Safety Notice

Please note that this is not a guide on how to connect and use 3-Phase power. Neither the author nor UKSLC accepts responsibility for death or damage or persons or property which results from any person attempting to perform electrical maintenance, installation, distribution or other action regarding mains electricity.

Mains electricity is dangerous, only suitably qualified persons should deal with it!

Introduction

So you want to know more about 3-phase power? You have come to the right place. Following on from the interest displayed in our very own forums with regards to an explanation about three phase power and its application, the UKSLC team now brings you a complete article devoted to its explanation.

Due to the different levels of understanding that are present within the UKSLC user base this article includes sections on the mathematics and electronic/electric theories that you will need to be able to understand the main content of the article. Some readers may be able to skip some of these sections, probably if they have A-level or higher mathematic understanding.

Foundation theory

What is AC?

Let us start at the very beginning. Ever since the demand for large-scale electricity generation and distribution there has been AC power. While early stations in the late 1800's generated DC power, is was quickly realised that direct current was less than ideal for distributing electricity. Transformers could not be used with the system, which means that electricity had to be generated, transmitted and used at one nominal voltage. Over long distances losses in the cabling became large, meaning many generating sites would have to be sited locally to where the power was required. Fortunately, a new AC system was proposed by George Westinghouse soon after, and todays generating, transmission and distribution systems still work on the same basic principles today.

An AC supply is a supply of electrical energy where the current flows in one direction around the circuit and then the other, much like getting a simple circuit powered from a single battery and reversing the polarity of the battery at regular intervals.

In the UK and Europe the change of polarity occurs one hundred times every second (50Hz).

The change of direction of the current doesn't occur instantaneously. The change between a positive maximum value and a negative minimum value occurs smoothly. This smooth variation between positive and negative values is sinusoidal. In other words takes the form of a sine wave.

Basics of AC - Sinusoidal waves

Although many will describe the way that the flow of current or the voltage changes in a AC system as a sine wave it should correctly be referred to as a Sinusoidal Wave. Sinusoidal Waves are sine waves with a amplitude other than one and can have a phase shift.

The majority of people will have already come across the sine wave in secondary school. To ensure that all readers have a suitable understanding of the sinusoidal functions and the correct terminology that is used when describing them this section will briefly explain them.

Below is an example of a sinusoidal function of voltage.

This function has two parameters. The first is the amplitude of the function. This is depicted here as V_max, as the amplitude of an AC voltage is also the maximum voltage that it can reach. The second parameter is the period of the wave. The time period of a wave, as shown here by the section labelled "T", is the time that it takes for one complete cycle of the wave to be completed.

The Time period of a wave can be linked to it frequency, the number of complete cycles are completed per second, with the following equation;

T = 1/frequency = 1/f

However with sine waves we work in angles there fore the link between the frequency and angular frequency, denoted ω (omega), is

ω=2πf

Where ω is in a unit of measuring angles called radians, this is not important to go into now however information about this unit of measurement is easy to come by on the internet. For standard 50Hz main supplies in the UK and Europe ω = 314rad sec^-1 (314 radians per second) or 18000˚ sec^-1.

Putting all of this together means that you can formulate a function of the sinusoidal wave displayed as below:

v(t) = V_max sin(ωt)

The function is equal to "v(t)" as the function gives the voltage relative to the time at which it is taken. This is known as the momentary voltage as it constantly changes.

There is a third common parameter that is applied to sinusoidal waves. This third and final one is very important in the explanation of three phase mains electricity. This final parameter is called "Phase".

Phase is denoted the symbol Φ (Phi) and is measured in either radians or degrees. A standard sine wave originates from the origin however if you were to delay the start of the sine wave it would start at a value above zero on the time axis. This "delay" between the origin and the first time that the wave inclines upwards up wards after the origin, consult the below diagram

On the diagram there are two sinusoidal waves. The black one is the same as that displayed in fig1. while the blue wave has the same frequency, period and amplitude but differs in phase by an angle Φ. Hence the black trace has Φ=0˚.

Basics of AC and RMS Values

We have now covered, very quickly and briefly, the basics of sinusoidal functions and had a very simple overview of AC supplies. Now these are going to be brought together and elaborated upon to bring us to RMS values of voltage and current. Although we don't need to understand this it is important to touch upon due to its implications when applying the sinusoidal theory we have just established.

