Tutorial 13 a - 3 Phase AC Systems

Learning Objective

To understand the nature of 3 phase electricity generation;

To explain how electricity is distributed through the National Grid;

To distinguish between star and delta connection systems.

Key Questions

What is 3-phase?

How do we describe 3-phase AC?

What is the National Grid?

What happens if the star system is unbalanced?

How do Star systems differ from Delta Systems?

Introduction to 3-phase AC supply

In an earlier tutorial, we looked at a simple generator, which showed us how the sinusoidal waveforms of AC were due entirely to the rotary motion of the coil in the magnetic field.

The output was a simple sine wave.


We use single phase AC at home, and we know that for flex the live is brown, the neutral is blue, and the earth wire is green and yellow.  For hard wiring (the permanent wires in the house), the live is often red and the neutral is black, with the earth wire being a bare conductor.  (In newer houses the live is brown and the neutral is blue.)  When the earth wire is exposed, it is covered with a yellow and green sleeve.


What is 3-phase?

Instead of a single sine wave, the generator produces 3 sine waves with a phase difference of 2p/3 radians or 120o.


The frequency has been set at 10 Hz for clarity.  The maximum voltage is 200 V in this case.  The wave formulae are:

  • Wave 1:

  • Wave 2:

  • Wave 3:

Question 1

What is the phase difference in degrees between Wave 1 and Wave 3?



A simple 3-phase generator can be set up like this:


Picture from Wikimedia Commons - Hawkins Electrical Guide

There are three simple coils passing through the magnetic field which is created by permanent magnets.  However this system needs six slip-rings, and that makes it more clumsy.


In large generators, the magnet is turned, like the magnet inside a bicycle dynamo.  In this case, the magnet is an electromagnet, called the rotor.  It spins past three coils called the stator.  The picture below is a rotor with two slip-rings.  When current passes through the slip-rings, the rotor becomes a magnet.


The stator does not move.  If we look end on at the generator, we can see that the stator consists of three pole pieces (coils of wire) placed 120o apart.

This kind of generator is often called an alternator.  You have one in a car, and the AC is turned into DC using diodes.  In old cars, a DC generator (called a dynamo) was used, but tended to be troublesome.  If the control box went wrong, the battery would try to turn the dynamo as a motor, which would have no chance of turning the engine.  The battery would rapidly drain and probably burn out the dynamo.  There is no chance of this happening with an alternator.

Picture from Wikimedia Commons


The stator of a power station generator is a massive piece of engineering.  The coils generate the three-phase AC.  The voltage is about 25 000 V, so the current is about 50 000 A.  The rotor carries a smaller current, about 1000 A, at a voltage of about 1500 V.  This is generated by a smaller generator called the exciter.


Question 2

Why is it better that the rotor current is DC rather than AC?



Star Configuration

With three coils, there would be six wires, which would be clumsy.  Electrical engineers use two different arrangements to wire up the generators.  This arrangement is called the star arrangement, as it is like a star.  It is the most common way of wiring a three-phase generator.


You can see that there are four wires.


Delta Configuration

The other way is the delta arrangement.

Delta is a Greek capital letter ‘D’ which looks like a triangle (D).


In this arrangement, there are three wires.  The end of one coil is connected to the start of the next coil.  This is less common in alternators, but common in motors and transformers.


Terms used in three-phase supplies

The conductors are called lines.  Each line is given a phase colour, red, yellow, and blue.  This was the standard in the UK until 2006, but nowadays the later EU standard is used:








UK – old






UK – New







The new colour coding reflects the wiring of plugs, with the live being brown, and blue being neutral. 


As there are so many quite modern installations using the older system, it makes sense to continue to use the red, yellow, and blue phase notation.  But be aware of the new notation if you are working on a brand new installation.  Clearly it is important not to mix the two systems up.


The phase sequence is the order in which the voltage waveforms pass.  The first is the red phase, then the yellow, then the blue.


The currents in the lines are known as line currents (IL) and the voltages between the lines are the line voltages (VL). 



