Comparative Study of a Fault-Tolerant Multiphase Wound-Field Doubly Salient Machine for Electrical Actuators

Transcription

1 Energie 2015, 8, ; doi: /en Article OPEN ACCESS energie ISSN Comparative Study of a Fault-Tolerant Multiphae Wound-Field Doubly Salient Machine for Electrical Actuator Li-Wei Shi * and Bo Zhou Aero-Power Science Technology Center, Nanjing Univerity of Aeronautic and Atronautic, Nanjing , China; zb3713@gmail.com * Author to whom correpondence hould be addreed; liwei10@nuaa.edu.cn; Tel.: ; Fax: Academic Editor: Paul Stewart Received: 3 November 2014 / Accepted: 20 April 2015 / Publihed: 29 April 2015 Abtract: New multiphae Wound-Field Doubly Salient Machine (WFDSM) for electrical actuator with ymmetric phae are invetigated and compared in thi paper. With a comparative tudy of the pole number and pole arc coefficient, the alient pole topology of the three-phae, four-phae, five-phae, and ix-phae WFDSM with little cogging torque i preented. A new winding configuration that can provide ymmetrical phae for the multiphae WFDSM i propoed. Suitable fault-tolerant converter for the multiphae WFDSM are preented. With the imulated reult in term of the pole topology, flux linkage, back EMF and converter, it can be concluded that the pole number of the new five-phae WFDSM are very large. The high accuracy poition enor hould be required to make the five-phae WFDSM commutate frequently and accurately at a high peed. The four-phae and the ix-phae WFDSM can be divided into two iolated channel, and both of them have a good performance a a fault-tolerant machine. All of the invetigation are verified by finite element analyi reult. Keyword: wound-field doubly alient machine; electrical actuation; fault-tolerant; multiphae

2 Energie 2015, Introduction Today conventional aircraft are characterized by complex hydraulic net. In order to reduce the weight of the pipeline, cylinder, pump, valve and witche of the hydraulic ytem, the aircraft i adopting more and more electrical ytem in preference to other. Now, reearcher and engineer have proved that electrical actuator can be ued to reduce or to remove the traditional hydraulic, and mechanical ytem in the next few year [1]. The more electric aircraft approach i widely dicued in the technical literature, which include the following three main drive [2]: The tarter-generator for the engine; The electrical actuator for the flight control; The electric machine for the fuel pump. There are many different type of actuator in a conventional aircraft [3], uch a the actuator in the wing and in the tail. In the hydraulic actuation ytem, the flight control i realized by a hydraulic pump and a hydraulic motor, everal fluid pipeline and hydraulic actuator. Now, more and more electric machine are being ued to replace or ait the hydraulic actuation ytem. For example, in the Boeing 787, the poiler and the horizontal tabilizer flight control are driven by electric machine in order to guarantee the operation in the cae of a hydraulic failure. A literature review reveal that everal type of machine can be ued a a drive motor for electrical actuator [4]. Among them, PM machine and Switched Reluctance Machine (SRM) were abundantly tudied in the pat year, becaue of their very-high power denity. In [5], a five-phae PM bruhle machine wa developed for an aircraft flap actuator application, and the machine can endure the fault of one or two open phae or a phae hort circuit. In [6], a PM fractional lot machine wa deigned, becaue the fractional lot winding have low mutual inductance between phae, which meet the magnetic iolation demand of phae winding for multiphae fault-tolerant PM ynchronou machine [7]. Such fault-tolerant PM machine were alo tudied in [8,9]. It i neceary to remark that the actuator of an airplane have to work in very harh ambient condition, with temperature variation from 60 C to +70 C and the air preure varie from almot 0 to 1 bar [2]. Thi harh environment put forward higher requirement for high performance PM material. Furthermore, many of the electrical actuator care little about the torque ripple becaue the noie of the airplane i very high. Therefore, witched reluctance machine were invetigated to drive the actuator in [10,11]. The Wound-Field Doubly Salient Machine (WFDSM) ha the ame rotor a the SRM that will not uffer from fault of the PM material or bruh fault of the wound-field ynchronou motor. The WFDSM i derived from a doubly alient PM machine (DSPM) [12] by uing field winding intead of permanent magnet excitation [13]. The WFDSM provide the excitation flux by the DC field winding intead of the PM. Therefore, the output torque and peed can be adjuted by the field winding and phae winding. What more, the phae winding of the WFDSM are iolated from each other, and it ha low mutual inductance between phae, which reduce the negative influence of the faulty phae. It ha broad application propect in the field that care little about the torque ripple, uch a mining machinery, electrical actuator, and tarter-generator.

