The demand for electricity is probably higher than it ever was. Due to the loud, polluting and potentially unsafe nature of power plants, electricity is generated at remote locations far away from cities. For this reason, Transmission Lines are used to distribute electricity to the surrounding population.

The Generation of Electricity

When we talk about power plants, think of coal power plants, wind turbines or water dams. They all serve one purpose: to harvest energy from nature.

Even though there are various different methods for harvesting energy, these processes have one thing in common: they use 3-phase electricity generators to turn nature’s energy to electricity.

The 3-phase Electricity Generator

Let’s take the wind turbine for example.

  • The wind rotates the blades.
  • The blades are attached to a shaft – that will rotate.
  • At the other end of the shaft we have the ‘Rotor’.

The rotor is essentially a magnet that is surrounded by the ‘Stator‘. The Stator consists of coil pairs. By coil pairs I mean, a wire that is rolled up as a coil on each side of the stator 180º apart. The coils in a coil pair oppose each other, so one is rolled up from inside-out the other from the outside-in.

In a 3-phase generator there are 3 wires like that each 120º apart.

Figure 1: 3-Phase Electricity Generator. The rotating magnet in the middle induces current flow in all 3 phases separately. The phases are 120º apart.

Working Principle of 3-Phase Generators

Based on Faraday’s Law of Electromagnetic Induction, if a coil is placed in a rotating magnetic field, an EMF will be induced.

In a 3-phase generator we have 3 sets of coil pairs 120º apart, meaning there will be 3 independent circuits with current induced in them. Thus, the term 3-phase.

  • One side of the conductors are connected together (Ground).
  • When we say 120º apart, we mean the coils that are attached directly to the transmission lines.
  • This is alternating current, it means the North pole of the magnet moves the electrons (current) in the wires to one side, the South pole to the other.

Distribution of Electricity

Electricity is generated at the power plants outside the city. But how does the electricity get to your house?

Diagram: Distribution of Electricity using Transmission Lines

Figure 2: Distribution of 3-phase electricity from power plant to cities. Note, the for simplicity the image only shows a red transmission line, but in real life this represents all 3 phases. For long distances we mostly use a so called ‘delta configuration’ which does not have a neutral line.

  • Power Plantwhere electricity is generated
  • Step up Transformer Increases the voltage (see below why)
  • Power Lines Transfer electricity to long distances
  • Step down Transformerdecreases the voltage
  • Distribution Lines – they distribute the electricity between the houses

Why are Power Lines High Voltage?

Because making them high voltage reduces losses. To understand why let’s have a look at a familiar law:

Ohm’s Law

Derivation for Power Equation in terms of I and R

Where:

  • V – voltage
  • I – current
  • R – resistance
  • P – power

The above equations tell us that if we have a long conductor with voltage across it and a current flowing in it, power will be dissipated.

Power is dissipated in form of heat in the case of a conductor.

A transmission line is a conductor which is super long. In order to minimise the heat generated in it, we have to minimise the Power. From the power equation (circled in red), we can do this in two ways:

  1. Reducing the resistance or
  2. Reducing the current
    • Since the current is squared in the equation, reducing I is more effective than reducing R. Reducing the current by half reduces the Power by 4x!

But don’t forget, we are delivering Power: P=IV. So, to maintain the same power throughout the transmission, V has to increase if I decreases.

Transformers do this. They can reduce the current while increasing the voltage.

Step Up and Step Down Transformers

  • We add a step up transformer just before the transmission lines.
  • This will increase the voltage and reduce the current, thus, preventing power dissipation throughout the long transmission lines.

 

  • At the end of the lines, a step down transformer reduces the voltage and alongside increases the current. This way we gain back the original power that now can be dissipated in the load.

Volume, Cross-section & Efficiency of Transmission Lines

Let’s have a simplified model for the transmission lines, where:

  • Vsvoltage from generator (single phase)
  • Rcresistance of conductor (transmission lines)
  • RLload resistance
Circuit Representation for Transmission Lines

The efficiency is the ratio of the Load Resistance and the total resistance in the circuit. From this relationship, it is easy to calculate the resistance of the conductor needed for a specific load with a desired efficiency:

Derivation: Conductor Resistance in terms of efficiency

Let’s break up the load resistance RL in terms of Voltage and Load Power. Next, we can substitute this in the above equation:

Derivation: Conductor Resistance in terms of Efficiency, Conductor Voltage and Power Dissipated in Load

Resistivity (ρ) is a property of the material the transmission line is made of. This is usually copper. We take this resistivity over the cross section (a very thin piece of the conductor). To get the total resistance of the wire we have to multiply it with the length. Next, we can write the conductor resistance equation in terms of resistivity (ρ), cross-sectional area (A) and length (L):

Derivation: Finding an equation for Area and Volume of Copper Conductors in Transmission Lines

From the Volume equation above: The amount (volume) of copper material needed to build a transmission line is inversely proportional to the square of the transmission line voltage.

So, the higher the voltage, the less material is needed.

Transmission Towers

It is worth noting that we are talking about great distances when it comes to transmission lines. Therefore, every detail is important and can save great costs. Having the power lines hung overhead on transmission towers reduces the need for expensive insulation.

In the UK there are 3 main types of transmission towers:

  • 400 kV
    • long distance,
    • each phase is split up to 4 individual lines.
  • 275 kV
    • long distance,
    • each phase is split up to 2 – 4 individual lines.
  • 132 kV
    • short distance,
    • each phase is split into 1 or 2 individual lines.
Circuit Representation for Transmission Lines

Figure 3: 3 Types of Transmission Line Towers. The Red, Green and Yellow dots represent each of the 3-phase respectively. The Blue colour represents an earth wire that is connected to the towers and is used as safety against lightning. For higher voltages, each phase is split between multiple lines (to have lower voltage in each). This is done to eliminate unwanted losses and effects.

  • The higher the transmission voltage, the higher the tower is.
  • Double Circuit Transmission Line – some towers carrie electricity from 2 (or more) generators.
  • For high voltages, each phase is split into 2, 4 or more lines.
    • This reduces the voltage in each line.
    • Reduces effective resistance due to Skin Effect:
      • DC lines have the current distributed uniformly in the wire.
      • AC lines, if we consider the cross section, the higher the frequency, the more the current travels at the outside perimeter of the wire. This adds resistance to the transmission line which is not what we want.
    • Eliminates Corona Discharge:
      • When the voltage is super high, it ionises the air.
      • This means the air gains or loses electrons – thus becoming conductive.
      • A flash of purple light happen alongside with a discharge sound. This is when electrons leak from the power line, re-balancing the air’s electron.
A single phase split into 4 individual lines to reduce some unwanted effects.

Figure 4: This is one phase split into 4 conductors.

Corona Discharge

Figure 5: Corona Discharge – happens when voltage is too high and ionises the air.

Additional parts of a Transmission tower:

  • Insulator Discs – made of porcelain or glass. They suspend the lines to the tower without electrical contact.
  • Vibration Dampers – to the right of the disc insulator in the photo below. They absorb vibration of the line.