Star connection

In a star system (sometimes called a Y-system), the coils are connected together at a central point:

The central point is connected to the neutral wire.  It is often called the neutral or star point. 


There are two sets of voltages that can be measured:

·         The phase voltages, the voltage between each phase and the neutral;

·         The line voltages, the voltage between each phase.

The difference is shown below:


The voltage VR is the voltage between the red phase and the neutral.  It is a phase voltage.  The voltage VYB is the voltage between the yellow and blue phases.  It is a line voltage.


In a star system, the line current is the same as the phase current:




Question 3

Use the diagram to identify the other:

(a) Phase voltages;

(b) Line voltages.



We can also consider the currents:


The currents in each line are called the line currents, and are equal to their respective phase currents.  By Kirchhoff I, we know that the neutral current is the sum of the currents in the red, yellow, and blue phases.


IN = IR + IY + IB


If the currents are equal, they add up vectorially to zero.  The graph below shows the idea.

Let us look at when the blue phase has a maximum current of -200 A (t = 43 ms).  We can easily see that the read phase and the yellow phase have equal currents of + 100 A.  So by Kirchhoff I, the sum of the currents is:


100 A + 100 A + -200 A = 0 A


Therefore the current in the neutral line is zero.  We can show that for other times as well.


Question 4

Show that IN = 0 for t = 25 ms



When all the maximum currents are equal, we say that system is balanced.


Remember that the signs are important.


The currents are not equal at the same time.  We need to remember that they are always 120o out of phase.




For a balanced system, we can also say:


VR = VY = VB;




ZR = ZY = ZB


IR = IY = IB


The line voltage (which is the potential difference between the red and the yellow phases) is given by:

VRY = VR + -VY


VY is negative, as it is in the opposite direction to VR.  In the phasor diagram, you can see the reverse vector shown as a dotted line.


Simple geometry will prove to us that the phase angle between VRY and VR is 30o.


Using the cosine rule:

VRY2 = VY2 + VR2 – 2(VRVY) cos 120


Since VY = VR, let’s say that they are both 1.


VRY2 = 12 + 12 – 2(1) cos 120




VRY2 = 2 - 2 cos 120 = 2 - (2 × - ½) = 3



VRY2 = 3VR





So for any balanced star connection, we can say that the line voltage is Ö3 times (= 1.732) the phase voltage.  Remember the line voltage is the potential difference between two lines, while the phase voltage is the potential difference between the phase and the neutral.


What happens if the phases are unbalanced?  Click HERE to go to the extension.

Why do we bother with 3-phase?

Clearly 3-phase AC is more complex to get our heads around than single phase AC.   Let’s compare a single phase AC wave-form to a 3-phase AC wave-form:


We can see that the voltage in the single phase drops below half the peak voltage for quite a period.  In a single phase, the power drops to zero as the voltage reverses.  In a single phase motor, the power delivery is “lumpy”, with the momentum of the motor keeping it going when the voltage drops to zero.


In the 3-phase, the voltage never drops below half the voltage.  Therefore power is being delivered all the time on one of the phases.  In a three-phase motor, the power is being delivered on one of the phases, so the delivery is much smoother.


Additionally, the same power can be delivered using less massive conductors than single phase or DC.  If the loads are balanced, then a neutral wire is not needed.


Delta Systems

While almost all generators are wired in a star system, loads can be wired in either a star or delta configuration.  The diagram shows a delta-wired load.

If you are designing industrial machinery, it is important to know whether the loads are star or delta, as the switch-gear is different. 


There are a couple of important points to make here for a delta connection.  The phase voltages and the line voltages are the same.

 The currents obey Kirchhoff I.  Let us see how:

Consider the current in the red phase.  By Kirchhoff I, we see that:

The minus sign is because the blue to red current is in the opposite direction to the red to yellow.  Let’s have a look at the phasor diagram:


We can see how the phasor IR is the vector sum of the vectors IRY + -IBR.


