Magnetic Fields Tutorial 8 - Transmission of Electricity

 

To carry the kinds of currents you get in a power station, you would need very thick wires.  Here is the 3-phase output of a power station alternator:

 

 

 

 

Heavy currents make even thick wires get hot.  The power lost is worked out using:

P = I2R

 

Question 1

This particular installation generates at 15 000 V.  Each alternator has a power output of 200 MW.  What is the current?

Answer

 

These high currents require very massive cables, which are cooled by oil.

 

Question 2

Each cable has a resistance of 0.001 W.  How much energy is lost per second in each of the cables?  How much is lost in total?

Answer

 

These cables are about 30 metres long.  Clearly the kinds of energy losses are completely unacceptable.  At this rate, a line a few kilometres long will dissipate all the energy, and would hardly light a torch bulb.

 

Question 3

A low voltage transmission line is carrying a current of 30 000 A.  Over its whole length, the resistance of the transmission line is 1.5 W.  How much power is lost?

Answer

 

Your answer would be about the whole output of a big power station.  That energy would be lost as heat, simply to warm up the countryside.  So electrical energy is distributed at very high voltages, and relatively low currents.

 

Question 4

A high voltage transmission line is carrying a current of 1000 A.  Over its whole length, the resistance of the transmission line is 1.5 W.  How much power is lost?

Answer

 

You can see that the lost power is much less.

 

The output from a power station goes through a step-up transformer.

 

 

Question 5

The input voltage is 15 kV, and the output voltage is 275 kV. A step up transformer is transmitting 500 MW of power.

(a) What is the input current?

(b) What is the output current?

(c)  What is the turns ratio of this transformer?

Answer

 

The National Grid

In power stations, alternating current is generated typically at 25 000 V (with a current of 30 000 A) from each alternator (ac generator).  The alternators are connected by short and massive cables to a step up transformer immediately outside the building.  The voltage is stepped up to 275 kV.  Much thinner cables can carry the electricity to where it's needed, using a network of high voltage transmission lines called the National Grid.  The transmission lines are carried by transmission towers (pylons) to substations where the voltage is reduced by step-down transformers:

While such high voltages are potentially extremely dangerous, the distribution from large power stations is much more efficient that lots of small local power stations, so less fuel needs to be burned overall.

 

When working out energy losses, we can model the wires as perfect wires in series with a resistance (just like we modelled the cell with an internal resistance as a perfect battery in series with an internal resistor).

 

The heavier the current, the greater the lost volts, and the lower the useful voltage to the load.  This is illustrated in Question 6.

 

Question 6

A farmer has an outlying barn 800 metres from his farm buildings.  He wants a 230 V power supply to power a machine that takes 3 kW.  He has the work done by a contractor who does the job on the cheap.  He uses domestic cable that has a resistance of 0.045 ohms per metre.  He buries the flex in a narrow trench that he digs across the fields with a pick-axe and spade.

 

(a) What is the total resistance of the cable to the barn?

(b) What is the resistance of the machine? 

(c) What is the current used? (Hint: take into account the resistance of the wires)

(d) What is the voltage across the machine?  Comment on the effect this would have on the performance of the machine.

(e) The farmer is not very pleased and gets another contractor who does the job properly.  Discuss what the new contractor should do.

 

Answer

 

The National Grid was started in the late 1920s, and the design for transmission towers has not changed a great deal since then. 

 

Our National Grid is connected to that of France by cables that run under the English Channel.  These cables carry 2000 MW of electricity at 270 kV for a distance of 73 km.  You may be surprised to note that this is direct current, not AC.  The reason for this is that underground cables are not very efficient when they carry AC, due to energy losses as a result of capacitance.  A coaxial cable makes a perfectly good capacitor.  Its value may be low per metre, but when they run for several tens of kilometres, the capacitance becomes significant.  The effect of capacitance is insignificant when a dc voltage is applied.

 

Converting AC to DC is easy; you use a diode rectifier bridge.  On this scale it's big, but the concept is easy.

 

Converting DC to AC is not so easy; you need an inverter.  With modern electronics, suitable devices can be made.  Inverters are now available in the shops to power a mains device from a car battery.