3 Energie 2015, For example, a WFDSM with two-ection twited-rotor wa developed a a tarter-generator for aeropace application [14]. Recently, ome new three-phae WFDSM with new winding arrangement have been developed to take the place of traditional electric machine [15,16]. In the energy converion area, a WFDSM worked a a DC generator wa equipped in an EV range extender [17]. A prototype of a 24/32-pole WFDSM wa developed a a low peed wind turbine generator [13]. Multiphae machine with more than three phae can be applied for high reliability application becaue they can till run even with one or two open-circuited phae [18]. To improve the reliability of the WFDSM, a traditional four-phae WFDSM wa tudied in [17], which wa imilar to the 8/6-pole DSPM decribed in [19]. A five-phae WFDSM wa developed a a generator in [20], which howed that it had good fault-tolerant characteritic. Therefore, the multiphae WFDSM i very uitable to be deigned a a fault-tolerant machine. However, the four-phae and the five-phae WFDSM dicued above are traditional WFDSM with their field winding wound around four and five tator pole, repectively. They have the diadvantage of phae aymmetry. The phae aymmetry of the three-phae WFDSM i not obviou, but we found that the phae aymmetry will increae with the number of phae. It wa conidered that the WFDSM cannot be deigned with ix phae, and there have been no report of ix-phae WFDSM until now. In thi paper, new multiphae WFDSM for electrical actuator with ymmetric phae will be invetigated and compared. With the comparative tudy of the pole number and pole arc coefficient, the alient pole topology of the WFDSM that have little cogging torque will be preented. A new winding configuration to provide ymmetrical phae will be propoed. Suitable fault-tolerant converter for the multiphae WFDSM will be preented. With the comparion in term of the pole topology, flux linkage, back EMF and converter, comparative concluion will be propoed to elect a multiphae WFDSM for electrical actuator. 2. Comparative Study of the Salient Pole Topology 2.1. Salient Pole Number There i a wide range of poible combination of the tator pole and the rotor pole. Neverthele, only few combination are uitable to be elected. To outline the pole combination, the principle of the alient pole number hould be tudied firt. A we can ee from the traditional three-phae WFDSM in Figure 1a, there are 6N tator pole and 4N rotor pole, where N i the number of element machine. Each phae coil i wound around one tator pole, and the field coil are wound around every three tator pole [17]. So the firt law of the tator pole can be written a: p = mi (1) where p hould be an even number, and it tand for the number of tator pole. m i the phae number and i i a poitive integer. If p i an odd number, the north field winding will not be equal to the outh field winding, and the machine will generate an unbalanced magnetic force. Let p r be the rotor pole number. The mechanical angle of one period β r can be obtained a:

4 Energie 2015, β r = 360 p r (2) (a) (b) (c) (d) Figure 1. Structure of the three-phae and multiphae DSG. (a) 12/8-pole three-phae of WFDSM; (b) 8/6-pole four-phae; (c) 20/16-pole five-phae; (d) 12/10-pole ix-phae. The mechanical angle of each tator pole β i: β = 360 p (3) Becaue the adjacent pole have the adjacent phae winding, the mechanical angle between two phae can be expreed a: and the difference between βr and β i ±βδ: β δ = β r β = m p (4) r ±β δ (5) From Equation (2) (5), we can get the econd law of the rotor and the tator pole: p m p m (6) r 1 When m = 3, the elementary machine of three-phae WFDSM ha ix tator pole and four or eight rotor pole, which i called 6/4-pole machine or 6/8-pole machine [14]. In the ame way, the elementary

5 Energie 2015, machine of a traditional four-phae WFDSM ha an 8/6-pole or 8/10-pole tructure. Table 1 give the pole combination of the WFDSM with different phae Pole Arc Coefficient Table 1. The pole combination of the WFDSM. Phae number Stator pole Rotor pole Example Three-phae 6N 4N or 8N 12/8 Four-phae 4N 3N or 5N 8/6 Five-phae 10N 8N or 12N 20/16 Six-phae 6N 5N or 7N 12/10 The WFDSM tator i equipped with both field coil and phae coil. The elf-inductance of the phae winding and the field winding change with the rotor poition and the pole arc [21,22]. If the pole arc i not well-deigned, the machine will generate torque ripple becaue the reluctance and the flux of the field winding will change with the rotor poition [23]. In order to minimize the cogging torque caued by the mutative reluctance of the field winding, the elf-inductance of the field winding hould be contant when the rotor rotate. Overall, the increaing phae number hould be equal to the decreaing phae number. For the common inner-rotor motor, the rotor pole number i uually le than the tator pole number. Hence the rotor pole i generally wider than the tator pole. A the narrow pole of the tator and the rotor determine the increaing or decreaing mechanical angle of the phae inductance, the increaing mechanical angle of the phae inductance can be decribed a: β working = p 360 α (7) where α i the tator pole arc coefficient, which i the proportion of the tator pole arc length l t and the pole pitch l p. α = Let the electrical angle of one phae voltage waveform be θ: α θ α p x l t l (8) p r p m (9) where x i the phae number that ha a mutative elf-inductance at any time, and x m. If x i large, there will be more phae that can output torque or voltage, and the fault-tolerant ability of the machine will be trong. Becaue the phae number with increaing inductance hould be equal to the phae number with decreaing inductance, it can be concluded that x hould be an even number. For the three-phae WFDSM, while p/pr = 3/2, θ = 120. We can draw from Equation (7) and Equation (8) that: p α 3p (10) r

