Winding Layout Considerations for Variable-Pole Induction Motors in Electric Vehicles

Winding layout plays a crucial role in enabling variable-pole operation in an induction machine (IM). Several winding design alternatives, which consist of toroidal and distributed single- and double-layer windings, have been shown to increase speed range and improve partial load efficiency in traction applications. These windings have different pole-changing capability, end-winding length, leakage, harmonic content, and inv erter requirements. This article compares these winding alternatives with a generalized variable-pole machine design framework that captures the impact of winding selection on key performance metrics such as losses, volume, and torque–speed envelop. This framework shows that the core aspect ratio, defined as ratio of stack length to rotor diameter, selected to minimize losses depends on whether a distributed or toroidal winding is used. When a toroidally wound IM is designed with a low aspect ratio, it can provide the largest torque–speed envelop with highest efficiency over a wide speed range. An experimental toroidally wound IM driven by an 18-leg converter is used to validate the design framework. The experimental setup is configured externally to emulate a single-layer winding and to show benefits gained from the extra pole-changing flexibility of a toroidal winding.


I. INTRODUCTION
E LECTRIC vehicle (EV) drivetrains require power-dense and efficient motors, operating over a wide speed range [1], [2], [3].Conventionally, the torque-speed envelop of fixed-pole induction machines (IMs) is constrained by the inverter output voltage at the base speed.This reduces the torque capability at the maximum speed, as shown in Fig. 1 [4], [5], [6].Overdesigning the inverter to improve the envelop decreased the efficiency and power density in [7] and [8].Alternatively, torque capability above the base speed can be improved substantially by electronically reconfiguring the IM to lower pole counts, as shown in Fig. 1 [9], [10], [11], [12].Specifically, Libbos et al. [8] showed that a multileg inverter can improve the high-speed torque capability Fig. 1.Torque-speed characteristic of an IM when operated with a fixed six-pole configuration versus variable six-, four-, and two-pole operations.High-speed torque capability is improved by reconfiguring to lower pole counts.by a factor of 2.2×, while simultaneously achieving higher efficiency, with less dc link capacitance, and simpler thermal management, compared with a conventional three-leg fixedpole design with the same motor.
The IM can be reconfigured to two-pole by reversing the current of one coil group.While this approach leads to smaller end-winding compared with conventional distributed windings, it suffers from a low winding factor when operated at two-pole [16].In summary, double-layer winding layout options are limited by a lower winding factor at either the higher or lower pole count when used in variablepole operation.The existing body of literature has proposed several winding options for electronic pole reconfiguration, the selection of which impacts both the torque-speed envelop and end-winding losses and leakage.Thus, an open question remains: How do these winding options compare in terms of torque production, efficiency, power density, and torque-speed envelop in a variable-pole design space?
The main contribution of this article is a variable-pole IM winding study that compares various winding layouts in terms of key performance metrics by tailoring core design to the winding type.Analysis shows that the aspect ratio, defined as the ratio of the stack length to the rotor diameter, plays an important role in reducing the end-turn length and, therefore, in reducing copper loss and leakage inductance.Distributed windings favor a smaller rotor diameter, which can be achieved at the expense of longer stack length, while toroidal winding length reduces with shorter stack length.A toroidal winding layout with a low aspect ratio is shown to provide the highest flexibility in terms of pole-changing capability, maximizing the achievable torque-speed envelop along with higher power density and efficiency.Its extra flexibility to reconfigure to four poles improves the efficiency in the intermediate torque-speed range by reducing core and copper losses.An experimental toroidally wound IM is used to validate the analysis and the results.The setup is configured externally to emulate a single-layer winding for comparison.Hardware results validate the improvement in the torque-speed envelop and efficiency improvement from the extra pole-changing flexibility of a toroidal design.The high number of inverter legs leads to fault-tolerant operation even when two of the inverter legs fail.The rest of the article is organized as follows.Section II shows comparison of the four winding options from an achievable pole selection perspective and their impact on the harmonic content of the airgap flux density.Section III presents the design framework that captures the impact of the aspect ratio on efficiency and power density while accounting for the different winding layouts.Finite element analysis (FEA) is used to verify and refine the analytically obtained design variables such as the stack length, airgap diameter, and yoke depth.Section IV shows comparison of the torque-speed envelop and efficiency over the entire operating regime.Section V uses an experimental toroidally wound 36-slot IM driven by an 18-leg converter to validate the analysis.Section VI concludes the article.

