|Introduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.)|
|8. Three-phase Current|
The most important property of the three-phase current is discussed here. For this purpose, we again start from three coils displaced by 120° from each other which are connected to a three-phase current according to Fig. 8.3. (Fig. 8.4.).
Fig. 8.4. Three-phase winding of a motor
Fig. 8.5. Development of the rotating field
a) Three-phase line diagram with points of time plotted on the diagram
b) Resulting magnetic field for the points of time plotted on
In each of the three coils, an alternating field will be brough about in accordance with the alternating voltage applied. The total magnetic field resulting from the magnetic fields of the 3 coils is subject to a closer examination below. For this purpose, we have to give some explanations regarding the representations. When the positive half wave of the alternating voltage is applied to the coil, a magnetic north pole will be formed at the end of the coil which is inside the arrangement in accordance with the sense of winding of the coil. This pole is represented by cross hatching. The density of the lines of hatching corresponds to the amplitude of the voltage present at the instant of observing. When the negative half wave is applied, the south pole is formed which is represented by longitudinal hatching. For the points of time entered into the three-phase current line diagram in Fig. 8.5.a, the magnetic flux produced in the three coils at the points of time a to g is shown in Fig. 8.5.b. The position of the total magnetic field brought about by the three individual fields is represented by the position of a rod magnet whose north pole is marked black. (A representation of the coils as given in Fig. 8.4. is omitted for the sake of clearness.) The position of the total magnetic field changes with the interval of time under consideration of the three-phase current line diagram. It is evident that the total magnetic field has turned through half a revolution from point of time a to point of time g. When further partial pictures would be represented, then a full revolution of the total magnetic field would be performed during the duration of a cycle of the three-phase current. This shows that, in a three-phase winding connected to three-phase current, a rotating magnetic field is formed which is called rotating field. The majority of electric motors and their mode of operation are based on the presence of the rotating field which enables extremely simple and sturdy designs of electric motors. Within a full cycle of the three-phase current one revolution of the rotating field is performed in an arrangement according to Fig. 8.5. When two times three coils are arranged at the circumference, then the rotating field will perform only half a revolution within one cycle. Such an arrangement is termed as design with two pairs of poles. There are also arrangements with a higher number of pole pairs. For the calculation of the rotational speed of the rotating field we have
nD = f/p
rotational speed of the rotating field
number of pole pairs
A three-phase current winding (also known as polyphase winding) with three pairs of poles is connected to a three-phase current having a frequency of 50 Hz. Determine the rotational speed of the rotating field per minute!
f = 50 Hz
To be found:
nD in rpm
nD = f/p
nD = (50 1/s)/3
Since the speed per minute is required, the above calculation will, however, result in the revolutions per second, multiplying by 60 s/min is necessary.
nD = (50 1/s · 60 s/min)/3
nD = 1000 rpm
The rotating field has a speed of 1000 revolutions per minute.
When exchanging two phases shown in Fig. 8.5. in the manner represented in Fig. 8.6., the sense of rotation of the rotating field is inverted. This property of the three-phase current is also of advantage to the construction of electric motors.
Fig. 8.6. Three-phase winding with the phases exchanged as compared to Fig. 8.5.
Inside a polyphase winding connected to three-phase current a rotating field is formed (rotating magnetic field) whose sense of rotation can be inverted by exchanging two connections. The rotational speed of the rotating field is dependent on the frequency and the number of pole pairs. Simple designs of motors are possible due to the rotating field involved in three-phase current.
Questions and problems:
1. Under which conditions is a rotating field formed?
2. Demonstrate the reversal of the sense of rotation due to the exchange of two phases as shown in Fig. 8.6. with the help of a representation as given in Fig. 8.5.b!
3. What is the technical importance of the rotating field?
4. Calculate the possible rotational speeds of the rotating field for arrangements with 1 to 10 pairs of poles when the frequency is 50 Hz!