A novel doubly-fed doubly-salient machine with DC-saturation-relieving structure for wind power generation

This paper presents a novel doubly-fed doubly-salient machine (DF-DSM) with DC-saturation-relieving effect for wind power generation application, which possesses the advantages of enhanced torque density, reduced torque ripple and improved power density. The key is that PMs are introduced into the stator slot openings to mitigate the saturation effect in stator core caused by DC ﬁeld excitation, and relatively large excitation current can be fed into stator ﬁeld windings, which contributes to improved power density of machine. In addition, with the armature winding artiﬁcially connected, the reluctance of all magnetic paths is kept the same, and the variation of self-inductance is compen-sated, and the torque ripple is greatly suppressed. In this paper, the machine structure and DC-saturation-relieving working principle are introduced. The slot-pole combinations are analysed, and dimension parameters are optimized. By using time-stepping ﬁnite-element analysis, the electromagnetic performance of optimal machine is evaluated which veriﬁes the validity of the proposed design.


Controller
optimized. In Section 4, the electromagnetic performance of the proposed machine is investigated by finite-element analysis (FEA). In Section 5, the conclusions are drawn from the investigation.

System configuration and machine structure
The configuration of the wind power system is denoted in Figure 1. It is mainly composed of wind blade for wind power capture, fixed gear to step up the wind speed for high-speed operation, and a three-phase DF-DSM for the electromechanical energy conversion. The AC armature winding of the machine is connected to AC-AC converter and then transformer 1, providing electricity for power grid, while the DC field winding is connected to an AC-DC converter and is supplied with the electricity coming from power grid. Voltage signals, current signals, as well as speed signals are transferred to the controller, and then the controller gives the switching signal to the AC-AC converter and AC-DC converter. Therefore, with changeable DC field excitation variable speed constant voltage wind power generation can be realized. Figure 2 shows the structure of proposed DF-DSM with DCsaturation-relieving structure. The machine is composed of a 24-slot stator and a 28-pole rotor, with a doubly salient structure. Since the rotor consists of only iron core, the machine is provided with good mechanical robustness. The stator has all excitation sources, namely, slot PMs, DC field winding, and AC armature winding is also located in stator side. While the DC field winding uses a single-layer concentrated connection, the AC armature winding adopts a double-layer concentrated connection as showed in Figure 3. In the machine, slot PMs are artificially introduced to mitigate DC saturation of the stator core caused by DC field excitation. All slot PMs are magnetized in tangential direction.
The merits of proposed DF-DSM with DC-saturationrelieving structure are listed as following. 1. The rotor is composed of only iron core, which provides a good mechanical robustness. 2. Tangentially magnetized PMs are inset into the slot opening, which can greatly reduce the DC saturation of the stator core caused by DC field excitation so as to improve the torque density of machine. 3. With the DC-field saturation relieving design, increased DC field excitation current can be flexibly controlled, which offers enhanced power production over a wide wind speed range and increases wind energy conversion. 4. With special selection of stator pole number, the rotor pole number, the DC field excitation pole number, as well as the phase number, the doubly salient machine can realize three phase symmetry of the flux linkage and back EMF, insignificant variation of the self-inductance, as well as reduced torque ripple.  When only slot PMs are used as shown in Figure 4(b), the flux linkage direction excited by slot PMs is opposite to that excited by DC current. Figure 5 presents the no-load flux distribution with both dc current and PM excitations when rotor position varies in DF-DSM with DC-saturation-relieving structure. As shown in Figure 5(a), when the rotor salient pole is aligned with stator tooth, the DC field excitation loop reluctance is minimized. In this way, the DC field coil flux attains the maximum value. On the contrary, as denotes in Figure 5(b), when the rotor salient pole is unaligned with stator tooth, the DC field excitation loop reluctance is maximized. In this way, the DC field coil flux reaches the minimum value. DC field coil flux is biased and has large DC component, which makes stator core easily saturated. However, tangentially magnetized PMs are mounted on the slot opening, which can efficiently mitigate the DC saturation of the stator core caused by DC field excitation. Due to the minimum reluctance principle, slots PMs flux links the stator core all the time, which would not be affected by the rotor position. It can be seen in Figure 5, since the constant slot PM flux direction is opposite to the DC field flux direction, the stator DC saturation can be reduced to enhance back-EMF and steady torque. Figure 6 gives the no-load flux variation with different rotor position. When the rotor salient pole is aligned with stator tooth, it is called aligned position. When the rotor salient pole is unaligned with stator tooth, it is called unaligned position. The d axis is corresponding to aligned position, and q axis is corresponding to medium position, between aligned position and unaligned position. As shown in Figure 6(a), with only DC field In this case, the stator core is saturated, DC field flux maximum value max1 is limited by stator core saturation. As shown in Figure 6(b), with introducing of slot PMs, the dc component excited by dc field current is reduced to dc2 . Since DC saturation of stator core are significantly relieved, DC field flux maximum value max2 is no longer limited by stator core saturation. In this case, the AC component ac2 is definitely larger than AC component ac1 , which leads to larger back-EMF and torque.

