Overhead Line Electrical Characteristics

1. Modelling a Transmission Line

When we analyse a simple circuit in a lab, we often use "lumped" components—a single resistor, a single capacitor, etc. We can do this because the physical size of the circuit is tiny compared to the wavelength of the AC electricity.

However, a transmission line can be hundreds of kilometres long. At this scale, we can no longer assume the voltage and current are the same at every point along the wire at the same instant. We need a more sophisticated model.

The video below explains why a simple "lumped" model isn't sufficient for long lines and introduces the idea of modelling the line as having properties distributed along its length.

As the video explained, the correct way to model a transmission line is to consider its electrical properties as being distributed uniformly along its entire length. We can imagine the line as being made of countless infinitesimally small segments, where each segment has a small amount of resistance, inductance, and capacitance.

These three characteristics—Resistance (R), Inductance (L), and Capacitance (C)—are the primary electrical parameters of a transmission line. Let's explore each one in detail.

2. Resistance (R)

Resistance is the most straightforward of the three properties.

• Definition: Resistance is the opposition to the flow of electrical current. As electrons move through the conductor, they collide with atoms, losing energy in the form of heat.
• Effect on the Grid: This is the primary source of real power loss in a transmission line. These losses are often called "$I^2R$ losses" (pronounced "I-squared-R losses"). Minimising these losses is why we transmit power at very high voltages.

The following document provides a clear explanation of resistance and a related phenomenon called the "skin effect."

To summarise the key points from that reading:

• DC Resistance: The fundamental resistance of a conductor is given by the formula $R = \rho \frac{l}{A}$, where $\rho$ (rho) is the material's resistivity, $l$ is the length, and $A$ is the cross-sectional area.
• AC Resistance & Skin Effect: For AC systems like the grid, the resistance is slightly higher than for DC. This is due to the skin effect, where the alternating current tends to concentrate near the surface (or "skin") of the conductor. This effectively reduces the cross-sectional area available for the current to flow through, increasing the total resistance. At the UK's 50 Hz frequency, this effect is present but not as extreme as it is at much higher frequencies.
• Temperature: The resistance of conductors also increases as they get hotter.

3. Inductance (L) and Capacitance (C)

While resistance is about energy loss, inductance and capacitance are about energy storage—in magnetic and electric fields, respectively. They are inherent properties that exist simply due to the physical construction of the transmission line.

This next video provides a wonderfully simple, intuitive explanation for why any pair of wires will always have inductance and capacitance.

Now let's look at each of these in a bit more detail.

Inductance (L)

• Definition: Inductance arises from the magnetic field that is generated around any conductor carrying a current. In an AC system, the current is constantly changing, which means the magnetic field is also constantly expanding and collapsing. This changing magnetic field induces a voltage in the conductor that opposes the change in current.
• Effect on the Grid: Inductance is a major factor in the total impedance of a transmission line. It causes a voltage drop along the line and is associated with the consumption of reactive power.

For a more formal definition, please read the following section.

The key takeaway is that the inductance of a transmission line is determined by its physical geometry: primarily the radius of the conductors and the distance between them.

Capacitance (C)

• Definition: Capacitance arises from the electric field that exists between conductors that are at different voltages. An overhead transmission line, which consists of conductors separated by air (an insulator), forms a natural capacitor between the conductors, and also between each conductor and the ground.
• Effect on the Grid: Because of this capacitance, a current (called a "charging current") will flow to "charge" the line, even if it is disconnected at the far end. This effect is particularly noticeable on long, high-voltage lines. Line capacitance is a source of reactive power.

The document we just looked at also has a good section on capacitance.

Similar to inductance, the capacitance of a transmission line is determined by its physical geometry: the radius of the conductors and their spacing and height above the ground.

Conclusion

In this lesson, we've moved from the physical structure of a transmission line to its fundamental electrical behaviour. We've seen that a line isn't just a simple wire, but a complex component with distributed electrical characteristics.

Here are the key takeaways:

• Transmission lines are modelled as distributed parameter systems, with properties spread along their entire length.
• Resistance (R): The opposition to current flow, determined by the conductor's material, size, and temperature. It is responsible for real power loss ($I^2R$ losses) in the form of heat. The skin effect increases this resistance in AC systems.
• Inductance (L): Arises from the magnetic field around the conductors. It opposes changes in current and is determined by the physical geometry of the line. It causes a voltage drop and consumes reactive power.
• Capacitance (C): Arises from the electric field between conductors. It stores energy and causes a "charging current" to flow. It is also determined by geometry and acts as a source of reactive power.

These three parameters—R, L, and C—are the building blocks we need to understand almost all aspects of transmission system performance, from power losses to voltage stability.

Preview of the Next Lesson

Now that we have a solid understanding of resistance, we are ready to tackle the next learning outcome: "Calculate power losses in transmission lines and explain why high voltages reduce losses." We will put the $I^2R$ formula into practice and quantify the enormous efficiency gains achieved by using high-voltage transmission.