From previous sections we have covered that AC supplies vary from a positive maximum to a negative minimum, that this change occurs as a sinusoidal function and that sinusoidal functions have three parameters; amplitude, period (which is directly linked to frequency and vice-versa) and phase.

In most environments you will come across a mains voltage of 230V. This is the voltage that people say when they are talking about the mains in the EU and the voltage that most equipment is rated for, please note that some equipment might be rated for 250V or 240V however the standard voltage of the UK has been altered to fall in line with a standard EU mains voltage.

You might assume, now with your knowledge of sinusoidal functions, that 230V is the peak value. However this is not the case. 230V is actually the RMS voltage of the mains in the EU.

The true peak value of the main is actually closer to 325V, which is 230V multiplied by the square root of 2 at 50Hz. RMS values are used for both current and voltage as then when you calculate power, such as the wattage of a lamp (light bulb), then you get the average power instead of the peak power, which is much more useful to both engineers and other users. I will not go into calculating RMS values for frequencies other than at 50Hz, again if you are interested in this there are places on the internet that have information on RMS values.

For 99% of the time electronic/electrical engineers, LX technicians, and the layman on the street all use the RMS values of Current and Voltage when talking about mains supplies.

Although we don't strictly need to know what RMS values are I though that it should be included for completeness.

The theory of Three phase power

We are now moving on the specifics of three phase power. While there was a lot of preliminary information it was necessary to ensure that all our users were able to understand this, the core, of the article.

This section of the article will cover what three phase power is, how it is generated, why it is useful and why it is used nationwide as well as how it can be used in the industry.

The theory of what three phase power actually is should not be a mystery to you for much longer, indeed with our understanding of sinusoidal waves it will may seem terribly simple! The difficulties can come with understanding why it is used at all.

What is Three phase?

Three phase power is usually available to us in the industry as a five pin connector with one pin larger than the other. This larger pin is the earth connection while out of the four smaller pins one is the common neutral and the other three carry three live voltages at different phases. Each of the three phases has an RMS voltage of 230V.

A sinusoidal wave completes one oscillation in 360˚. The three different phases are evenly spaces. There is one that is considered to be at 0˚ while the other two are at 120˚ and 240˚ relative to the first.

This means that if you had an instrument where you could see the voltages as a function of time down each of the three phase cores, relative to 0V or ground, then you would see a wave function like below.

Here the black wave is taken as the one at zero phase with the red one lagging the first by 120˚ and the blue one lagging that by a further 120˚ adding up to a total phase difference from the origin of 240˚.

Single phase voltage, such as that which you get from blue ceeform connectors or from usual household 13A connectors, is at 230V. This is referred to as the phase voltage, i.e. the voltage between a single phase and neutral.

The benefits of three phase supplies

Now we know what three phase is, after a very brief description thanks to the preliminary work that we covered before about sinusoidal functions and AC voltages we can now ask what are the benefits of having a three phase system?

The primary reason is efficiency. It is more efficient to generate three phase current in a single generator that to use single phase generators. The differences between a single and three phase generator will be explained in a short section later in this article.

Three phase power is also useful for powering large amounts of kit, like in an outdoor festival situation. Not only does this allow use of separate phases for audio and lighting kit, it also allows smaller (lighter and easier to handle!) cables to be used. Despite usually containing five cores, remember that your three phase cable carries three *individual* phases, yet only requires a single neutral and earth core. A significant benefit vs three individual single phase cables, or one very large and difficult to handle single phase lead.

Three phase electricity is also used on the larger scale, in the national grid, due to some benefits that arise in the distribution of the electricity, this is briefly covered in a later section.

415V?

Now if you think to those warning stickers that you see on three phase distribution kit or boiler rooms and the like in a public building, office block or possibly on the output of a generator you may recall that they often read "Danger 415V".

Now some people will be confused as to how having three phases, each with a RMS voltage of 230V, can add up to this stated 415V RMS. Now without going into the long and drawn out process of mathematically describing this I am going to cover it quantitatively so that you at least have the concept and reason while not having a mathematical proof.

Now we need to start by considering what each of the phases are individually. They are each sinusoidal functions whose value changes with time. Now each of the three has a different value at any point in time, hence they are never at a peak value at the same time nor are they all at zero all of the time.

If you add the values of the three phases together at any moment in time they total 415V, this is known as the line voltage, and is the voltage measured between any two live phases.

You can find the RMS value of adding three phases together of a given voltage by adding the RMS voltages together and dividing by the square root of three. However if you do this with 230V you will discover that something is awry! The next section has all the answers.

