resembles the letter T.
\(Z/2\)Shunt
\(Y\)Series
\(Z/2\)R
The complete shunt admittance is placed at the midpoint.
The ABCD constants for the nominal-T model are:
9. Long Transmission Line
A long transmission line is one for which the electrical parameters must be treated as distributed continuously along the line. The pasted reference uses a length greater than approximately 240 km. Other conventional textbook classifications use approximately 250 km as the boundary. The exact limit depends on the convention being followed.
Unlike the short-line approximation, the long-line model accounts for resistance, inductance, capacitance and leakage conductance distributed along the entire length. A small length of line has a small series impedance and a small shunt admittance; these small sections are connected continuously to represent the full line.
9.1 Per-unit-length parameters
Here, \(r\), \(l\), \(g\) and \(c\) are resistance, inductance, conductance and capacitance per unit length. The symbols \(z\) and \(y\) represent the series impedance and shunt admittance per unit length.
9.2 Propagation constant
The propagation constant describes how voltage and current vary along the line. It is represented by \(\gamma\):
It is commonly written as \(\gamma=\alpha+j\beta\), where \(\alpha\) is the attenuation constant and \(\beta\) is the phase constant.
9.3 Characteristic impedance
The characteristic impedance of the line is:
9.4 Long-line ABCD constants
For a uniform long line of length \(l\), the exact distributed-parameter model gives:
The functions \(\cosh\) and \(\sinh\) are hyperbolic cosine and hyperbolic sine. These equations are used because the line parameters are distributed continuously rather than concentrated at a few points.
10. ABCD Constants and General Line Equations
Short, medium and long transmission-line models can all be represented using four constants called ABCD parameters or transmission parameters. For a balanced three-phase line, the equations are commonly applied to one phase using the per-phase equivalent circuit.
Here, \(V_S\) and \(I_S\) are sending-end phase voltage and current, while \(V_R\) and \(I_R\) are receiving-end phase voltage and current. The underlining indicates phasor quantities.
| Line model | A and D | B | C |
|---|---|---|---|
| Short line | \(1\) | \(Z\) | \(0\) |
| Medium nominal-π | \(1+YZ/2\) | \(Z\) | \(Y(1+YZ/4)\) |
| Medium nominal-T | \(1+YZ/2\) | \(Z(1+YZ/4)\) | \(Y\) |
| Long line | \(\cosh(\gamma l)\) | \(Z_c\sinh(\gamma l)\) | \((1/Z_c)\sinh(\gamma l)\) |
For a reciprocal, symmetrical transmission line, \(AD-BC=1\) and \(A=D\). These are useful checks when solving problems involving the standard line models.
11. DC Transmission Line
A DC (direct-current) transmission line transfers electrical power using direct voltage and current. In a DC circuit, current flows in one direction. High-voltage direct-current transmission is commonly called HVDC.
HVDC is especially useful for some bulk-power and long-distance transmission projects, long submarine or underground cable links, and connections between AC systems that are not operating in synchronism. Whether AC or DC is more economical depends on the transmission distance, power rating, converter costs, route, losses and project conditions.
11.1 How an HVDC link works
An HVDC link normally uses converter equipment at both ends:
- Sending-end converter station: Converts AC power from the sending network into DC power.
- DC transmission line or cable: Carries the DC power over the route.
- Receiving-end converter station: Converts the received DC power back into AC for the receiving network.
systemRectifier
AC → DCDC line
+ / −Inverter
DC → ACReceiving AC
system
Simplified functional diagram; actual HVDC schemes may use different converter technologies and pole arrangements.
11.2 Basic DC power and line-loss formulas
For a DC circuit, electrical power is the product of voltage and current:
The resistive loss in a DC conductor is:
The voltage drop along a conductor of resistance \(R\) is:
For a two-conductor DC link with equal conductor resistance \(R_c\), the total loop resistance is \(2R_c\), so the conductor loss is:
These simple expressions describe resistive DC-line quantities. Converter losses and other equipment losses must also be included when calculating the efficiency of a complete HVDC transmission scheme.
11.3 Why is HVDC selected for some transmission projects?
- It can be advantageous for transmitting large amounts of power over long distances, depending on project economics.
- It is suitable for many long submarine and underground cable applications.
- It can connect two AC networks that are not synchronised.
- For a given power, increasing DC voltage reduces current, which can reduce resistive conductor loss if the other conditions remain the same.
However, HVDC converter stations are expensive and technically complex. For shorter distances, the converter cost can make an AC solution more economical. Therefore, neither AC nor DC is always cheaper; the correct choice is made through a project-specific technical and economic study.