By simple geometry, we can say that the line –IBR bisects the angle between IRY and IYB.  So that angle is 60o.  Then IR bisects the 60o angle to give 30 degrees.


So we end up with a phase vector triangle like this:

We can see that the vertical components are equal and opposite, so they cancel out.


Taking the horizontal components, we see that:

Since the horizontal components of the vectors IRY and IBR are in the same direction, and have equal value, we can write:

Now cos 30 = 0.866 = Ö(3/2), so it doesn’t take a genius to see that:

Therefore the line currents are Ö3 times the phase currents.

In the next worked example, we will compare the currents in a star and delta arrangements.










Worked Example

Three coils each have an impedance of 5 W and are connected to a 3-phase 415 V supply.  In the first instance, they are connected in a star configuration.  Then they are reconnected in a delta configuration.  For each configuration, work out:

a.       The line and phase voltage;

b.      The line and phase currents.


Star connection:

VL = 415 V

V= 415 ÷ Ö3 = 240 V


IP = V/Z = 240 ÷ 5 = 48 A

IL = IP = 48 A

Delta connection:

VL = 415 V

V= 415 V


Phase current IP = VP/Z = 415 ÷ 5 = 83 A

Line current IL = Ö3IP = Ö3 × 83 = 144 A



Note that when a load is connected as a delta configuration, the supply current is three times greater than in a star configuration.  In this case 48 A was used in the star configuration, while 144 A was used in the delta configuration.



Question 5

Three loads of 50 W each are connected in star configuration to a 400 V 3-phase supply.  Work out:

a.      The phase voltage;

b.      The phase current;

c.      The line current.


Question 6

Three loads of 50 W each are connected in delta configuration to a 400 V 3-phase supply.  Work out:

a.      The phase voltage;

b.      The phase current;

c.      The line current.


Electricity Distribution Systems

We are all familiar with the pylons that carry wires across the countryside.

Photo by kind permission of User Rept0n1x at Wikimedia Commons

Strictly speaking, we should use the term transmission towers, which carry overhead electricity transmission lines.  The National Grid is a network of transmission lines between power stations, and sub-stations.  The substations step down the voltages for use in factories, offices, and homes.  The National Grid uses 3-phase power transmission, and the ideas we are discussing are used on a large scale.


Electricity is generated at 25000 V, and is stepped up to 275 kV, or 415 kV.  The picture shows a 415 kV transmission line.  In this case, there are two three-phase sets of conductors.  There is a thin wire on the top of the towers that acts as a combined neutral and earth conductor.


In the substations transformers step down the voltage to the following values:

·         33 kV for local transmission;

·         25 kV for railways;

·         11 kV for heavy industry;

·         415 V for light industry;

·         230 V for offices and homes.


In heavy industry, there will be transformers to reduce the voltage to any value needed for the machinery in the factory.

The picture shows the step up transformers at the output of a power station that raise the voltage from 25 000 V to 275 000 V.  The current is reduced.  Note the very heavy cables (n the pipes at the back) coming in, and the relatively thin metal strips going out.

This next picture shows the very heavy cables between the transformers and the alternator.

Three-phase electricity transmission can be easily converted to single phase, by taking the output of one of the phases and connecting it to the load.  The other end of the load is connected to the neutral.  In streets, some homes are connected to the red phase, some to the yellow phase, and others to the blue phase.


This diagram shows how this can be achieved.



Use the diagram to answer Question 7 and 8.

Question 7

What is the phase voltage?  Explain your answer.


Question 8

Explain why the line voltage is 415 V



Note that if a device has the legend “415 V, 3-phase” marked on it, the line voltage is 415 V, i.e. the voltage between the red and the yellow phases.  But the phase voltage, i.e. the voltage between the red phase and the neutral, is 240 V.

In theory it is possible for a 4-phase system to be used with phases 90o out of phase.  This would give no significant advantage over 3-phase, but would require an extra conductor.  So 3-phase is the natural solution, and 4 phases are never used.

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