6 Energie 2015, Therefore, to make the machine have no cogging torque, reluctance and flux of the field winding the pole arc coefficient of the three-phae WFDSM α i equal to 0.5. While p > pr, the rotor pole width i not generally thinner than the tator pole width. For the three-phae WFDSM, the mutual inductance of the field winding and the phae winding Lpf are hown in Figure 2. When αr = 0.5, the machine can be eaily controlled by a BLDC controller, becaue one period can be divided into ix equal part like a BLDC machine. When αr = 0.333, the machine can output a large torque becaue the rotor pole and the tator pole are monopaced and the leakage flux i mall. Overall, the tator and the rotor pole arc coefficient hould comply with α = 0.5 and αr = 0.5 or working (a) working (b) Figure 2. Lpf of the three-phae WFDSM with different αr. (a) αr = 0.333; (b) αr = 0.5. It can be concluded that the pole arc coefficient of three-phae WFDSM hould comply with Equation (11): p 3 : α = 0.5; α r= or 0.5 pr 2 p 3 (11) : α = 0.25; α r= or 0.5 pr 4 However, the four-phae WFDSM hould not be deigned with αr = 0.5. A we can ee from Figure 3, if αr = 0.5, there will be three changing inductance at any time, x = 3. With thi tructure, the reluctance of the field winding will change with the poition of the rotor, which will generate a big cogging torque, a well a field winding back EMF. In order to olve the problem of changeable field reluctance, a new four-phae WFDSM i propoed, whoe pole arc coefficient complie with Equation (15):

7 Energie 2015, p p r p p r 3 : α = 0.667; α r= : α = 0.4 ; α r= (12) Armature winding A Stator pole Rotor pole A A Lpf working Laf Lbf Lcf Ldf (a) Armature winding Stator pole Rotor pole A A A Lpf working Laf Lbf Lcf Ldf (b) Figure 3. Lpf of the four-phae WFDSM with different αr. (a) α = 0.5, αr = 0.375; (b) α = 0.667, αr = 0.5. For thi new machine, there are two increaing phae inductance and two decreaing phae inductance at any time, a hown in Figure 3b. The field inductance i teady, and it will not generate cogging torque. The phae voltage waveform electrical angle of thi machine i 180, and the phae number with mutative inductance at any time x = 4. Therefore, all of the four-phae winding can output torque at any time, which improve the fault tolerance of the machine. Similarly, we can alo deduce the pole arc coefficient of the other multiphae WFDSM, ince the phae voltage waveform electrical angle of the five-phae WFDSM i 144, and the angle of the ix-phae WFDSM i 120. In hort, it can be newly concluded that the pole arc coefficient of the multi-phae WFDSM hould comply with Equation (13). In hort, to reduce the torque ripple caued by the field winding of multi-phae WFDSM, the tator pole, rotor pole and pole arc hould follow topology criteria a hown in Equation (1), (6) and (13). The three piece of topology criteria not only give a deign bai for the WFDSM with le than ix phae, they can alo be ued to deign PM doubly alient machine and hybrid excitation doubly alient machine. What i more, thee topology criteria alo provide a derivation example for the WFDSM with more than even phae.

