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Transformers and the grid The National Grid
Using transformers

The National Grid relies on transformers. There are at least five transformers between a power station and a domestic user.

This is because we use high voltage for carrying the electric current over large distances and we use small voltages in our homes. The high transmission voltages are to reduce large losses from joule heating in the transmission cables. And the low voltages in the home are for reasons of safety.

Interactive graphic of transmission system
Picture 5.3 The power delivered is V x I We can either use a small voltage and draw a big current or use a higher voltage and draw a smaller current. Which one is less wasteful?
Transmission voltages
Imagine we want to supply a small town with electricity. The average power needed by the town is 100 MW. The National Grid has to supply this power. If we use a small transmission voltage (of 20 kV), there will need to be a large current in the transmission cables (5000 A). This will make the transmission lines very hot and waste energy. The wasted power increases with the square of current.

If we use a high transmission voltage, then the current that needs to flow to the town will be less (and still deliver the same power). A smaller current causes less heating in the transmission cables. So there is less waste.

The table below shows the calculations.

Quantity Formula used Low V High V
Power requirement of town (W) Pout 100, 000, 000
Supply voltage at the town (V) Vout 20, 000 400,000
Current needed to provide the power (A) Pout = Vout x I 5, 000 250
Joule heating in power cables (W) Pwaste = I2R 75,000,000 187,500
Power that the power station needs to supply (W) Pin = Pwaste + Pout 175, 000, 000 100,187,500
Efficiency of system (%) eff = (100 * Pout) ÷ Pin 57.1 99.8
Table 4. Worked examples for a low transmission voltage (20 kV) and a high voltage (400 kV). Resistance of cable is taken to be 3W.

Notice that when the transmission voltage is 20 times bigger, the current needed is reduced by a factor of 20 as well. However, the wasted power is reduced by a factor of 400 (= 202). This is because the joule heating depends on the square of the current.

Better transformers
Transformers are highly efficient. The very best may be 99.5% but most are more like 98% efficient. Since the electricity has to pass through at least 5 transformers before it reaches the consumer, their combined efficiency is around 92%. In the UK, about 8.5% of all generated electricity is wasted in the grid and distribution system.

Most transformers in the system were installed during the 1960s when demand for electricity increased rapidly. The efficiency of many of these 40 year old transformers is poor compared to the best practice of today. In fact, relatively poor transformers are still being installed so the system isn't necessarily improving with new transformers.

It is therefore desirable to manufacture and install more efficient transformers.

Losses occur:

  • in the primary coil and secondary coil (because of their electrical resistance)
  • in the core (because energy is lost as the magnetic field changes, and because small currents are induced in the core, and these waste energy).

The core losses are minimised by using high quality steel for the core.

The losses in the coils are known as load losses. They increase with the square of the current being taken from the transformer. Load losses are minimised by using copper windings for low resistance and by using appropriate construction techniques to reduce eddy current losses.

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Question 16
Imagine you want to supply electricity to a remote house, which has a peak requirement of 11.5kW. The 3 km cable to the house has a resistance of 50W. It is suggested that the transmission cables uses the same voltage as the house - 230V. Work through the parts to see if this is sensible (use the peak power for all the parts).

a) What will the current in the transmission cable be?

b) What will the joule heating in the cable be?

c) What is the total input power needed to provide 10kW to the house?

d) How efficient is this system?

Imagine that we increase the supply voltage by a factor of 30.
e) How much smaller will the current in the cables be?

f) How much smaller will the joule heating be?

We will need a step down transformer at the house to get the voltage back to 230 V.
g) What will be the turns ratio of the step down transformer.

h) Why do we need to reduce the voltage?