A Novel Wound Rotor Type for Brushless Doubly Fed Induction Generator

Abstract

The rotor configuration of the brushless doubly fed induction generator (BDFIG) plays an important role in its performance. In order to make the magnetomotive force (MMF) space vector in one set rotor windings to couple both magnetic fields with different pole-pair and have low resistance and inductance, this paper presents a novel wound rotor type for BDFIG with low space harmonic contents. In accordance with the principles of slot MMF harmonics and unequal element coils, this novel rotor winding is designed to be composed of three-layer unequal-pitch unequal-turn coils. The optimal design process and rules are given in detail with an example. The performance of a 700kW 2/4 pole-pair prototype with the proposed wound rotor is analyzed by the finite element simulation and experimental test, which are also carried out to verify the effectiveness of the proposed wound rotor configuration.

1. Introduction

Brushless doubly-fed induction generator (BDFIG), regarding to be an alternative of doubly-fed induction generator (DFIG), has gained broad appeal to be ideal future generators in wind turbines. The advantages of the BDFIG-based wind turbines includes eliminating brush and slip rings, lower operation and maintenance fees, taking fractional rated capacity of converters and superior crowbarless fault ride-through (FRT) capability [1-3]. Owing to these clear superiorities, the commercial potential of BDFIG is enormous.

In order to couple both of the two magnetic fields between two stator windings in BDFIG, some configurations of specific rotor winding types have been proposed in the literatures. A cage-type rotor of the BDFIG, which is known as the “nested-loop”, was originally proposed and investigated by Broadway and Burbridge [4]. To reduce the rotor spatial harmonics, a novel cage rotor configuration comprising loops connected in series was presented in [5], and it was shown that the rotor harmonics have a direct impact on the referred rotor leakage reactance and the effective performance of the machine. Compare with the conventional wound rotor windings, large cage-type rotor winding designs are deemed to create higher space harmonic contents. A comparison analysis of nested-loop rotor windings and series-loop wound rotor winding was presented in [6]. Focus on the electrical and manufacturing, it shows the latter may be preferable to large machines, but they did not propose methods to reduce harmonic content which cannot be ignored for BDFIG.

The purpose of this paper is to present the general method to design a wound rotor winding for BDFIG. Moreover, the rules to reduce the harmonic content are also given. In this paper, a double-layer unequal element coils wound rotor structure of the BDFIG is presented to reduce the harmonic contents and improve the winding factors. A detailed analysis and design principles of the proposed rotor winding is given in section 2. Thereafter, an analytical model is given to calculate the proposed unequal element coil in section 3. Optimization and selection of winding elements is implemented base on this model. On the basis of previous analysis, both simulations and experimental results are presented to illustrate the performance of a prototype with the proposed rotor winding type in section 4. Experimental testes were implemented on a D560 frame-size 700kW 2/4 pole-pair wound rotor BDFIG.

 

2. Winding Design

The stator of BDFIG has two independent windings. In general, stator winding 1 acts as an electrical terminal for directly generating power and is therefore named as the power winding (PW). For another, stator winding 2, named as the control winding (CW), acts as an electrical terminal to connect with a variable voltage variable frequency converter which owns only a partial rated power capacity. These two stator windings can be distinguish from each other in pole pairs for generating two funda-mental magnetic fields. The number p1 and p2 represent the pole-pair of PW and CW respectively. A BDFIG-based wind turbine system is shown in Fig. 1.

Fig. 1.Wind turbine system based on BDFIG

The rotor of the BDFIG is required to be designed to couple both of the two magnetic fields, p1 and p2, which were generated by the two windings in the stator. However, the other order of harmonic contents in rotor winding (RW) should be as little as possible. Due to any order of harmonic except for p1 and p2 will not induce voltage in the stator, from the BDFIG standpoint, it manifests as harmonic reactance.

Approximately, the relation of the air gap peak flux densities for two fundamental, Bδ1 and Bδ2, is given by [4]

where kNr1 and kNr2 are the winding factors for two fundamental in RW. This is a critical operation rule of BDFIG and it indicates that the winding factors of two fundamental, p1 and p2, have a inherent relation with the relevant two air gap flux densities, therefore, the design goal of the RW is to achieve high winding factors for two fundamentals and low winding factors for other harmonics.

With the above conclusion in mind, we should set constraints for the design optimizations of the RW firstly. They are: (1) the winding factors of p1 and p2 pole-pair both should be above 0.7; (2) the resultant MMF percent of the highest harmonic content should be kept less than 3%. These constraints are obtained considering the performance of the initial design models and the previous prototypes.