8 Energie 2015, p 3,, ; three phae α = 0.5 α r= or 0.5 pr 2 p 3,, ; three phae α = 0.25 α r= or 0.5 pr 4 p 4,, ; four phae α = α r= 0.5 pr 3 p 4,, ; four phae α = 0.4 α r= 0.5 pr 5 p 5,, = 0.5 ; α r = 0.4 five phae α pr 4 p 5 five phae,, α = 0.333; α r= 0.4 pr 6 p 6 ix phae,, α = 0.4 ; α r= pr 5 p 6 ix phae,, α = 0.571; α r= pr 7 (13) Becaue the pole number and the witche of the converter increae with the phae number, the WFDSM with more than ix phae i not uitable to be applied becaue of the weight and the cot of the converter i unacceptable, a well a the pole number. Therefore, their application propect are not a broad a thoe of WFDSM with le than ix phae, becaue they are too complicated. Thi paper focue on the WFDSM with le than even phae Simulation Reult Figure 4 how Lpf and back EMF waveform of the traditional multiphae WFDSM, which are 12/8-pole three-phae, 8/6-pole four-phae 10/8-pole five-phae and 12/10-pole ix-phae with the ame tator pole arc coefficient α = 0.5, and the rotor pole are a wide a the tator pole. The imulated reult in Figure 4a how that Lpf of the three-phae and four-phae WFDSM are conitent with the analyi reult in Figure 2 and 3. The back EMF waveform in Figure 4b how that the electrical angle of the phae voltage waveform of the four machine are approximately 120, 135, 144 and 150. Thi verifie the calculation reult in Equation (8). With the total torque formula given in Equation (14), we can ee that there i a torque component 1 2 dlf i f which ha nothing to do with the phae current ip. It can be called a cogging torque. 2 dθ 1 dl 2 p dlpf 1 2 dlf T ip ipif if (14) 2 dθ dθ 2 dθ where ip and if are the phae current and field current. In order to reduce the negative impact of the armature reaction, the number of turn of the field winding i much larger than the number of phae winding.

9 Energie 2015, Back EMF(V) Inductancef(mH) Figure 4. Lpf and up of multi-phae WFDSM. (a) Lpf; (b) The back EMF. The elf-inductance of the field winding L f i much larger than the mutual inductance between the phae winding and field winding L pf. Therefore, if L f change with the rotor poition, and machine will generate a large cogging torque. For the four-phae WFDSM with α = 0.5, θ = 135, and x = 3, there are three inductance changing at any time. Thi ituation doe not conform to Equation (13). With the elf-inductance of the field winding Lf waveform in Figure 5a, we can ee that Lf will change with the rotor poition, which will produce cogging torque ripple. If α = and x = 4, the elf-inductance of the field winding Lf will be a contant, a hown in Figure 5b. Therefore, if x i an odd number, the machine will not generate cogging torque. Figure 5. Lf of the four-phae WFDSM. (a) α = 0.5; (b) α =

10 Energie 2015, Comparative Study of the Symmetrical Phae Winding Configuration 3.1. The Symmetrical Phae Winding Configuration A hown in Figure 1a, there are four field coil that are ued to provide the magnetic field. Each field coil i wound around three tator pole. In Figure 1b, there are four tator pole in a field coil, which provide the magnetic field. Therefore, each excitation ource of traditional m-phae doubly alient machine couple with m-phae coil. A the red line how in Figure 1b, the magnetic circuit of phae A and D which are cloe to the excitation ource i much horter than phae B and C, and the inductance of phae A and D are larger than that of phae B and C. Overall the amplitude of the inductance of the traditional four-phae WFDSM have the relationhip given by Equation (15): max( ) max( ) max( ) max( ) Laf Ldf Lbf L cf (15) If the phae coil with hort flux road are divided averagely, the total inductance added by the erie coil will be equal [12]. Let j tand for the number of phae coil that coupled by a field coil. The tator pole can be calculated with: p mk jp (16) where k and P are two natural number. Therefore, P i the leat common multiple of m and j at leat. Together with Equation (6), we can lit the pole number of the four-phae WFDSM with different j in Table 2. Table 2. The pole number of the four-phae WFDSM with different j. j Pole of an element machine Four-phae Five-phae Six-phae j = 1 8/6 10/8 12/10 j = 2 8/6 10/8 12/10 j = 3 12/9 30/24 12/10 j = 4 8/6 40/32 24/20 j = 5 10/8 30/25 j = 6 12/10 When j = m, the machine i a traditional WFDSM with aymmetric phae. If j = 4 in the five-phae WFDSM and ix-phae WFDSM, the number of tator pole will be very large ince it increae with the leat common multiple of j and m. And if j = 2, the field winding coil will increae, which in turn increae the copper conumption of the field winding. A three-phae 6/4-pole variable flux reluctance doubly alient machine wa reported in [16], which verified that the WFDSM can operate well when j = 1. With the ame configuration in [16], every tator pole of the multiphae WFDSM i wound with a field winding. In the traditional 8/6-pole WFDSM, a hown in Figure 6a, each field coil i wound around four tator pole. All the coil of phae A and phae D are nearby the field coil lot, and the coil of the other two phae are in the middle of the two field coil lot. Therefore, the total reluctance of phae B i larger than the reluctance of phae A.

