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Overview

Introduction

Three Phase supply systems are used throughout the world to produce, transmit and distribute electrical power to industrial, commercial and domestic premises.  In this Section you will learn how Three Phase supplies are produced by generators.  

Your home is likely powered by a Single Phase Alternating Current (AC) mains supply, having Live, Neutral and Earth connections.  In the UK, Single Phase AC is defined by BS7671 as 230V RMS +10%, -6%, 50Hz.  For applications requiring higher power, such as industrial machines, Three Phase AC is used, which, has three live conductors, at 415V RMS +6%, -10%, 50Hz in the UK. 

Three Phase has some advantages over Single Phase:

• Higher Rating
  The rating (i.e. the output) of a three-phase machine is nearly 1.5 times the rating (output) of a Single Phase machine of the same size.

• Constant Power
  In Single Phase circuits, the power delivered is pulsating. Even when the voltage and current are in phase, the power is zero twice in each cycle. Whereas, in the Three Phase (polyphase) system , the power delivered is almost constant when the loads are in balanced condition.

• Power Transmission Economics
  The Three Phase system requires only 75% of the weight of conducting material of that required by Single Phase system to transmit the same amount of power over a fixed distance at a given voltage.

• Superiority of 3 Phase Induction Motors
  Three Phase induction motors have a widespread field of applications in industry because of the following advantages:

  1. Three Phase induction motors are self-starting whereas the Single Phase induction motor is not. This means the Single Phase motor has no starting torque and hence it needs some auxiliary means to start at the initial stage.

  2. Three Phase Induction motors have higher power factor and efficiency than that of a Single Phase induction motor.

• Size and Weight of alternator
  The Three Phase Alternator is small in size and light in weight as compared to a Single Phase alternator.

• Requirement of Copper and Aluminium
  Three Phase systems require less copper and aluminium for the transmission system in comparison to a Single Phase transmission system. 

• Frequency of Vibration
  In Three Phase motors the frequency of vibration is less when compared to Single Phase motors because in Single Phase the power transferred is a function of current and varies constantly. 

• Dependency
  A Single Phase load can be efficiently fed by a Three Phase load or system, but a Three Phase system cannot depend on or be fed by a Single Phase system. 

• Torque
  A uniform or constant torque is produced in a Three Phase system, whereas in a Single Phase system pulsating torque is produced. 

Three Phase Generation

Three Phase synchronous generators are the primary source of all electrical energy we consume. The most common type is the revolving field generator. A stationary armature, called a stator, consists of 6 windings forming complimentary pairs.  Each winding is 60 degrees apart from the next.  Rotating within the stator is a rotor, which is a field coil energised with a Direct Current (DC) to form an electromagnet.  See Figure 1:

Figure 1: Three Phase Generator close-up showing Stator and Rotor

Wikimedia / CC0

An external power source (the prime mover, for example water or wind flow) causes the rotor to turn, and by Faradays law of electromagnetic induction, the interaction (flux cutting) between the rotor field and the stator windings causes a voltage to be induced in the stator windings. This is the Three Phase voltage supply, shown in Figure 2, with each phase 120 degrees out of phase with the next (shown as Red, Yellow, then Blue – corresponding to the old UK wiring colours for three phase systems – which you will still find on old equipment).

Figure 2: Three Phase Generation

© L.Gray UHI

The output voltage can be increased by increasing the Ampere-Turns on the rotor field winding, thus increasing the magnetic flux density.  This can be done by:

1. Increasing the DC current in the rotor field coil, called the Excitation Current.
2. Increasing the number of turns on the rotor field coil. Of course, this is a physical change so less easy to do than (1).

The equations representing the instantaneous values of the three phase sinusoidal outputs, using phase 1 as a reference are:

$v_{P1}=V_{P1\text{peak}}\text{sin}\left(\theta \text{°}\right)V$ 

$v_{P2}=V_{P2\text{peak}}\text{sin}(\theta -120\text{°})V$ 

$v_{P3}=V_{P3\text{peak}}\text{sin}(\theta +120\text{°})V$ 

Similar equations represent the instantaneous values of the line voltages, using line 1 as a reference:

$v_{L1}=V_{L1\text{peak}}\text{sin}\left(\theta \text{°}\right)V$ 

$v_{l2}=V_{L2\text{peak}}\text{sin}(\theta -120\text{°})V$ 

$v_{L3}=V_{L3\text{peak}}\text{sin}(\theta +120\text{°})V$ 

Star (or Wye) connected Three Phase Generators

The Three Phase Generator is connected in Star (or Wye) configuration in Figure 2, where one end of each stator pole-pair winding is connected to Neutral.  Diagrammatically this is shown in Figure 3 with the equivalent Circuit Schematic Symbols.  You can see that it looks like a Star.

Figure 3: Star Connected Three Phase Generator

© L.Gray UHI

If the Neutral is connected to a wire, this is a 4-wire system and if it is not, this is a 3-wire system.

The phasor diagram showing the magnitude and relationship between the three phase voltages is unsurprisingly similar to the circuit symbol:

However, if we analyse the circuit in more detail, as in Figure 4 with a 4-wire system, we see that in addition to the phase voltages measured from V_P1, V_P2 and V_P3 to the neutral point, there are also line voltages, which by Kirchoff’s Voltage Law = V_P1 - V_P2 (V_L12), V_P2 - V_P3 (V_L23), and V_P3 - V_P1 (V_L31).  The phasor diagram showing all of these is also in Figure 4 (remember that to subtract phasors you add the 180° rotated phasor – as shown by the dotted lines).  

Figure 4: Star Connected Generator showing Line and Phase voltages and currents with a Voltage Phasor Diagram

© L.Gray UHI

The voltage phasor diagram shows that the line voltage phasors are longer than the phase voltage phasors so have greater magnitude.  In a balanced 3-phase, 4-wire, Star connected system:

It can also be seen from the phasor diagram that the phase sequence of the line voltages is V_L12, V_L23, V_L31 and that they are 120˚ apart.

Another thing we can see clearly from Figure 4, is that the current flowing through each phase (phase current) of the generator also flows along the output wires (line current).  So the equation relating line and phase currents, in a balanced 3-phase, Star connected system is:

Delta connected Three Phase Generators

There is another way to connect up the stator coils, which is to omit the neutral point and connect the end of each winding to the start of the next.  Diagrammatically this is shown in Figure 5.  This looks like the Greek capital letter Delta (Δ).

Figure 5: Delta Connected 3-Phase Generator

© L.Gray UHI

If we analyse the circuit in more detail, as in Figure 6 with a 4-wire system, we can see that the phase voltages V_P1, V_P2 and V_P3 are the same as the line voltages V_L12, V_L23 and V_L31.   So the voltage phasor diagram for a Delta connected generator is much simpler than for a Star connected one and is shown in Figure 6.

Figure 6: Delta Connected 3-Phase Circuit Diagram and Voltage Phasor Diagram

© L.Gray UHI

In a balanced, 3-phase, Delta connected system:

However, by Kirchoff’s Current Law, the phase currents I_P1, I_P2 and I_P3, algebraically add at the junctions to produce the line currents, giving, for a 3-phase, balanced, Delta connected system:

Hopefully you see the similarity and the difference between these Delta system equations and the Star connected system equations.

Conclusion

In this section you have learnt about the construction and operation of three-phase generators.  You have also learnt about how these can be connected with star or delta connected windings, and how the connection type affects the phase and line current and voltage equations.  You have learnt how to draw phasor diagrams for star and delta connected generators.  In the next section, Outcome 2, you will learn how to analyse star and delta connected balanced loads.