Colleagues Xiao S and Ms. Can discussed a winding scheme for a certain type of motor in order to effectively reduce electromagnetic noise. When the topic of phase bands came up, Xiao S seemed a bit lost, saying that although he had always had the concept of 60 or 120-degree phase bands, he didn't have as clear a understanding of phase bands as he did of fractional turns or sinusoidal windings.
According to Ms. Can, Xiao S's situation is somewhat representative. Although there are many types of motors, most motor windings are standard 60-degree phase bands, and even 120-degree phase band windings are rarely involved. Naturally, few people pay attention to non-standard phase bands and related issues.
In view of the above, Ms. Can believes it is necessary to discuss the phase band and its selection. To ensure the symmetry and maximum absolute value of the composite vector of the slot potential or magnetomotive force of the three-phase winding and the minimum harmonic content, the selection of non-standard phase band windings is usually the best option.
Star diagram of tank potential
When discussing phase bands and their selection, it is necessary to study the slot potential star diagram. When the potential of the conductors in each slot of the armature changes sinusoidally using vectors, these vectors form a radial star diagram, called the slot potential star diagram.
Method for drawing a star diagram of tank potential
Figure 1 shows the circumferential distribution of conductors in the stator slots of a three-phase synchronous generator. The number of poles is 2p=4 and the number of slots is Z=36. The steps for drawing the star diagram of its slot potential are as follows:
1) Slot pitch electric angle α1
When the distance between two adjacent slots is expressed in electrical degrees, it is called the slot pitch electrical angle. Since the entire armature circumference is 360° mechanically, when calculated in electrical degrees, the range of a single pole pitch is equal to 360° electrical degrees. When the motor has p pole pairs, the armature circumference should be p360° electrical degrees; therefore, the slot pitch electrical angle is...
α1=p360°/Z……（1）
In the formula, p is the number of pole pairs of the motor, and Z is the number of armature slots. For the motor shown in Figure 1, α1 = p360°/Z = 2 × 360°/36 = 20°
Figure 1
2) Draw the star diagram of the tank potential.
Assuming that the magnetic flux density of the magnetic poles is distributed sinusoidally along the circumference of the air gap, and the rotor rotates at a constant speed in the counterclockwise direction, the induced electromotive force of the conductors in each slot of the stator will change sinusoidally with time.
Since the slots differ from each other by an electrical angle α1 in space, the potentials of the conductors also differ from each other by an angle α1 in time. As shown in Figure 2a), assuming the potential of the conductor in slot 1 is represented by vector 1, then under the direction shown in the figure, the potential of the conductor in slot 2, vector 2, lags behind vector 1 by 20°. Similarly, vector 3 lags behind vector 2 by 20°. And so on, the star diagram of the slot potentials shown in Figure 2a) can be drawn.
Figure 2
Physical meaning of the star diagram of the tank potential
As can be seen from Figure 2a), vectors 19, 20, 21... coincide with vectors 1, 2, 3... respectively. This is because they are in the corresponding positions under the magnetic poles, so their induced electromotive forces are in phase.
Generally speaking, for an integer number of slot windings per pole and per phase, if the motor has p pole pairs, there are p overlapping slot potential star configurations. More generally, when p and Z have a greatest common divisor t, there are t overlapping slot potential star configurations. For the synchronous generator shown in Figure 1, the greatest common divisor of p and Z is 2, therefore there are two overlapping slot potential star configurations.
The concept and physical meaning of phase band
Each phase occupies a spatial electrical angle
As shown in Figure 2a), each 360° electrical angle circle is divided into 6 equal parts, and each part spans 60° electrical angle. That is, each phase of the three-phase AC winding AX, BY, and CZ occupies a spatial range of 60° electrical angle. Similarly, as shown in Figure 2b), each phase of the three-phase AC winding A, B, and C occupies a spatial range of 120° electrical angle.
Phase bands and their physical significance
The term "phase band" refers to the electrical angle occupied by each phase winding in the 360° electrical angle space, as shown in Figure 2. Its magnitude actually reflects the distribution level or concentration of the armature winding. The larger the phase band electrical angle value, the lower the winding concentration, and the smaller the harmonic content in the composite electromotive force or magnetomotive force wave, but the lower the winding utilization rate or distribution coefficient.
Selection and Principles for Non-Standard Phase Bands
When studying low harmonic windings to reduce electromagnetic noise, the electrical angle occupied by each phase winding in the 360° electrical angle space is not limited to 60° and 120° as shown in Figure 2. However, the windings of variable pole multi-speed motors often use non-standard phase bands other than 60° and 120° phase bands.
Regardless of the winding phase selection, the following principles must be followed:
With a certain number of conductors, a larger fundamental potential and fundamental magnetomotive force can be obtained;
1. In a three-phase winding, for the fundamental wave, the three-phase electromotive force and magnetomotive force must be symmetrical, that is, the three phases are equal in magnitude but 120° out of phase; and the three-phase impedances must also be equal.
2. The waveforms of electric potential and magnetomotive force should be as close to sine waves as possible. To achieve this, the harmonic components in the electric potential and magnetomotive force should be as small as possible.