Slot-pole combination
In this paper, an analytical and FEA combined method is applied to find out the optimal slot-pole combination. For conventional DSMs, the relationship between the number of stator poles N s , the number of rotor poles N r , the number of DC field excitation poles N dc , as well as the number of phases m are not purposely selected. Therefore, the conventional DSMs exist several shortcomings as following: 1. Because of different relative positions of phase windings to the DC field coils, magnetic circuits of all phases are asymmetrical. The flux passing through the coil on the middle tooth is less than flux passing through the coil wound on the tooth near DC field winding slots. Therefore, the back EMF waveform of each phase is not identical. 2. When salient pole of rotor is aligned with the stator tooth, the flux linkage of each AC armature coil reaches the maximum value. In contrast, when salient pole of rotor is unaligned with the stator tooth, the flux linkage of each AC armature coil attains the minimum value. The variation of flux linkages near two position are different because of the stator iron saturation. Therefore, the left and right sides of the EMF waveform are asymmetric and current will be deformed. 3. For the existing DSMs, the self-inductance of each AC armature coil varies simultaneously with rotor movement and each AC armature coil has the same pattern of variation of self-inductance. Because of the series connection of AC armature coils per phase, the resulting variation of self-induction per phase is actually an integer multiple of the variation of each AC armature coil. Therefore, the variation of self-inductance per phase is large, which would lead to large torque ripple.
In order to solve above mentioned problems, two criteria are proposed. First, every phase composes of coils distributed in all locations relative to each DC field excitation pole. Therefore, the number of phase coils under a DC field excitation pole should be different from the number of phases. The first criterion can be donated as: where k and k 1 are positive integers and k < m. Second, the stator slot pitch should be equal to the angular difference of two adjacent phases, which can be expressed according to number of rotor poles and the number of stator poles. The second criterion can be expressed as: where, k 2 is positive integer and is slot pitch. For example, when m = 3 and N dc = 6 is given, N r = 20∕28 and N s = 24 can be deduced from Equations (1) and (2). Therefore, FEA models with 24/20 and 24/28 slot-pole combinations are compared. Fundamental data of proposed machine is given in Table 1. Dimension parameters are depicted in Figure 7 and initial values of dimension parameters are shown in Table 2.
Considering the slot-pole combination is counted as the most leading design parameter, a simplified comparison is adopted in this process, which greatly saves optimization time. All the models share the same design parameters apart from the rotor pole number as well rotor tooth width. Besides, DC field excitation is the main source for torque generation. Hence, only DC field excitation without slot PMs is regard as the criterion for comparison. In this case, slot PMs is removed.
With FEA analysis, the steady torque with 24/20 and 24/28 slot-pole combinations are shown in Figure 8. It can be seen that, comparing with 24/20 case with 16.46 Nm rated torque,

