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 in each of the three cables?

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.  Assume that the input and output are single phase.

(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 the cables 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.

 

 

Electric Cars (to think about)

Electric cars are nothing new.  The example below was built by Andreas Flocken (1845 - 1913) in Coburg.  Built in 1888, it is one of the oldest cars in Germany.

 

Image by Henrtsirhenry, Wikimedia Commons

 

It is a horse-drawn carriage from which the horse has been removed (and put out to pasture).  A large lead-acid battery powers an electric motor that drives the rear wheels.  It was by no means unique and in the late Nineteenth Century, there were many such vehicles on the road.  They didn't need horses (which are expensive to maintain) and were clean and quiet.  The problem was that they did not go very far, and finding a place to charge the battery was not always easy.   The batteries were heavy.

 

The internal combustion provided a good answer.  It could be started easily, and the cars had a reasonably good range.  As petrol engines improved, cars became a lot more popular and competition between manufacturers gave them incentives to improve cars.  Cars nowadays are much better than they were forty years ago.  They are safer, more comfortable, more economical, and much more reliable.

 

The problem with the internal combustion engine is that it has many moving parts which wear out.  There are a number of sources of pollution caused by cars, for example exhaust emissions.  Global warming has become a major concern with governments.  Petrol engines were a major culprit.  Therefore the diesel car became more popular.  The fuel consumption of diesel cars is quite a bit lower (15 % or more) than the petrol equivalents.  Unfortunately they are dirty, spewing out a lot of carbon particulates and nitrogen oxides.  Modern diesel cars have complex exhaust systems to reduce the pollutants, but not with total success.  You can see that for yourself as you walk into your school.  These systems are not always reliable and can be expensive to fix.  Now petrol cars are coming back into favour.  However they still perform badly in stop-start driving, the kind you get in cities.  Many now have systems whereby the engine stops while waiting in a queue.  It starts again when the car is ready to move off.  However, the repeated use of the starter motor (which takes a huge current, about 500 - 1000 amps) will wear the component out and cane the battery.  Both are expensive.

 

A solution to this has been the hybrid car, which uses an internal combustion engine in conjunction with an electric motor and a battery.  However they tend to be rather expensive.  In the early part of the twenty-first century, the Mayor of London, A B de P Johnson, ordered the introduction of diesel hybrid buses.  These vehicles were driven by electric traction motors using very large batteries that were kept charged by a 4 litre diesel engine.  Unfortunately the batteries tended to fail, and there are piles of them behind the bus garages.  The vehicles are now driven by their diesel engine using an electric transmission.  They are heavy vehicles and the resulting performance is rather poor.

 

Electric cars are also coming back.  They are particularly good for short distance motoring in stop-start traffic.  They are quiet, comfortable, and reliable.  They have lively performance.  When going downhill they can generate electricity to charge up the battery.  But despite improvements in battery technology, the batteries are bulky and have a limited range.  For example a Nissan Leaf has a range of 222 km, but this is reduced to 100 km if the heater and other accessories are on. 

 

This car is a Renault Zoe, a popular electric super-mini:

 

Image by Vauxford, Wikimedia Commons

 

The power of the motor is 66 kW (90 PS).  It has a battery of capacity 41 kWh.

 

Question 7

The car has a maximum speed of 140 km h-1.  Calculate the range of the car if it is driven at this speed.

Answer

 

One electric supercar has a motor that can give out 800 kW (1200 PS).  You can imagine that when you put your foot to the floor, the battery would go flat almost at once!

 

Most electric cars have lithium batteries.  They are much lighter than lead acid batteries.  They have large capacities.  However the disadvantages are that they are expensive.  Also they can catch fire if the casing is punctured (in an accident), or if the current demand is too high.  Many people who buy electric cars have to hire the batteries which adds considerably to the monthly cost of electric motoring.

 

Electric cars are charged at home.  It is possible to get chargers that plug into a standard 13 A socket, but these take a long time to charge up.

 

Question 8

Calculate how long it would take to charge a battery from a Renault Zoe if the charger took 3 kW off the mains.

Answer

 

Larger chargers are available, but these need to be wired in to the house wiring.  They take about 30 A, about the same as an electric shower.  Suppose you have the electric shower on, the car charger on, the electric cooker, and a couple of electric heaters.  (Possible for a small family.)   The current will rapidly add up to above 100 A, quite sufficient to blow the board's fuse at the meter.

 

Then consider that, if every house had a charger, a considerable current demand would occur.  This may have significant implications if the electrical infrastructure is old and/or in poor condition, as it is in many places.  A government that chickens out at the cost of providing a couple of thousand gantries for the electrification of the railway between Kettering and Sheffield is hardly likely to take on the task of providing infrastructure for every house to accommodate a charger for their electric cars.  And that isn't even considering the facilities needed for electric lorries or buses.

 

The extra loads have considerable implications for the National Grid, much of which was erected in the nineteen twenties and thirties.

 

And that doesn't start to address what would happen if, as is the case in many of our crowded cities, you find you can't park outside your house...

 

It is proposed to ban internal combustion vehicles by 2040.  I will be well past my sell-by date then, and will have progressed to the status of old codger.  But you, dear reader...