2.1 Theory of slot MMF harmonics

In practical induction machines, the coils of the windings are always placed in slots along with the air gap. Unless the winding distribution is sinusoidal, under the action of currents, the polyphase windings will create a fundamental MMF with a wide range of harmonics. The harmonic contents with ν=kZ/p±1=2kmq±1 (k=1, 2, 3,...) orders are the slot MMF harmonics, and Z is the number of slots, m is the number of the phases, p and q is the number of pole-pair and slots per pole per phase respectively. All slot MMF harmonics have the same distribution factor with the fundamental, so they may not be destroyed [7].

In the following analysis, it must to clarify that only space harmonics on account of distributed winding are included, while permeance harmonics on account of slotting effects will be intentionally ignored. In practice, the geometrical profile of the air gap, rather than the size and arrangement of the coils, determines the permeance harmonics. Based on the same consideration, harmonics due to magnetic field saturation effect are also ignored.

For the v-th order slot MMF harmonic,

where f is the 3-phase MMF generated by the A-, B- and C-phase currents, θ is the angular displacement, ω is the angular speed and t is the time.

When ν=1, the resultant MMF of the fundamental is,

When ν=2mq-1, the resultant MMF of ν-th harmonic is,

Comparing (3) and (4), it is shown that the rotating direction of ν=2mq-1-th slot MMF harmonic is reverse with that of the fundamental. As shown in Fig. 2, voltage phasor diagrams for three-phase symmetrical winding with Z=6, p1=2 and p2=4 are given. The first order slot MMF harmonic for p1 pole-pair is v = 2, which is also the fundamental component for p2 pole-pair. Meanwhile, the first order slot MMF harmonic for p2 pole-pair is ν=0.5, which is also the fundamental component for p1 pole-pair.

Fig. 2.Voltage phasor diagrams for (a) Zr=6, p1=2 and (b) Zr=6, p2=4

Summarize the analysis above: (1) The MMFs of p1 pole-pair and p2 pole-pair appear simultaneously; (2) the MMFs rotating directions of p1 pole-pair and p2 pole-pair are reverse; (3) The winding factors of p1 pole-pair and p2 pole-pair are the same.

In consideration of the basic operation rule of the BDFIG, the RW should have the ability to generate two opposite rotating MMFs which also differ in pole-pair. By using the principle of slot MMF harmonic, the design of the RW can satisfy the rotor structure requirement of the BDFIG and the number of the rotor slots should be choose as,

2.2 Method of slot-number phasor diagram

The phase distribution of the induced electromotive force (EMF) for each coil sides is illustrated with a voltage phasor diagram in Fig. 2, which is presented in electrical degrees and is an effective tool to analysis winding [8]. However, it is cumbersome to draw the voltage phasor diagram with a large number of slots. In this paper, a new analysis method, slot-number phasor diagram, is adapted to explain the design process of the RW in BDFIG. The slotnumber phasor diagram develops as an imaginary process of “cutting” and “unrolling” the rotary voltage phasor diagram to a linear counterpart.

The three-phase coils for the RW with Z=6, p1=2 and p2=4, which mentioned above, can be found from the slot-number phasor diagrams as Fig. 3 shown. The slot numbers demonstrate the space vectors of the EMFs or MMFs produced by the coils (or the upper layer coils) inserted in the slots, the sign “–” in front of the slot numbers demonstrate the reverse polarity coils (or the upper layer coils) in 360 electric degrees.

Fig. 3.Slot-number phasor diagrams for (a) Zr=6, p1=2 and ) Zr=6, p2=4

2.3 Slot division and discard

According to (5), when p1=2 and p2=4, the number of the rotor slots Zr should be chosen as 6 (named as Case 1), however, an amount of MMFs harmonic contents except for that of p1 pole-pair and p2 pole-pair still exists. Since less rotor slots leads to a relatively high referred rotor harmonic leakage inductance, consequently, next step should be taken to effectively expand the number of slots. In order to maintain the MMFs of p1 pole-pair and p2 polepair appear simultaneously, an integral multiple of Zr could be adopted and expressed as following,

where k is a positive integer. The number of the rotor phase mr should be deliberately designed to (p1+p2)/mk, where mr and mk also should be positive integers. The slot-number phasor diagram of Zr=84 and p1=2 is plotted as shown in Fig. 4, make a comparison with Fig. 3, the number of the rotor phase is 6, the slot number in each phase seems to be divided to 14 (named as Case 2).