Are you sure about 230V and 415V?

Now I can imagine that many people will be used to saying that the standard phase to neutral voltage is 240V_rms and some people will remember it being 250V_rms. Due to our national grid being connected with Europe via France we have had to change our standard phase-neutral voltage slightly to 230V_rms (Most European countries had to move up from 220V_rms).

However, if you stick a multi-meter in a mains socket, which you SHOULD NOT DO unless you are qualified properly and know what you're doing, you will probably find that the RMS voltage is still nearer to the 240V mark. Just don't tell Brussles!

415V still lives on. As I said at the end of the last section if you calculate the voltage that is obtained if you add together the three phases when each has a RMS value of 230V then you will not get 415V_rms however this value still lives on as the recognised voltage. This is because the national grid was not suddenly 'adapted' to work at 230v, the cost and inconvenience of making this small alteration would have been huge. Instead, wider tolerances allowed 230V_rms and 240V_rms equipment to interoperate, and all new installations by local electricity boards since then to domestic premises have been designed to run at 230V_rms. 

Three phase generation

While you will only typically come across three phase generation at outdoor events, which for many isn't that often, I thought that it might still be of interest to many readers to know how they work.

As you may or may not know, electrical generators are basically large magnets that are spun round quite fast. The moving magnetic field which is generated ‘links' with coils of wire (being static, this part is named the stator) which surround the spinning part (coined the rotor, for obvious reasons!). As the wire is influenced on by a changing magnetic field a current is induced in the wire.

If the generator had a single winding it would produce the familiar single-phase AC voltage trace. A three phase generator, which is the type of which most generators are, have three sets of windings which are offset around the spinning section of the machine so that the voltage traces they produce are offset by 120˚.

In terms of generation three phase power was opted for due to three phase generators being more efficient than single phase types.

Three phase AC transmission

Now this is something that you are probably even less likely to come across while working in a theatre, unless you have a step down transformer or a pylon complete with transmission line but I thought that it, again, might be of interest to some out there.

If you look at electrical transmission systems, especially the large metal ‘pylons' (which are called transmission towers by engineers) that connect the country from coast to coast, you will see that they either have four or seven cables. One is usually noticeable thinner than the others, it is commonly the one right at the top of the standard towers that carry seven cables. This is actually the cable that goes from the neutral in your house back the generator, the reason that it is smaller than the rest will be explained in the small section about three phase distribution.

The other three or six cables are the three phases, when there are six cables there are the three phases in duplicate to allow higher current capacity while maintaining a balanced structure (this is relating to the physical structure of the tower, those cables are heavy so one either side balances it out).

On the more standard large pylons with six cables the bottom two are 0˚, the middle two are 120˚ and top two are 240˚, with the very top one on it's own being neutral.

Three phase distribution

Due to characteristics of three phase supplies, which I am not going to go into, it is possible to arrange the load on a three phase generator in order to have no residual current that is required to go back to the generator.

If you have a single phase generator and, for simplicities sake, a light bulb you take a feed from one terminal of the generator then link that to the light bulb and then you complete the circuit by connecting the other terminal of the light bulb to the other terminal of the generator. However with three phase systems you can arrange the generators and loads like below.

By connecting one terminal of each of the generators and the loads together in this formation due to the ways the sinusoidal waves interact if the three loads to the right of the image are equal then there is no residual current as it cancels out. Of course, this assumes three absolutely identical loads, and the only real situation where this will be experienced would be in three phase motors, heating elements and the like.

In the real world these loads can be hundreds of houses and businesses. These loads are very dynamic, and even though utility companies do their best to balance loads between phases (after all, it pays them to do so - a balanced load is the most efficient) things will never be perfect. Every consumer will run loads of different power consumption, sometimes on and sometimes off, some will be resistive, other inductive, and other capacitive, and this does of course mean that they will all vary in power factor too! This inevitably leads to a small amount of current that does not 'cancel out', and this residual current is carried back down the neutral conductor. As it is carrying much less than the live phase transmission lines though it does not need to be anywhere near as thick as they are.

The loss of Neutral in a three-phase system can be disastrous where unbalanced loads are distributed across multiple phases. If it were to become disconnected then there would no longer be anywhere for this residual current to return other than via the other phases, effectively allowing the neutral to 'float' at practically anything between 0 and 415v. This will almost undoubtedly result in the destruction of any connected equipment by allowing 415v to be present where normally there would only be 240v.