Design and Analysis of Single Inverter-Fed Brushless Wound Rotor Vernier Machine

In this paper, a brushless wound rotor vernier machine (Bl-WRVM) with a single inverter configuration is proposed to achieve the brushless operation. In the proposed topology, a single inverter is connected with series-connected ABC and XYZ windings through which the current flow produces the magnetomotive force with fundamental and sub-harmonic components, respectively. The XYZ windings have similar pole pairs to the excitation windings, whereas its number of poles is different from the ABC winding. A 24-slot stator, 4-pole armature ABC winding, 2 Pole armature XYZ and excitation windings, and 44-pole field winding for the outer rotor is designed and 2D finite element analysis is carried out to determine the performance of the machine. The proposed topology makes the Bl-WRVM cost-effective by applying only a single inverter as compared to a dual-inverter Bl-WRVM and it improves its torque quality.


I. INTRODUCTION
In recent years, the Permanent Magnet Vernier Machines 12 (PMVMs) have gained a lot of interest due to their increasing 13 demand in direct drive applications. PMVMs are capable of 14 generating high torque at low speed due to the magnetic 15 gearing effect as compared to the other types of PM machines. magnetic gearing effect due to flux modulation. The earlier 23 vernier reluctance machine is the base from which PMVMs 24 are derived [3]. The output power achieved in PMVMs is 25 The associate editor coordinating the review of this manuscript and approving it for publication was Alfeu J. Sguarezi Filho . three times to equivalent of conventional PM machines for 26 a similar volume and current. Furthermore, PMVM is com-27 monly designed for low-speed rotation due to a large number 28 of magnet poles [4]. Because rare-earth permanent magnets 29 are used in PMVMs, they are expensive as well [5]. PMVMs 30 with dual-stator have auxiliary inner stator with no windings 31 and the outer stator only comprise the windings. In this 32 way torque density of the machine is improved because the 33 whole volume of the structure is reduced. As a result, this 34 machine will be lacking in manufacturing and thermal prob-35 lems because this configuration does not have windings on 36 the inner stator [6]. The hybrid excited PMVM was proposed 37 in order to regulate flux in both directions, which have all of 38 their excitation sources on the stator, thus it helps in regulat-39 ing the temperature rise of magnets [7]. Axial flux PMVMs 40 to improve power factor, and torque density and minimize 41 the torque ripples by using spoke-type PM, notched-shaped 42 PM and two-stage parallelogram-shaped PM were proposed 43 In the conventional topology of the Bl-WRVM, the stator 106 winding is spatially distributed into two equal parts to gener-107 ate fundamental and subharmonic magnetomotive force. Both 108 the stator windings (ABC and XYZ) are designed to gen-109 erate the two four-pole armature windings. In order to gen-110 erate subharmonic and fundamental magnetomotive forces, 111 one armature winding is supplied with half of the current 112 as opposed to the other half armature winding. Thus, the 113 resultant armature magnetomotive force would have both the 114 fundamental and subharmonics components. Figure 1 shows 115 the schematic representation of the conventional dual-inverter 116 Bl-WRVM. This is the brushless sub-harmonic topology 117 introduced in [13] and also used for BL-WRVM in [14]. 118 In this topology, 2 separate inverters supply currents to the 119 distributed windings in the stator. The difference in mag-120 nitudes of currents from two inverters produces the sub-121 harmonic component of the MMF. This component of MMF 122 is used for the rotor excitation, through the induction in 123 excitation winding. The induced voltages are then fed to the 124 rotating rectifier on the rotor converting it to DC current for 125 the final use of field winding so that it produces the rotor field 126 flux without the use of brushes and slip-rings.

127
The excitation winding of the conventional Bl-WRVM is 128 comprised of the two-pole structure in order to link with 129 the subharmonic component of the armature magnetomotive 130 force. The voltage induced in the excitation winding is rec-131 tified with the help of the full-bridge rectifier in order to 132 provide the excitation to the field winding. The field winding 133 is comprised of a 44-pole concentrated winding arrangement 134 in order to generate the vernier effect for the Bl-WRVM. 135 Figure 2 shows the winding layout of the double-layer arma-136 ture windings of the conventional dual-inverter Bl-WRVM. 137 Both the armature windings have a coil span of 6 slots and 138 is generating four poles. The winding coils are arranged in 139 both forward and backward directions with the coils span of 140 6 for the ABC winding and 6 for the XYZ winding. The basic 141 equation for the vernier operation is given by equation (1) as 142 below.
where P r stands for the rotor pole pairs, Q s represents the 145 stator slots and P s represents the stator pole pairs.

146
The currents supplied by inverter 1 to the stator winding 147 ABC are given by the following equation.   The currents supplied by inverter 2 to the stator winding XYZ 152 are given by the following equation. 153 3 ) where I signify the current amplitude and ω e denotes angular 157 frequency.

III. PROPOSED SINGLE INVERTER BL-WRVM TOPOLOGY 159
In the proposed topology of Bl-WRVM, the stator winding 160 is connected with a single inverter to generate a fundamental 161 and subharmonic components of the magnetomotive force. 162                 current, field current, and output electromagnetic torque.

228
The results are compared for the conventional and proposed 229 design 1 and II. its torque starts from 0 Nm. Gradually it achieves its average 241 torque of 6.516 Nm with a torque ripple of 78.26%. The high 242 ripple is due to the harmonic content in the airgap MMF and 243 the fluctuation in rotor field current.
244 Figure 9 represents the induced currents in the rotor exci-245 tation windings and the currents which are rectified by 246 the rotating rectifier and fed to the field winding on the 247 rotor.
248 Figure 10 shows the flux density distribution plot for the 249 conventional BLWRVM. The unbalanced magnetic field on 250 the left and right sides of the machine is due to the fact that the 251 left side stator winding of the machine is connected to inverter 252 I with a higher amplitude of current, while the right-side stator 253      The performance is not very impressive as it fails to compete 259 with the conventional model.   Figure 14 shows the torque produced in the proposed 272 model design II which is 8.08 Nm. Using the 6 slots 273 for the XYZ winding resulted in increased torque as 274 compared to the conventional model and proposed model 275 design I. Furthermore, a considerable reduction in the torque 276 ripple (37.12 %) is achieved with the proposed model 277 design II.
278 Figure 15 presents the excitation and field current plot 279 of the proposed model design II. The induced excitation 280 current has increased and so is the field current. The increased 281 field current is responsible for the increased electromagnetic 282 torque production. Also, with the proposed model design II 283 smooth field current is obtained as compared to the conven-284 tional and proposed design I.   To create the harmonic air gap component, the XYZ winding 312 is configured for two-poles on a four-pole vernier machine.

313
The working of the topology was verified by the 2D FEA.