12. Different Types of HVDC Links
HVDC transmission systems are connected in different ways depending on the number of conductors, their polarity and the path used by the return current. The three traditional arrangements are the monopolar link, bipolar link and homopolar link.
The converter stations at the two ends of an HVDC link control the conversion between AC and DC. The arrangement of the DC conductors and the return path determines which type of link is used.
12.1 Monopolar HVDC Link
A monopolar link uses one high-voltage DC conductor, traditionally operated with negative polarity. The return current flows through earth or sea using suitable electrode arrangements. In some installations, a metallic return conductor is used instead of using the earth as the normal return path.
converter One DC conductor
− polarity Receiving-end
converter
The return path is through earth/sea electrodes or, where provided, a metallic return conductor.
How it works: The sending-end converter converts AC into DC. The DC power travels along the single high-voltage conductor to the receiving-end converter, where it is converted back into AC. The return current completes the circuit through the designed return path.
Earth electrodes: The supplied reference describes earth electrodes installed at a distance of approximately 15 to 55 km from the respective terminal stations. This is a source-reported arrangement, not a universal design distance; actual electrode location and design depend on the project, geology, environmental requirements and applicable standards.
Advantages:
- Requires only one high-voltage transmission conductor.
- Can be used as a relatively simple arrangement for a point-to-point DC link.
- A metallic return conductor may be provided where earth return is not suitable or permitted.
Limitations:
- Earth or sea return can cause environmental and corrosion concerns if not properly designed and controlled.
- Electrode systems require careful engineering and monitoring.
- A single-conductor arrangement does not provide the same pole redundancy as a bipolar link.
The source article notes that monopolar links are not widely used nowadays. In practice, monopolar operation is also used as an operating mode in some schemes, including when one pole of a bipolar system is unavailable.
12.2 Bipolar HVDC Link
A bipolar link has two DC conductors: one positive pole and one negative pole with respect to earth. A converter station is installed at each end. The neutral or midpoint of the converter arrangement is connected to an earth-electrode system, subject to the design of the installation.
converter Positive pole
+V Receiving-end
converter
converter Negative pole
−V Receiving-end
converter
The converter midpoints/neutral arrangement is earthed through the designed electrode system. The two poles have opposite polarity relative to earth.
In a symmetrical bipolar scheme, the positive and negative pole voltages have equal magnitudes with opposite signs relative to earth. If each pole operates at a magnitude \(V\) relative to earth, the pole-to-pole voltage is:
How it works: Under normal balanced operation, current flows out through one pole and returns through the other pole. Ideally, the earth electrode carries little or no continuous current during balanced operation, although the actual neutral and grounding arrangement depends on the scheme.
Major advantage – continued operation after a pole fault: If one pole is out of service, some bipolar schemes can continue operating with the healthy pole in monopolar mode using an earth or metallic return path, provided the converter, line, electrode and operating limits permit it. The transferred power is reduced; it is often approximately half of the bipolar rating when the two poles are identical and equally rated, but it is not guaranteed to be exactly half in every installation.
Advantages:
- Two conductors operate with opposite polarity.
- Provides greater operating flexibility than a simple single-pole arrangement.
- Can maintain partial power transfer when one pole is unavailable, if the system is designed for monopolar operation.
- Commonly used in high-capacity HVDC transmission systems.
12.3 Homopolar HVDC Link
A homopolar link uses two or more conductors having the same polarity, traditionally negative polarity. The conductors are normally operated in parallel, and the return current flows through earth or through a metallic return arrangement.
converter Conductor 1
− polarity Receiving-end
converter
connection Conductor 2
− polarity Parallel pole
connection
Both main conductors have the same polarity; earth or a metallic conductor provides the return path.
How it works: The two same-polarity conductors are connected in parallel so that they share the transmitted current. The return current completes the circuit through the earth or a metallic return conductor, according to the design.
Why was it considered? Using conductors of the same polarity can reduce the insulation requirement between the poles compared with a bipolar arrangement. However, the use of earth as a continuous return path can create environmental, corrosion and interference concerns.
The supplied reference states that homopolar systems are not used presently. They are generally regarded as uncommon compared with bipolar HVDC arrangements.