Machine parameter optimization
Once the slot-pole combination is determined, other dimension parameters should be further optimized to boost machine  electromagnetic performance. However, it is difficult to optimized machine dimension parameters by traditional analytical method owning to the complexity of magnetic field distribution. An intelligent algorithm, namely, genetic algorithm (GA) is used and communicates with Maxwell to achieve combined optimization [17]. GA is a biologically inspired searching and optimizing algorithm, which can generate high quality results relying on the computer technology. GA has three significant operators, namely, selection, crossover as well as mutation, the same as the process of nature selection. The flowchart of the GA and maxwell coupled optimization is presented in Figure 9 and the GA parameters are shown in Table 3. In this paper, the maximum torque density and minimum torque ripple are taken as two optimization objectives. The initial population are produced randomly, and then they are evaluated by fitness function (muti-objective function). Relatively high-quality ones have more opportunities to be selected, and then go through crossover and mutation. Therefore, a new generation is born. All cases in the new generation should analysed by FEA. Several stop criteria determine whether the loop stop or not. If it is satisfied, we get final population and optimal results.
The optimal results of each case in the last generation are shown in Figure 10. It can be noticed that some cases have relatively lower average torque and lower torque ripple, while some cases have relatively higher average torque and higher torque ripple. However, it exists some cases have relatively higher aver-  age torque and lower torque ripple, which are needed results. The optimization ranges of the machine dimension parameters, their initial values, as well as final optimal values are listed in Table 4. The torque comparison between initial and optimal cases is shown in Figure 11. It can be concluded that the average torque of the DF-DSM can be improved by 24.6% and torque ripple can be reduced by 55.9% with FEA and GA combined optimization.

ELECTROMAGNETIC ANALYSIS OF THE MACHINE
Based on the above optimized results, the 24/28 slot-pole combination optimized DF-DSM is shown in Figure 2, and its electromagnetic performance is further analysed with FEA in this section.

4.1
No-load performance Figure 12 shows no-load flux distribution under different excitation sources. It can be noticed that both DC field excitation and slot opening PMs can generate magnetic field. The flux distribution generated by DC field excitation passes through the stator, air gap, and rotor which is showed in Figure 12(a). In the meanwhile, the flux distribution generated by slot PMs does not pass through the rotor or air gap, and only focuses on the stator, which is denoted in Figure 12(b). Figure 12(c) presents the flux distribution with both DC field excitation and slot PMs. Slot PMs can greatly mitigate the stator core saturation caused by DC field excitation. Figure 13 shows no-load flux linkage of each coil of phase A. It can be seen that the flux linkage of each coil of phase A has almost zero phase shifts no matter with or without slot PMs.
Comparing Figure 13(a) with Figure 13(b), the flux linkage of A3 A4, A7, A8 remains unchanged, while the flux linkage of A1, A2, A5, A6 becomes smaller. From Figure 2, we know that coil A1, A2, A5, A6 are near slot PMs, while coil A3, A4, A7, A8 are relatively far from slot PMs. It can be concluded that the slot PMs have great DC-saturation-relieving effect on the coils near them, while have little effect on the coils far away from them.
Moreover, it can be seen that the left and right side of the flux linkage of each coil of phase A is asymmetric, while the flux linkage of each coil of phase A is not identical due to the different displacements of coil of phase A to the DC excitation coils, no matter with or without slot PMs.
Excited by both dc current and slot PMs, the self-inductance of coil A1 and A2 at rated positive and negative current are shown in Figure 14. It can be observed that their variations are reversed. Similar variations can be found in the coil A3 and A4, A5 and A6, A7 and A8. Therefore, when connecting the coils in series, the resulting variation of self-inductance can be significantly diminished.
Excited by both DC current and slot PMs, the self-inductance of phase A and corresponding mutual inductance between phases A and B are plotted in Figure 15. It can be seen that the mutual inductance is much smaller than the self-inductance due to the nature of concentrated windings.
Comparing Figure 14 with Figure 15, the self-inductance average value of phase A is nearly as large as eight times of self-inductance average value of coil A1. However, the selfinductance peak-to-peak value of phase A is almost the same as the self-inductance peak-to-peak value of coil A1. It is confirmed that the proposed machine offers much smaller variation of self-inductance with special winding connection.
Moreover, the no-load flux linkage is presented in Figure 16. The DC excitation current is given 200 A. Three phase noload flux linkage with slot PMs is denoted in blue dashed lines. It is obvious that flux linkage realizes three phase symmetry. Compared the blue dashed lines with black solid line, with the introducing of slot PMs, the flux linkage maximum value of phase A increases from 0.0742 to 0.0925 Wb. Meanwhile, the flux linkage minimum value of phase A decreases from −0.0742 to −0.0925 Wb. The flux variation range changes from 0.1482 to 0.185 Wb. Comparing Figure 16 with Figure 13, with the special winding connection, the flux linkage of phase A becomes much more symmetric than that of each coil of phase A.
In addition, since the flux linkage is symmetric with almost liner rise-up and fall-off slops, the resulting back EMF is symmetric and exhibits a wide flat-top range as shown in Figure 17. The blue dashed lines present three phase back-EMF with slot PMs, which achieve three phase symmetry. Compared the blue dashed lines with black solid line, through adopting slot PMs, the black-EMF maximum value of phase A enhances from 105.93 to 133.42 V, and the black-EMF minimum value of phase A reduces from −113.7 to −138.88Nm. This agrees with the previous analysis that the slot PMs can relieve the saturation