Fig. 4.Slot-number phasor diagram for describing slot division (Zr=84, p1=2)

After slot division, we should discard some usefulness coils in the next step. Taking phase A1 for example, firstly, we should discard some coils which exceed 180 electrical degrees in the slot-number phasor diagram. As shown in Fig. 5, slot 12, 13 and 14 exceed the boundary of the 180 electrical degrees in the slot-number phasor diagram with p2 pole-pair (The winding arrangement after this step was named as Case 3). Secondly, in order to improve the winding factor of the two fundamentals, slot-number 9 and 10 can be discarded. At this moment, the slot-number of phase A1 is constituted of 1, 2, 3, 4, 5, 6, 7, 8 and 9 (named as Case 4).

Fig. 5.Slot-number phasor diagram for describing slot discard (Zr=84, p2=4)

The proportional relation of the fundamental resultant MMF and ν-th harmonic resultant MMF that created by mr-phase symmetrical currents can be expressed as [7],

where pv and kNv is the pole-pair and winding factor for ν-th harmonic, respectively. To analyze the above cases, the winding factors and the resultant MMFs calculated from (7) are shown in Table 1, where signs “+” and “–” represent the opposite rotation of the resultant MMFs in forward direction and reverse direction. Make a comparison with Case 1 to Case 4, the effect of the above design processes is obvious. Case 4 can basically satisfy the design requirements of RW as shown in Table 1, but at the same time some harmonic contents are still high and will affect the performance.

Table 1.Winding harmonic analysis of Case 1~Case 4

 

3. Optimal Design by Unequal Element Coils

In this section, to guarantee the better performance of the machine, the winding arrangement was optimal design by unequal-pitch unequal-turn coils, which is also called unequal element coils as Fig. 5 shown. The goal of the optimization is to make the space harmonic content as less as possible and the MMF space vector of a phase winding along with the air gap close to sinusoidal distribution by choosing and regulating the coil turns and coil pitches reasonably. An analytical model is given hereinafter to calculate and choose the unequal element coils.

For a general winding with unequal element coils, the number of coils with N1 turns is c1, the number of coils with N2 turns is c2, the vector sum of all the coil electrical potentials for phase A1 can be expressed as,

where y1 and y2 is the short pitch of the two element coils, respectively; c1 and c2 is the number of upper conductors for the two element coils, c is the pitch between them, respectively; v is the harmonic order; α is the slot pitch, which is 2π/84 in this example. The complex numbers are used to represent the phase differences. The winding factor of the v-th harmonic of the unequal element coils can be express as,

Using the introduced winding factor, the harmonic spectra of the MMF of unequal element coils can be investigated.

The pole pitches of p1 pole-pair and p2 pole-pair are,

To enlarge the winding factors of p1 pole-pair and p2 pole-pair and lessen the winding factors of the other harmonic, y1 and y2 should be set in the range of τ1 and τ>2, pitch y1 was set to 12. Meanwhile, the size of the slot should be considered, the layer of the RW has better to be limited to three-layer, therefore pitch y2 was set to be 10.

The coil turns of the two element coils, N1 and N2, are needed to be calculated and regulated by using the design program according to (8) and (9). In this paper, the turns of the two element coils were set to be 4 and 3. The winding arrangement of phase A1 was describe in Fig. 5 (named as Case 5). In the slot-number phasor diagram, when the upper and lower conductors were both represented, the MMF produced by the unequal element coils was a good match for quasi-sinusolidal distribution as Fig. 6 shown. The comparison of winding factors and the resultant MMFs before and after optimization was shown in Table 2, Case 5 satisfies the design requirements and had been chosen to implement in the prototype.

Fig. 6.Winding arrangement for unequal element coils of phase A1

Table 2.Winding harmonic analysis of Case 4 and Case 5

 

4. Results and Discussion

The winding configuration proposed and analyzed hereinbefore is applied to design of a 700kW 2/4 pole-pair wound rotor BDFIG. The cross-section of the rotor type is shown in Fig. 7, which will be used to demonstrate the performance with a finite element (FE) method.

Fig. 7.Slot-number phasor diagram for unequal element coils of phase A1 (Zr=84, p2=4)

To calculate and analyze the air gap flux density in the proposed RW structure, a magneto-static FE simulation is built firstly to present a no-load operating condition. Only the three-phase RW are energized with the currents:

The obtained air gap density with the corresponding harmonics spectrum is provided in Fig. 8. There is a good agreement between the space harmonic spectra from magneto-static FE simulation and that from the predictions in Table 2.