11 Energie 2015, (a) (b) (c) (d) Figure 6. The connected coil of the multiphae WFDSM. (a) Traditional 8/6-pole four-phae; (b) new 12/9-pole four-phae; (c) 30/24-pole five-phae (half of the pole); (d) 12/10-pole ix-phae. The new 12/9-pole WFDSM ha four field coil and twelve phae coil, which can be divided into four phae. A hown in Figure 6b, each field coil i wound around three tator pole, and the two neighboring field coil are in the oppoite direction. Every phae ha three coil, one i in the middle of

12 Energie 2015, the two field coil lot, and the other two phae coil are nearby the field coil lot. Therefore, the total reluctance of the four phae are equal. With the above analyi, the preferred configuration of the four-phae WFDSM with ymmetry phae i with a 12/9-pole tructure. Similarly, we can draw the connected coil of the 30/24-pole five-phae WFDSM and the 12/10-pole ix-phae WFDSM according to Table 2. Therefore, the elementary machine of the five-phae WFDSM with ymmetry phae ha a 30/24-pole tructure. In the ix-phae WFDSM, if we wind the field coil around two or more tator pole, the ix-phae WFDSM will till ha the eriou drawback of aymmetric phae, which will be verified by the imulation reult in the next ection Therefore, each tator pole of the 12/10-pole ix-phae WFDSM hould have a field coil if we want to get ymmetrical phae Simulation Reult To compare the above multiphae WFDSM, the imulation model of the traditional 8/6-pole and new 12/9-pole four-phae WFDSM were etablihed. Figure 7a how the flux of the 12/9-pole machine. Figure 7b how the inductance between phae winding and field winding of the traditional 8/6-pole four-phae WFDSM. Thi verifie the formula of Equation (17). Figure 7c how the ame inductance of the new 12/9-pole four-phae WFDSG. It i hown that the amplitude of the inductance have the relationhip with: max( ) max( ) max( ) max( ) Laf Ldf Lbf L cf (17) The 2D-FEA reult agree well with the theoretical analyi reult. Figure 7d,e how the waveform of the back EMF of the four-phae WFDSM. The back EMF of the traditional 8/6-pole WFDSM have light difference in the amplitude and the hape of the waveform. A the preferred five-phae WFDSM ha a 30/24-pole tructure, j = 3; it flux ditribution i hown in Figure 8a. Figure 8b how the inductance between the phae winding and the field winding of the traditional 10/8-pole five-phae WFDSM. The ame inductance of the new 30/24-pole four-phae WFDSG i hown in Figure 8c. It how that the traditional five-phae WFDSG ha the diadvantage of aymmetric phae. The new WFDSG with it field coil wound around three pole can olve thi problem. The theoretical analyi reult are verified with thee 2D-FEA reult. Figure 8d,e how the waveform of the back EMF of the five-phae WFDSM. It can be calculated that the back EMF of different phae of the traditional 10/8-pole WFDSM have a difference of about 10.9%. From the above analyi, we know that the traditional ix-phae WFDSM with j = 6 ha the phae aymmetry problem becaue the field coil i wound around ix tator pole. We have et up the imulation model of the ix-phae WFDSM with different j. But even if we let j = 5, 4 or 3, there will be phae aymmetry problem. If j = 2, the 12/10-pole ix-phae WFDSM ha a field coil wound around every two tator pole, and it alo ha the problem of aymmetric phae. A hown in Figure 9a, when the rotor pole i liding to the pole of phae B, the back EMF of the phae B will be le than phae A becaue the pole of phae A ha a lot of flux at thi time. When the rotor pole i liding to the pole of phae A, the back EMF of the phae A will be larger than phae B becaue the pole of phae B ha no flux at thi time. Thi i verified

13 Energie 2015, by the Figure 9d, which how that the amplitude of ua and ub are not equal. Therefore, the phae are till aymmetric even with j = 2. (a) (b) (c) (d) (e) Figure 7. Comparion of the traditional and the new four-phae WFDSM. (a) The flux of the 12/9-pole WFDSM; (b) Lpf of the traditional 8/6-pole WFDSM; (c) Lpf of the new 12/9-pole WFDSM; (d) Back EMF of the 8/6-pole WFDSM; (e) Back EMF of the 12/9-pole WFDSM.