II. WINDING OPTIONS FOR VARIABLE-POLE IM
This section shows comparison of the four winding layouts in terms of their winding factors, stator magnetomotive force (MMF) total harmonic distortion (THD), differential leakage, and achievable pole counts.As an example, a 36-slot stator is considered and the maximum number of inverter legs is limited to 18. Fig. 3 shows the winding distributions for the four layouts.The toroidal winding (option a) allows the most flexible excitation pattern as the physical coil pitch does not act as an additional constraint [10], [11], [12].To connect the 36-slot stator to an 18-leg inverter, coils in adjacent slots are connected in series to form an 18-terminal stator winding [11].This configuration enables reconfiguring the IM to a wide range of pole counts, including six, four, and two.Pole changing is achieved by applying phase shifts between two adjacent independent windings (e.g., C1 and C2 in Fig. 3), using a technique known as pole-phase modulation (PPM) [10].To achieve pole count p, phase shift θ p given by is introduced, where n inv is the number of inverter legs.Table I summarizes the required phase shifts to enable the two-, four-, and six-pole operations.In the distributed single-layer winding layout (option b), the number of inverter legs reduces to nine as each coil spans two slots (e.g., C1 in slot 1 has a return conductor C1' in slot 19), as shown in Fig. 2.This winding is designed as a standard two-pole distributed winding and can be Fig. 3. Winding layout and inverter connections for variable-pole IM for the four alternatives for a 36-slot machine.For the toroidal winding, the return conductors are on the outer periphery of the stator core and, hence, not shown.) to be out-of-phase while a four-pole configuration requires them to be in-phase.Option c considers a double-layer, two-pole winding short-pitched by 20 • with the same inverter configuration as (b).Finally, a four-pole double-layer winding with a 120 • phase belt that can be reconfigured for the two-pole operation [9], [16] is considered as option d.Because of the lower p max to p min ratio, this configuration requires only six inverter legs, the lowest among all the four windings.The next step is to compute the fundamental winding factors and stator MMF THD of the four winding options using winding functions.The winding function of an m-phase/ p-pole excitation is given by [26] where N c is the number of conductors in a slot, v is the harmonic number, q is the number of slots per pole per phase, θ is the electrical angle, and k w ( p, v) is the winding factor.k w ( p, v) and phase number m are given by where α is the short pitch angle at the minimum pole count p min , and Q s is the total number of slots.Using (3) and assuming Q s = 36, the fundamental winding factor and the THD of each winding configuration for all the feasible pole counts are computed and summarized in Table II.THD and differential leakage coefficient σ d are computed using [26] THD .
Toroidal and single-layer windings, driven by 18-leg and nine-leg inverters, respectively, have a relatively high winding factor for every pole configuration because they use high phase numbers.Double-layer windings have a low fundamental winding factor at either the higher or lower pole count, as short-pitching the winding at a given pole configuration leads to excessive flux cancellation in the other [9], [15], [16].For example, shortening winding (c) by an angle α = 20 • results in a 14.4% drop in winding factor for the six-pole operation and α = 40 • leads to a 50% drop.All the winding types have highest THD and differential leakage at p max which is used to deliver high torque at low speeds.Doublelayer (d) has the lowest distortion and differential leakage near peak torque as it uses a four-pole configuration rather than a six-pole configuration which may help reduce stray losses.In general, the number of stator slots can be further increased to decrease THD in all the winding types.Section III uses these winding factors to analytically design the stator for a given specification.

III. VARIABLE-POLE IM DESIGN CONSIDERING DIFFERENT WINDING LAYOUTS' FRAMEWORK
The design objective to be explored here is to deliver a specified torque at the base speed and maximize the torque capability at the maximum speed, by reconfiguring motor operation to lower pole counts using suitable stator excitation from a multileg drive.The design specifications and constraints are summarized in Table III.A copper rotor cage is used to reduce rotor bar losses [27], [28].The machine aspect ratio is captured explicitly in the framework because it plays an important role in minimizing the winding length and volume.After selecting the variable-pole winding option based on Section II, the stator core is designed using the following approach.
1) Size the stator core to deliver rated torque at base speed.
2) Model electrical losses to capture the impact of winding design and aspect ratio on efficiency.3) Refine stator and rotor slot designs using FEA.