FIGURE 19
No-load back-EMF under different speeds effect in the stator core, thus more current can be injected to boost the back-EMF under no-load condition. Figure 18 denotes the cogging torque under no-load condition, which shows that the cogging torque is almost unchanged, no matter with or without slot opening PMs. Figure 19 shows no-load back-EMF under different operation speeds. It can be found that through regulating the DC field current, the no-load back-EMF can remain the same, which illustrates the variable speed constant voltage wind power generation can be realized.

4.2
On-load performance Figure 20 presents Table 5, even though copper loss remains unchanged, while core loss and eddy current loss are higher with the introducing of slot PMs, the rated efficiency increases slightly. It is confirmed that the slot PMs can mitigate the saturation effect of stator core, hence greatly enhance the steady torque, power density, and improve the efficiency.

Comparative study
A comparison study between proposed DF-DSM and conventional DSM is conducted. The structures of these two machines are shown in Figure 22. The excitation sources of the proposed DF-DSM are DC field winding, AC armature winding, as well as slot PMs, while the excitation sources of the conventional DSM are radial yoke PM and AC armature winding. Their rotors all consist of only iron, which provide mechanical robustness. Two machines share the same design except for different excitation sources and their arrangement. As shown in Table 6, the outer radius of stator, stack length, airgap length, stator slot number, rotor pole number of these two machines are the same. However, the proposed DF-DSM has higher rated torque, power density, while has better flux regulation capability than the conventional DSM. Comparing to conventional doubly salient machines,

FIGURE 24
Average torque with respect to current density the proposed machine has slightly higher core loss and copper loss. However, the power density and efficiency of proposed machine is higher than the conventional doubly salient machine. Figure 23 gives the steady torque of these two machines under rated current density about 6 A/mm 2 , which presents excellent torque performance of the proposed DF-DSM. Figure 24 presents the average torque with respect with different current density. When the current density varies from 0 to 24 A/mm 2 , the average torque of proposed DF-DSM is always higher than conventional DSM, which illustrates better torque performance of proposed DF-DSM over conventional DSM.

CONCLUSION
In this paper, a novel doubly-fed doubly-salient machine (DF-DSM) with DC-saturation-relieving effect is proposed and verified by FEA. With controllable DC field excitation, the flux can be flexibly controlled, which can extend speed range and capture more wind power. Moreover, with tangentially magnetized PMs mounted on the slot opening, the saturation effect of the stator core can be largely suppressed, hence the steady torque can be enhanced by about 39.61%, power density can be also improved by 39.61%. Last by not least, the comparative study between proposed DF-DSM and conventional DSM is conducted, which illustrates the proposed DF-DSM has better flux regulation capability, and the better overload capability.
In addition, the power density of proposed DF-DSM is significantly higher than the conventional DSM. Although the proposed machine is designed for low power application, it is also suitable for high power application with main excitation source of DC field excitation.