12.4 Comparison of the Three HVDC Link Types
| Feature | Monopolar link | Bipolar link | Homopolar link |
|---|---|---|---|
| Number of main DC conductors | One | Two | Usually two or more |
| Polarity | Traditionally negative | One positive and one negative | Same polarity, usually negative |
| Return path | Earth/sea or metallic return | Normally the opposite pole; electrode return may be used during certain operating conditions | Earth or metallic return |
| Normal current path | Single pole and return path | Current travels through one pole and returns through the other | Parallel same-polarity conductors and return path |
| Operational flexibility | Limited pole redundancy | Can allow reduced-power monopolar operation after a pole outage if designed for it | Parallel conductors, but earth-return concerns remain |
| Use described in the reference | Not much in use nowadays | Commonly used | Not used presently |
- Monopolar: one conductor, traditionally negative polarity, with earth/sea or metallic return.
- Bipolar: two conductors, one positive and one negative.
- Homopolar: two or more conductors with the same polarity, traditionally negative.
- Bipolar systems can sometimes continue at reduced power in monopolar mode after one pole is unavailable, if designed and permitted to do so.
- Homopolar systems use parallel same-polarity conductors and an earth or metallic return.
12.5 Important practical note about earth return
Earth return is not simply a wire-free connection to the ground. HVDC electrode systems require purpose-designed electrodes, connecting conductors, suitable locations and monitoring. Engineers must consider corrosion of buried or nearby metallic structures, interference with pipelines and communication systems, environmental effects and local regulations. A metallic return conductor may be selected to avoid or reduce continuous earth-current operation.
13. Comparison of Short, Medium and Long AC Transmission Lines
| Feature | Short line | Medium line | Long line |
|---|---|---|---|
| Approximate length used in this article | Below 80 km | About 80–240 km (some books use 250 km) | Above about 240–250 km |
| Series impedance | Included as lumped \(Z\) | Included as lumped \(Z\) | Distributed continuously |
| Shunt capacitance | Usually neglected in the basic model | Included as lumped \(Y\) | Distributed continuously |
| Leakage conductance | Often neglected in simplified analysis | May be included in \(Y\) | Distributed as part of \(y\) |
| Usual model | Series impedance | Nominal-π or nominal-T | Exact distributed-parameter model |
14. Simple Worked Examples
Example 1: Identify the type of AC transmission line
Question: A transmission line is 60 km long. Which conventional line model is normally used?
Solution: The line length is 60 km, which is below the approximate 80 km boundary used for a short line.
Example 2: Calculate resistive power loss
Question: A DC conductor carries 500 A and has a resistance of 0.2 Ω. Calculate the power loss in that conductor.
Given: \(I=500\text{ A}\), \(R=0.2\ \Omega\).
Answer: The loss is 50,000 W or 50 kW in that conductor. If the stated resistance is for one conductor of a two-conductor DC link and both conductors have the same resistance, the total line-conductor loss would be twice this value.
15. Important Points and Frequently Asked Questions
Q1. What are the two broad types of transmission lines in this classification?
AC transmission lines and DC transmission lines.
Q2. How are AC transmission lines classified according to length?
They are commonly classified as short, medium and long transmission lines.
Q3. Which four parameters determine AC transmission-line behaviour?
Resistance (R), inductance (L), capacitance (C) and shunt or leakage conductance (G).
Q4. Why is capacitance neglected in the basic short-line model?
Because the charging current is generally small for the short-line approximation. The capacitance effect is therefore omitted to simplify the calculation.
Q5. How is capacitance represented in the nominal-π model?
The total shunt admittance is divided equally into two branches, \(Y/2\), at the two ends of the line.
Q6. Where is the shunt admittance placed in the nominal-T model?
The complete shunt admittance \(Y\) is placed at the centre of the equivalent circuit.
Q7. How are the parameters of a long line represented?
Resistance, inductance, capacitance and conductance are treated as distributed continuously along the line.
Q8. What is the propagation constant?
Q9. What is the characteristic impedance of a long line?
Q10. What is the main function of the converter stations in an HVDC link?
The sending-end converter changes AC to DC, and the receiving-end converter changes DC back to AC.
Q11. What is one important advantage of HVDC?
It can transfer power between two AC systems that are not synchronised.
- Transmission by current type: AC and DC.
- AC line by length: short, medium and long.
- Four AC line parameters: R, L, C and G.
- Short line: shunt capacitance neglected in the basic model.
- Medium line: use nominal-π or nominal-T model.
- Nominal-π: \(Y/2\) at each end; nominal-T: \(Y\) at the centre.
- Long line: parameters are distributed along the line.
- Long-line propagation constant: \(\gamma=\sqrt{zy}\).
- Long-line characteristic impedance: \(Z_c=\sqrt{z/y}\).
- DC power: \(P=VI\); conductor loss: \(I^2R\).
- HVDC converter stations convert AC to DC and DC back to AC.