14 Energie 2015, (a) (b) (c) (d) (e) Figure 8. Comparion of the traditional and the new five-phae WFDSM. (a) The flux of the 30/24-pole WFDSM; (b) Lpf of the traditional 10/8-pole WFDSM; (c) Lpf of the new 30/24-pole WFDSM; (d) Back EMF of the 10/8-pole WFDSM; (e) Back EMF of the 30/24-pole WFDSM. The flux of the ix-phae WFDSM with j = 1 i hown in Figure 9b. Thi new WFDSG ha it field coil wound around every tator pole, and olve the problem of phae aymmetry. The 2D-FEA reult in Figure 9f verified thi theoretical analyi. However, thi new machine ha a drawback of large copper lo, becaue there are field coil in every lot, and the reitance and the weight of the field winding will be increaed.

15 Energie 2015, Lpf(mH) (a) Laf Lbf Lcf Ldf Lef Electric Angle ( ) (c) Lgf (b) (d) (e) (f) Figure 9. Comparion of the new 12/10-pole ix-phae WFDSM. (a) The flux of the WFDSM with j = 2; (b) The flux of the WFDSM with j = 2. (c) Lpf of the WFDSM with j = 2; (d) Lpf of the WFDSM with j = 1; (e) Back EMF of the WFDSM with j = 2; (f) Back EMF of the WFDSM with j = Comparative Study of the Converter and It Fault-Tolerant Performance 4.1. The Fault-Tolerant Converter Multiphae machine can be divided into machine with prime number phae and machine with compoite number phae. Becaue a compoite number ha at leat one poitive divior other than 1 or the number itelf, the machine with compoite number phae can be divided into everal channel

16 Energie 2015, which have little effect on each other [24]. For example, the four-phae WFDSM can be divided into two independent channel. However, the five-phae WFDSM ha no poitive divior, and the machine may be uceptible to be uffer fault if the phae winding are connected together. The fault-tolerant machine i uually equipped with a fault-tolerant converter. There are variou type of fault-tolerant converter for different phae machine [25], and the four-phae converter will be dicued a an example in thi paper. The four-phae WFDSM i uually powered with a four-phae full bridge converter [26]. When there i a fault in one phae, the machine can keep on working becaue the fault i iolated from the other two phae, a hown in Figure 10a. (a) (b) (c) Figure 10. Comparion of the four-phae fault-tolerant converter. (a) The traditional four-phae converter; (b) The four-phae H bridge converter; (c) The half bridge four-phae converter.

17 Energie 2015, The mot excellent converter i the four-phae H bridge converter, a hown in Figure 10b, becaue all of the phae are iolated from each other. The machine can be deigned a a modular machine, which offer potential fault-tolerant capability becaue the phae winding are iolated. When there i a fault in one phae, the other phae can keep on working without any infection from the fault phae. However, thi converter deign i not helpful to reduce the weight and the cot. Figure 10c how a half bridge four-phae converter. If phae A ha an open circuit fault in thi fault-tolerant converter, phae C of the machine can keep on operating with the help of plit-phae capacitor C1. However, the five-phae WFDSM cannot be divided into two or three iolated channel, o it doen t have uch flexible fault-tolerant converter, and the fault of the machine may be uceptible to be infected if the phae winding are connected together. A we can ee from Figure 10, the witche increae with the phae number, and WFDSM with more than ix phae are not uitable becaue the weight and the cot are unacceptable. The WFDSM with ix phae or four phae can be divided into two iolated channel, which will improve the fault tolerance of the machine Fault-Tolerant Performance Comparion The torque-angle characteritic of the multiphae WFDSM are hown in Figure 11a. A we can ee from the figure that the waveform of the 12/9-pole four-phae WFDSM i wider than the other, becaue the electrical angle of the phae voltage waveform of the four-phae WFDSM in Equation (8) i 180 and the phae voltage waveform electrical angle of the five-phae WFDSM i 144, and the angle of the ix-phae WFDSM i 120. There are four phae with mutative elf-inductance at any time in all of the three WFDSM, which can be decribed a x = 4 in Equation (8). If one phae of the four-phae WFDSM i iolated becaue of an open circuit or hort circuit fault, the other three phae can keep on working. If the phae current maintain the ame value becaue there i no fault, the fault-tolerant torque will be three-quarter of the normal torque. Thi i verified with Figure 11b. To compare the fault-tolerant performance, the torque waveform with one phae open of the five-phae and the ix-phae WFDSM are hown in Figure 11b too. If the five tep in one period are named a five beat, then in the five beat of the five-phae WFDSM, there i a beat where the fault phae ha no current. At thi time, the output torque i equal to the normal torque. In the other beat, the fault-tolerant torque will be three-quarter of the normal torque too. The ame reult can be obtained with the ix-phae WFDSM. Thi phenomenon i hown in Figure 11b. Becaue the WFDSM are bruhle DC machine, and their torque ripple are relatively large, which i mainly caued by the commutation torque ripple in the four-phae WFDSM. It hould be noted that the commutation torque ripple of the WFDSM can be reduced by the optimal control method, which i invetigated in [27]. Beide the commutation torque ripple, the five-phae and the ix-phae WFDSM alo have the torque ripple caued by the difference between fault-tolerant beat and normal beat.