A. Variable-Pole Core Design to Meet Torque Requirement at Base Speed
Variable-pole IMs are sized to deliver the rated torque T rated at base speed using the largest pole count p max [26] T rated = π where D is the rotor diameter, B g, p max is the peak fundamental airgap flux density at p max , K s is the surface current loading, σ r is the rotor leakage coefficient, k w, p max is the fundamental winding factor at p max , η is the estimated motor efficiency, and cosφ gap is the estimated machine power factor.Sizing the machine to deliver rated torque using the highest pole count helps minimize the stator yoke thickness given by Fig. 4 and Table IV illustrate the impact of pole changing on the airgap and core flux densities for a toroidal winding layout.For the same core flux density limit, lower pole counts (four-and two-pole) can push a smaller airgap flux density than six-pole.Because lower pole counts are only used with a partial flux density, variable-pole IMs benefit from both a smaller back yoke of higher pole count designs and improved high-speed torque of lower pole configurations.
Although in this analysis the airgap flux density is assumed to be sinusoidal, the actual airgap flux density has harmonics due to winding distribution, stator slotting effects, and saturation, as explained in Section II and shown in Fig. 5.As the average of the actual airgap flux density is higher compared with the sinusoidal assumption, the FEA solutions in Fig. 4 show localized tooth flux densities beyond 1.8 T. This mismatch can be accounted for analytically by introducing a scaling factor α p in ( 8) and ( 9) [29] and using a sufficient number of sampling points in FEA to accurately represent harmonics.By approximating stator slots as trapezoids as in [9], (7) can be rewritten as (10) where A slot is the total slot area occupied by stator windings, A core is the rotor core surface area, and J s is the stator current density.For given flux and current densities, (10) shows that the product A core A slot must be constant.Using ( 7)-( 10), the core dimensions are selected to meet the rated torque specification in Table III and illustrate the impact of A core and A slot on the active machine volume.Fig. 6(a) shows that there is a tradeoff between A core and A slot .Cores with smaller A slot require larger A core to maintain the same peak torque capability.This is because for a given J s , reducing A slot decreases the net current which is traded off against a larger magnetic flux achieved by increasing A core .The choice between a larger A slot or A core is a tradeoff between net current and magnetic flux.Fig. 6(b) shows that core designs with larger A slot and smaller A core have smaller volume.Thus, lower aspect ratio designs, illustrated in Fig. 2(a), require smaller active volume to produce the same torque, as shown in Fig. 6, because their larger diameter D accommodates a larger net current.Eventually, tip speed and mechanical requirements provide a lower bound constraint on aspect ratio.

B. Impact of Aspect Ratio on Electrical Efficiency
The next step is to quantify the impact of winding layout on stator copper loss, which is influenced by the total winding length including the overhang.The toroidal winding length is l wind,tor = 2(d cs + l e ) + l OH (11) where l OH is the overhang length, assumed to be 10% of the winding length.The winding lengths for winding options (b)-(d) are given by Minimizing the end-winding length and its associated losses looks different for toroidal and distributed windings.Distributed windings favor a shorter rotor diameter, which can be achieved at the expense of larger stack length, while toroidal winding length reduces with shorter stack length.For example, Wan et al. [30] used toroidal windings for a highspeed permanent-magnet alternator design with large diameter to reduce the end-winding length and its extra losses compared with a two-pole distributed winding.However, in the case of a large stack length-to-diameter ratio, toroidal windings had more copper losses compared with a distributed double-layer design [22].
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE V DESIGN SUMMARY OF FOUR WINDING OPTIONS TO MEET SPECIFICATIONS
The stator and rotor copper losses P cu,s and P cu,r can be estimated as where k cu is the coil fill factor, F s (α) is the ratio of ac-to-dc resistance [26], V cage is the cage volume, and ρ cu is the copper resistivity.The core losses are modeled using a Steinmetz equation where C h and C e are the hysteresis and eddy current coefficients, respectively, and B core is the peak stator flux density.Fig. 7 shows the impact of the aspect ratio on electrical efficiency, which consists of copper and core losses at 50 • C, at base and maximum speed.The highest pole p max is used at ω b and p min is used at ω max .The efficiency of the toroidally wound IM increases with decreasing aspect ratio because this minimizes the stator winding length and copper losses in Zone 1.This is advantageous since Fig. 6 shows that volume is minimized with low aspect ratio.
Single-layer winding efficiency is lower than for a toroidal winding over all the aspect ratios because the coil pitch must be sized for a two-pole layout to achieve variable-pole operation.Double-layer windings (3) and ( 4) are more efficient than toroidal windings in high aspect ratio Zone 2. Flux cancellation of double-layer windings leads to lower efficiency at either high or low speeds.Although option (4) is most efficient in Zone 2 at ω b , it is the least efficient option at ω max because of the poor winding factor in the two-pole operation.

C. Design Summary
Table V shows comparison of the toroidal, single-, and double-layer windings for a variable-pole IM designed to meet the specifications in Table III and refined using FEA.Toroidal machine (a) with aspect ratio 0.4 has the smallest volume and highest efficiency.Distributed winding designs (b)-(d) are selected to have an aspect ratio of 0.8 to maintain high efficiency without significantly increasing the volume.Option (d) is most efficient among distributed winding layouts because, unlike (b) and (c), its coil is sized for the four-pole operation.Design (d) has low core losses because it delivers peak torque using a four-pole configuration rather than a sixpole configuration.However, design (d) has the largest volume because it must deliver rated torque in the four-pole operation and requires a larger back yoke.
The toroidal design has the lowest copper loss because the low aspect design, combined with a small back yoke, minimizes the stator coil length.This also explains why the toroidal configuration has low leakage even though it has an extra return path outside the core that does not contribute to torque production.The toroidal design with low aspect ratio has the highest rated efficiency, smallest volume and weight, and has the highest torque capability at ω max .

