A Design on Reduction Cogging Torque of Dual Generator Radial Flux Permanent Magnet Generator for Small Wind Turbine

Abstract

In this paper, the design for an electromagnetic structure and reduction cogging torque of a dual generator structured RFPM generator, which is a combination of the inner- and outer-rotor types, has been proposed. We call this a dual generator radial flux permanent magnet generator. To reduce the cogging torque, firstly, stator tooth pairing was designed; secondly, stator displacement was designed and finally, stator tooth pairing and stator displacement were carried out simultaneously. We found the optimal design condition about stator tooth pairing angle combination and stator displacement angle for cogging torque minimization. As a result, a cogging was reduced by 93.3[%] by this study.

1. Introduction

Small scale wind power applications require a cost effective and mechanically simple generator in order to be a reliable energy source. The use of direct driven generators, instead of geared machines, reduces the number of drive components, which offers the opportunity to reduce costs and increases system reliability and efficiency [1].

A small wind turbine using a permanent magnet essentially refer to a RFPM(Radial Flux Permanent Magnet) generator. The RFPM generator, which has a iron core slot in the stator, is easy to manufacture and has a high output voltage and power as well as efficiency. However, because of the existence of iron core slot of the stator, the RFPM generator experiences cogging torque [2].

The cogging torque can bring about an increase in the torque ripple, the vibration and noise generation. It is an important factor to consider for determination of the minimum wind intensity required to generate power in a wind generator [3].

Cogging torque is produced by the interaction between the rotor permanent magnet and the stator teeth. Many methods, such as a fractional number of slots per pole[3], [4], slot skewing [5, 6] magnet skewing [7, 8] auxiliary slots or teeth [3], magnet segmentation [9], pole-arc optimization [3], magnet displacing and shaping [10], etc. have been proposed to reduce the cogging torque [11].

The purpose of this paper is to reduce cogging torque and the design of the electromagnetic structure of the RFPM generator. To reduce the cogging torque, firstly, stator tooth pairing was designed; secondly, stator displacement was designed and finally, stator tooth pairing and stator displacement were carried out simultaneously. The RFPM generator designed in this study was analyzed by the two-dimensional FEM(Finite Element Method).

 

2. Design of Dual Generator Radial Flux Permanent Magnet Generator

The RFPM generator is classified into inner-rotor and outer-rotor types.

An inner-rotor type RFPM generator is shown in Fig. 1. The rotor located inside of the stator, thereby having a robust mechanical structure as well as excellent massproduction capability. However, because the rotor is positioned at the inner side where a permanent magnet is attached, its diameter is relatively smaller because of the structural limitation. This limitation causes difficulty in obtaining a high output power because of the relatively small cross-sectional area of the effective output as compared to the total volume, and requires a speedincreasing gear between the generator and a blade because of the low voltage generated at a low speed caused by the lack of a multi-pole structure.

Fig. 1.Inner-rotor type RFPM generator

The outer-rotor type RFPM generator is shown in Fig. 2. Since the rotor in this generator is positioned externally thereby creating a bigger effective output power crosssectional area than that in the inner-rotor structure; this is advantageous in terms of the output power, and low-speed power generation is possible because of the presence of a multi-pole structure. However, in this case, since the inside of the stator is empty, dimensional efficiency is reduced and the cogging torque increases significantly as compared to that in the case of the inner-rotor type RFPM generator.

Fig. 2.Outer-rotor type RFPM generator

In this paper, the design for an electromagnetic structure of a dual generator structured RFPM generator, which is a combination of the inner- and outer-rotor types, has been proposed. We call this a DG-RFPMG(Dual Generator- Radial Flux Permanent Magnet Generator) in this paper.

Fig. 3 shows the shape of the DG-RFPMG. The DGRFPMG is divided into inner and outer stators for dual generation, and has a rotor to which the permanent magnets positioned between the two stators are attached. Table 1 shows the design specifications of the DG-RFPMG.

Fig. 3.Shape of proposed DG-RFPMG

Table 1.Specification of DG-RFPMG

 

3. Cogging Torque

Cogging torque is the oscillatory torque caused by the tendency of the rotor to line up with the stator in a particular direction where the permeance of the magnetic circuit by the magnets is maximized. Cogging torque exists even when there is no stator current. When the PM machines running, additional oscillatory torque components can result from the interaction of the magnet with spaceharmonics of the winding layout and with current harmonics in the drive current. These additional oscillatory torque components are electromagnetic and are generally referred to as torque ripple, while the term cogging torque is often reserved for the zero-current condition. In a well designed PM machines the torque ripple and the cogging torque should both be negligible, but it is possible for the torque ripple to exceed the cogging torque by a large amount if the PM machines has an inappropriate combination of winding layout, drive current, and internal geometry [12].

Cogging torque can be reduced by using some minimization technique. Fig. 4 shows the cogging torque minimization technique. The methods of reducing the cogging torque, such as slot skewing and pole-arc to polepitch ratio for specific permanent magnet machines, were obtained by the experience, experiments and FEM [11].