18 Energie 2015, (a) (b) Figure 11. The torque of the multiphae WFDSM. (a) The torque-angle characteritic; (b) The torque with one phae iolated in an H bridge converter. What more, a a bruhle DC machine, the WFDSM i uually equipped with Hall enor. Therefore, the five-phae WFDSM need five Hall enor, and the ix-phae WFDSM need only three Hall enor, becaue phae A and phae D of the ix-phae WFDSM have advere EMF. The accuracy of the enor hould increae with the rotor pole number. Becaue the rotor pole number of the five-phae WFDSM with ymmetrical phae i larger than the other, therefore, it i not an optimal olution for a fault-tolerant machine. 5. Concluion The four-phae WFDSM with α = ha four changing inductance phae at any time, and it elf-inductance of the field winding Lf will be a contant, which will not produce cogging torque. If it i ued a a fault-tolerant machine, it ha fewer witche in the converter than five-phae or ix-phae machine. The elementary machine of the five-phae WFDSM with ymmetric phae ha a 30/24-pole tructure. It doe not have cogging torque becaue the phae number with mutative inductance at any

19 Energie 2015, time i four. Different from the other five-phae machine with few pole, thi five-phae WFDSM need an expenive incremental encoder to provide ufficient poition accuracy for the commutation control, but it can be a high performance fault-tolerant generator becaue it doen t need poition enor. If we wind the field coil around two or more tator pole, the ix-phae WFDSM will have the eriou drawback of aymmetric phae. The 12/10-pole ix-phae WFDSM which ha a field coil around each tator pole ha ymmetric phae, although it improve the copper lo of the field winding. Like the four-phae WFDSM, the ix-phae WFDSM can be divided into two iolated channel, which will improve the fault tolerance of the machine. Becaue the witche of the converter and the pole number increae with the phae number, WFDSM with more than ix phae are not uitable becaue the weight and the cot of the converter are unacceptable, a well a the pole number. Acknowledgment Thi work wa upported and funded by the National Natural Science Foundation of China ( ), the Shandong Provincial Natural Science Foundation (ZR2014JL035), and the Fundamental Reearch Fund for the Central Univeritie (NP ). Author Contribution Bo Zhou conceived the idea of thi paper, provide guidance and uperviion; Li-Wei Shi implemented the reearch, performed the analyi and wrote the paper. All author have contributed ignificantly to thi work. Conflict of Interet The author declare no conflict of interet. Reference 1. Villani, M.; Turini, M.; Fabri, G.; Catellini, L. Electromechanical actuator for helicopter rotor damper application. IEEE Tran. Ind. Appl. 2014, 2, Boglietti, A.; Cavagnino, A.; Tenconi, A.; Vachetto, S. The afety critical electric machine and drive in the more electric aircraft: A urvey. In Proceeding of the 35th Annual Conference of IEEE Indutrial Electronic, Porto, Portugal, 3 5 November 2009; pp Bennett, J.W.; Atkinon, G.J.; Mecrow, B.C.; Atkinon, D.J. Fault-tolerant deign conideration and control trategie for aeropace drive. IEEE Tran. Ind. Electron. 2012, 5, Garcia, A.; Cuido, J.; Roero, J.A.; Ortega, J.A.; Romeral, L. Reliable electro-mechanical actuator in aircraft. IEEE Aerop. Electron. Syt. Mag. 2008, 8, Villani, M.; Turini, M.; Fabri, G.; Catellini, L. High reliability permanent magnet bruhle motor drive for aircraft application. IEEE Tran. Ind. Electron. 2012, 5, Hao, L.; Du, H.Y.I.; Lin, H.; Namuduri, C. Deign and analyi of PM fractional lot machine conidering the fault operation. IEEE Tran. Ind. Appl. 2014, 1, Stewart, P.; Kadirkamanathan, V. Commutation of permanent-magnet ynchronou AC motor for military and traction application. IEEE Tran. Ind. Electron. 2003, 3,