Fig. 8.BDFIG cross-section with proposed rotor winding. Different colors are used to distinguish rotor three-phase

A 2-D time-harmonic field application analysis is carried out later to model the BDFIG and study the air gap magnetic fields. The design parameters and main dimensions of the prototype are listed in Table 3. The flux lines of the generator are shown in Fig. 9. In line with (1), the flux density of 4 pole-pair is nearly twice as large as that of 2 pole-pair. It is predicted that the magnetic fields of 4 and 2 pole-pair are induced in the RW simultaneously to ensure that the magnetic fields generated by two stator windings are indirect coupling.

Fig. 9.Diagrams obtained from magneto-static FE simulation (a) Air-gap flux density (b) relevant space harmonic spectra

Table 3.Main machine dimensions

Fig. 10.Flux distributions in time-harmonic FE simulation of the prototype BDFIG

It is worth comprising the electromagnetic performance of each winding configurations. Fig. 11 compare the values of the predicted flux linkage for the winding configurations, it is clear that Case 5 has the maximum flux linkage, this means that the rotor winding of Case 5 obtain more cross coupling than other cases. The torque curves for the four winding configurations are presented in Fig. 12. It can be seen that Case 5 has the highest value of output torque and the lowest value of ripple torque.

Fig. 11.Diagrams obtained from time-harmonic FE simulation: (a) Air gap flux density; (b) relevant space harmonic spectra

Fig. 12.Comparison of the rotor winding flux linkage for each winding configurations

The experiments have been implemented on a 700kW prototype BDFIG as Fig. 14 shown. The CW is supplied with a three-phase converter, while the PW is in open circuit situation and measured by a voltmeter. The PW induced voltage was kept at 450Vrms/60Hz, the CW excited voltage was regulated with the rotor speed and PW voltage. The FE calculated and experimental measured CW voltage versus rotating speed for the prototype BDFIG is presented in Fig. 13. It is evident that, intermediate the stator two windings, the optimized winding arrangement (Case 5) owns a more sufficient ability for creating cross coupling.

Fig. 13.Comparison of torque curves for each winding configurations (Tavg is the average torque and Trip is the peak to peak value of the torque ripple divided by Tavg)

Fig. 14.CW excited voltage against rotor speed (the induced voltage of the open circuited PW is 450Vrms, 60Hz)

Fig. 15.Pictures of the proposed wound rotor BDFIG

Before the proposed wound rotor type BDFIG construction, the most widely used type is the nested-loop cage rotor BDFIG which makes a great contribution to BDFIG analysis [2-6]. The nested-loop cage rotor contains multiple loops and can be regarded as a concentrated winding, thus, it is difficult to obtain high winding factors for both two pole pairs. Under the conditions of the consistent rotor slot area, the consistent number of rotor conductors and excited by the same value current, compare with the nested-loop cage rotor, the proposed wound rotor BDFIG will obtain higher copper usage efficiency due to the higher winding factors of the two pole pairs.

Another issue is the copper loss. Compared with the same size BDFIG with nested-loop cage rotor, the higher value of the referred rotor resistance for wound rotor may leads to higher rotor copper losses [7]. Nonetheless, large reduction of the rotor harmonics and the referred rotor leakage inductance are more effective in improving performance of the generator and counteracts the negative influence of the increased rotor copper loss.

From the viewpoint of manufacture and generator performance, the specially fabricated nested-loop cage rotor is made of copper alloys and brass, which needs more manufacturing complexity and higher cost, and this special welded construction also needs safety evaluation for wind turbines. In addition, the bars of the nested-loop cage rotor must be insulated which is hard to cast. However, the manufacturing process required for the proposed wound rotor type BDFIG is as straightforward as the traditional wound rotor DFIG design. It dose not change much, except for needing two types of coils with different number of turns. Therefore, upgrading the production line from DFIG to wound rotor type BDFIG is very convenient for wind turbines manufacturers.

 

5. Conclusion

The space harmonics of air gap flux density has a strong impact on the performance of a BDFIG. Based on slot MMF harmonic principle and unequal element coils, a low space harmonic content wound rotor type BDFIG is described for the first time in this paper. The proposed wound rotor with unequal element coils shows a good performance and the manufacturing process required for the proposed wound rotor BDFIG construction is similar with the traditional wound rotor DFIG design. Hence, this research has significant meaning in advancing the commercial use of BDFIG in wind turbines.