Fig. 4.Summary of cogging torque minimization technique

3.1 Energy method of cogging torque

The cogging torque is the amount of energy variation with respect to the rotation amount of a rotor and can be represented as follows:

Where T, W(α), α, are the cogging torque, energy in the air-gap, angle of rotor, respectively.

Since the energy variation does not occur substantially except in the air-gap areas, the cogging torque can be obtained by calculating the energy in the air-gap areas. The energy in these areas can be calculated as follows:

Where μ0 , G(θ) , B(θ, α) , LS , R1 , R2 are permeability of air, relative air-gap permeance function, flux density function, stack length, permanent magnet radius and stator radius, respectively.

The relative air-gap permeance function G(θ)2 and flux density function B(θ,α)2 of (2) can be represented by (3) and (4), respectively, using the Fourier series expansion.

Where NS , NP are number of slot and number of permanent magnet, respectively.

Therefore, by using (3) and (4) and the orthogonality of the trigonometric function, we can represent (2) as (5):

Where NL is least common multiple of NP and NS .

The cogging torque can be represented by (6) by the partial differentiation of the energy in the air-gap with respect to the rotational angle of a rotor.

The cogging torque can be reduced if GnNL or BnNL can be assumed to be zero in (6) [11, 13].

 

4. Cogging Torque Reduction Design

4.1 Stator tooth pairing design

Fig. 5 shows a stator tooth paring design in which the stator tooth widths a and b are paired.

Fig. 5.Stator tooth pairing(tooth widths a and b)

GnNL of (6) can be represented by (7) as follows:

By reducing the GNL value among values of GnNL when n is 1, we can eliminate a dominant component of the cogging torque. That is, if a combination of tooth widths a and b that satisfies (8) is found, then a dominant component of the cogging torque can be eliminated [13].

Table 2 presents the details of the stator tooth paring design where the stator teeth a and b have the maximum GNL value and the sum of the design angles a and b is the same for different GNL values.

Table 2.Stator tooth pairing widths design

Fig. 6 shows one cycle of the cogging torque according to the stator tooth paring design. The analysis result showed that the smallest cogging torque occurred at the combination of 6.5-11.5[deg.(m)], which has the smallest GNL value.

Fig. 6.Cogging torque characteristics according to stator tooth pairing

4.2 Stator displacement design

The objective of the stator displacement design is to reduce the cogging torque by placing the inner and the outer stators in a staggered pattern as shown in Fig. 7 [14].

Fig. 7.Definition of stator displacement

The cogging torque generated in the DG-RFPM generator is the sum of the inner and the outer stator and can be represented as follows:

Where τC , τouter , τinner , θC are total cogging torque, outer side cogging torque, inner side cogging torque, cogging torque phase, respectively.

The sum of the total cogging torques can be made equal to zero by transitioning the cogging torque phase, which is generated in the outer stator as per (9), by 180 [deg.(e)] as shown in (10).

NC denotes the number of occurrences of the cogging torque per rotation in a rotor generated in the inner and the outer stators and can be represented as follows [15]:

Where , HCF{NS, NP} is the highest common factor of the number of slot and number of permanent magnet.

Therefore, the mechanical angle at which the cogging torque occurs once is as follows:

Then, by expressing this as an electrical angle, we obtain the following:

Therefore, the stator displacement transition angle to move the cogging torque phase by 180[deg.(e)], which is generated in the outer stator, can be represented as follows:

Fig. 8 shows one cycle of the cogging torque according to the stator displacement design. At the initial 0[°], a cogging torque of 3.88[Nm] was generated. While displacing the stator, we observed that the cogging torque was reduced by 86.6[%] to 0.52[Nm] when the stator location was moved by 30 [deg.(e)].

Fig. 8.Cogging torque characteristics according to stator displacement

 

5. Stator Tooth Pairing and Displacement Combination Design

The combined design optimization was considering to reduce the cogging torque. Fig. 9 shows two-dimensional FEM model of DG-RFPMG which has designed both the stator tooth pairing and the stator displacement.

Fig. 9.Two-dimensional FEM model of DG-RFPMG(1/4 model)

Fig. 10 show the distribution curve of the maximum cogging torque for different angles when the stator tooth paring and the stator displacement design are applied simultaneously. And Table 3 shows analysis results of cogging torque. The analysis results shows that the minimum cogging torque was 0.26[Nm], which was observed at the stator tooth pairing of 6.5-11.5[deg.(m)] and stator displacement of 30[deg.(e)].

Fig. 10.Distribution curve of the maximum cogging torque

Table 3.Cogging torque unit : [Nm]

 

6. Conclusion

In this paper, we proposed the design of electromagnetic structure of DG-RFPMG and cogging torque reduction. To reduce the cogging torque, a stator tooth pairing and stator displacement design was applied. We found the optimal design condition about stator tooth pairing angle combination and stator displacement angle for cogging torque minimization. As a result, a cogging was reduced by 93.3[%] by this study.