20 Energie 2015, Du, Q.; Lu, E.; Shi, X. Deign and analyi of five-phae tangent magnetic field permanent magnet generator for electric vehicle. Int. J. Electric Hybrid Veh. 2012, 4, Rottach, M.; Gerada, C.; Wheeler, P.W. Deign optimiation of a fault-tolerant pm motor drive for an aeropace actuation application. In Proceeding of the 7th IET International Conference on Power Electronic, Machine and Drive, Mancheter, UK, 8 10 April 2014; pp Coar, C.; Kelly, L.; Miller, T.J.E.; Whitley, C.; Maxwell, C.; Moorhoue, D. The deign of a witched reluctance drive for aircraft flight control urface actuation. IEE Colloq. Electr. Mach. Syt. More Electric Aircr. 1999, 11, Hennen, M.D.; Hennen, M.D.; Heyer, C.; Brauer, H.J.; De Doncker, R.W. Development and control of an integrated and ditributed inverter for a fault tolerant five-phae witched reluctance traction drive. IEEE Tran. Ind. Electron. 2012, 2, Gong, Y.; Chau, K.T.; Jiang, J.Z.; Yu, C.; Li, W. Deign of doubly alient permanent magnet motor with minimum torque ripple. IEEE Tran. Magn. 2009, 10, Zhang, Z.; Yan, Y.; Tao, Y. A new topology of low peed doubly alient bruhle DC generator for wind power generation. IEEE Tran. Magn. 2012, 3, Chen, Z.; Wang, H.; Yan, Y. A doubly alient tarter-generator with two-ection twited-rotor tructure for potential future aeropace application. IEEE Tran. Ind. Electron. 2012, 9, Liu, C.; Chau, K.T.; Zhong, J.; Li, J. Deign and analyi of a HTS bruhle doubly-fed doubly-alient machine. IEEE Tran. Appl. Supercond. 2011, 3, Liu, X.; Zhu, Z.Q. Electromagnetic performance of novel variable flux reluctance machine with DC-field coil in tator. IEEE Tran. Magn. 2013, 6, Yu, L.; Zhang, Z.; Chen, Z.H. Analyi and verification of the doubly alient bruhle DC generator for automobile auxiliary power unit application. IEEE Tran. Ind. Electron. 2014, 12, Sui, Y.; Zheng, P.; Wu, F.; Yu, B.; Wang, P.F.; Zhang, J.W. Reearch on a 20-Slot/22-Pole five-phae fault-tolerant PMSM ued for four-wheel-drive electric vehicle. Energie 2014, 7, Cheng, M.; Hua, W.; Zhang, J.; Zhao, W. Overview of tator-permanent magnet bruhle machine. IEEE Tran. Ind. Electron. 2011, 11, Zhao, Y.; Wang, H.; Zhao, X.; Xiao, L. Characteritic analyi of five-phae fault-tolerant doubly alient electro-magnetic generator. In Proceeding of the IECON 2013 The 39th Annual Conference of the IEEE, Vienna, Autria, November 2013; pp Liu, X.; Zhu, Z.Q. Stator/Rotor pole combination and winding configuration of variable flux reluctance machine. IEEE Tran. Ind. Appl. 2014, 6, Shi, J.T.; Liu, X.; Wu, D.; Zhu, Z.Q. Influence of tator and rotor pole arc on electromagnetic torque of variable flux reluctance machine. IEEE Tran. Magn. 2014, 11, doi: /tmag Gauen, B.; Hoang, E.; Barrière, O.D.; Saint-Michel, J.; Lecrivain, M.; Gabi, M. Analytical approach for air-gap modeling of field-excited flux-witching machine: No-load operation. IEEE Tran. Magn. 2012, 9, Hill, C.I.; Zanchetta, P.; Bozhko, S.V. Accelerated electromechanical modeling of a ditributed internal combution engine generator unit. Energie 2012, 5,

21 Energie 2015, Bojoi, R.; Neacu, M.G.; Tenconi, A. Analyi and urvey of multi-phae power electronic converter topologie for the more electric aircraft application. In Proceeding of the 2012 International Sympoium on Power Electronic, Electrical Drive, Automation and Motion (SPEEDAM), Sorrento, Italy, June 2012; pp Chen, Z.; Chen, R.; Chen, Z. A fault-tolerant parallel tructure of ingle-phae full-bridge rectifier for a wound-field doubly alient generator. IEEE Tran. Ind. Electron. 2013, 8, Qin, H.; Wen, J.; Zhou, B.; Xue, H.H. Conideration of harmonic and torque ripple in a large power doubly alient electro-magnet motor drive. In Proceeding of the 2012 Aia-Pacific Sympoium on Electromagnetic Compatibility (APEMC), Singapore, May 2012; pp by the author; licenee MDPI, Bael, Switzerland. Thi article i an open acce article ditributed under the term and condition of the Creative Common Attribution licene (