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Three Phase Electricity Supplies and Systems
The generation and supply of electricity within the U.K is achieved through the use of a 3-phase system.
This consists of 3 separate phase conductors along with a neutral conductor transmitting supplies to a given destination.
Simple three phase transmission
Consider a single phase generator to generate a single phase electricity supply. It would consist of a coil of wire which is rotated within a magnetic field.
It’s output would be as shown below.
If we took three of these generators (A,B & C) and positioned them equidistantly (120o apart) around a rotating magnet we would generate three separate a.c. waveforms each with a phase displacement of 120o^ from each other.
Such an arrangement would provide us with a 3 phase supply but we would need 6 conductors in order for it to function. However if we take each coil and interconnect it with the other coils in particular ways we can achieve a three phase supply in either a 3 wire (Delta) system, or a 4 wire (Star) system.
Delta Connection (3-phase, 3 wire system)
Using this method of connection each of the three coil windings are wound in such a way so they each have a start and a finish to their winding.
Then the finish of winding 1 is connected to the start of winding 2. The finish of winding 2 is connected to the start of winding 3. The start of winding 3 is connected to the start of winding 1.
Remember!
Delta = 3 phase, 3 wire system
Star = 3 phase, 4 wire system (3 phase + Neutral)
Maths of star and delta systems
The voltages and currents that exist within a three phase system have particular relationships.
Voltages measured across any phase winding are known as ‘Phase Voltages’ and are symbolised VP. Voltages measured between any pair of lines are known as ‘Line voltages’ and are symbolised VL.
Currents measured through any phase winding are known as ‘Phase Currents’ and are symbolised IP. Currents flowing along any line are known as ‘Line currents’ and are symbolised IL.
Indicate all line and phase voltages and all line and phase currents in the diagrams below.
Delta systems
Voltage Relationships
VL =VP Therefore VP = VL
Current Relationships
IL = 1.732 x IP & IP = IL 1.
Star Systems
Voltage Relationships
VL = 1.732 x VP & VP = VL 1.
Current Relationships
IL = IP Therefore IP = IL
You must remember these relationships by committing them to memory.
A delta connected load will have identical phase impedances. The impedance of each phase will therefore be identical both in terms of it’s magnitude AND phase angle. When this is the case the current that flows in each phase will be identical and the sum of the currents will be zero. The system is said to be balanced and there is no need for a 4th^ wire (neutral conductor).
It is also possible to have a star connected load where the impedance of each phase is identical in terms of it’s magnitude and phase angle. As with the delta system this will lead to identical phase currents and no excess current to flow back to neutral. Again, the system is said to be balanced and there is no need for a 4th^ wire (neutral conductor).
It is more usual however, to connect dissimilar loads to each phase of a star system. This will result in differences in phase currents which in turn will create some ‘leftover’ current which will flow back along the 4th^ wire (neutral) to the star point of the supply origin. Such a system is known as an unbalanced system and usually arises as a result of connecting separate single phase loads to each phase of a three phase star connection.
Progress
What is meant by a 3 phase balanced system?
Is there any need for a 4th^ wire (neutral) in such a system?
How does an unbalanced system differ?
What function does the 4th^ wire serve in an unbalanced system.
Which type of 3 phase system is more likely to be found with an unbalanced load?
For Level 3 students a powerpoint presentation exists to explain the calculation of neutral current in a 3 phase balanced and unbalanced system.
Power in three phase sytems.
Each phase of a 3 phase system will result in some power consumption.
If the system you are dealing with is balanced there will be an equal power dissipation per phase and therefore it is necessary only to calculate the power dissipated in one phase and multiply the result by 3 (for the 3 phases).
When doing this however you must remember that each phase is an a.c system and as such the power factor is required in addition to phase voltage and current.
Power/phase = VpIpCos è
If the system is balanced: Total Power = 3VpIpCos è
For an unbalanced system it is necessary to calculate each phase power in turn and add them in order to find total power.
An alternative power formula exists which utilises the line voltages and currents:
Total Power = 1.732 x VLILCos è
These formula apply to both Star and Delta connected systems equally.
Progress
A star connected balanced load has a phase voltage of 230v and line current of 9A. The system power factor is 0.65.
Calculate the total power for the system using both total power formulae.
Once you have calculated total power calculate the power per phase.