IV. COMPARISON OF WINDING DESIGNS OVER
THE ENTIRE TORQUE-SPEED REGIME Traction applications operate over wide torque-speed ranges and rarely operate at rated conditions.This section shows comparison of an 18-leg variable-pole design with three-leg fixed-pole designs.The torque-speed envelops of the winding configurations are compared.The efficiency maps over the entire torque-speed regime are presented and discussed.

A. Torque-Speed Envelope
To plot the torque-speed envelope generated by these winding configurations, a detailed variable-pole IM model that captures the impact of pole count p on machine parameters is needed.The parameters are obtained using FEA and RMxprt and are shown in Table VI.These parameters can be estimated using models in [26] and [12].The impact of pole count on machine parameters is captured mainly in the magnetizing inductance L m, p [11], [12], [31] where N c is the turns count per slot, C s and C p are the number of series and parallel connected windings, respectively, g e is the effective airgap length including the Carter coefficient [9], and k sat is a saturation factor.Turns count where V dc is the dc link voltage, and M max is the maximum drive modulation index.
Fig. 8 shows the torque-speed envelope for these configurations.All the designs deliver rated torque through ω b .
Above ω b , the toroidal winding maintains the largest envelope over most of the speed range and at ω max , as it can reconfigure to the four-pole operation in the intermediate speed range and has lower leakage.In a narrow speed range around 0.6 p.u., double-layer option (c) has higher torque capability than the toroidal option because it is overdesigned due to the poor winding factor at six poles and reconfigured in that region to two poles which has a high winding factor.Double layer (d) also has higher torque capability around 0.6 p.u. speeds compared with the toroidal option because it has a thicker back yoke, as it is designed to deliver peak torque at a four-pole rather than a six-pole configuration, which allows for a larger airgap flux density in the two-pole operation.However, this same reason constrains design (d) to the lowest torque at ω max because its two-pole configuration enters flux weakening at a lower speed than for other designs.Single-layer design (b) and its short-pitched double-layer version (c) have lower torque capability at ω max compared with the toroidal design because long end turns produce extra leakage.

B. Efficiency Comparison Over Entire Torque-Speed Range
This section shows comparison of the electrical efficiencies over the entire torque-speed regime.Core losses are obtained using a transient FEA simulation.Copper losses are obtained based on the stator and rotor resistances obtained using RMxprt.End-winding leakage and copper losses for distributed winding designs are also determined using RMxprt.For toroidal windings, the leakage and resistance of the extra conductor on top of the winding are assumed to be equal to those of the slot conductor.The winding temperature is set to 50 • C. The loss minimization approach proposed in [11], is used to select the pole count at each operating point, as shown in Figs. 9 and 10 illustrates this method by showing the copper and core loss distribution for the toroidal configuration.The highest pole count p max is only used near peak torque where the peak core and copper losses occur.Transitioning to lower pole counts at partial loads improves the efficiency Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.while the two-pole configuration is the most efficient for low torque levels and high speeds due to lower core losses [11].Fig. 10 shows efficiency colormaps of these designs.All are efficient at high speeds because they reconfigure to the twopole operation, which reduces ac and core losses by shifting to a lower fundamental frequency.The extra flexibility of toroidal design (a) improves the efficiency in the intermediate torque-speed range.Single-layer design (b) has the lowest efficiency near rated torque because its windings are long which leads to high copper loss, as shown in Fig. 12.The short-pitched version of this winding, as in option (c), improves the efficiency map by reducing the winding length and stator copper loss, especially near rated torque.Doublelayer design approach (d) has higher efficiency near rated torque than other distributed winding options because of lower stator copper loss due to shorter windings.However, option (d) has lower efficiency at high speed compared with other designs, as seen in Fig. 9. Fig. 13 shows that the lower efficiency of option (d) is linked to higher core loss.This is a direct consequence of designing the machine to deliver peak torque in its four-pole configuration, which requires a thicker yoke.This leads to larger core volume and flux density in the two-pole operation compared with the other designs.The poorer winding factor of option (d) in the two-pole operation also contributes to additional core and copper losses.
To summarize, a single-layer design is the least efficient option near rated torque for a variable-pole IM due to high stator copper losses.For low-speed and high-torque operation, toroidal design (a) has the highest efficiency.This is because the toroidal winding uses a low aspect ratio, leading to lowest  stator copper loss, as shown in Fig. 12.The toroidal design has less core loss because of its smaller core volume and better winding factor.Overall, a toroidal design is highly efficient over the entire torque-speed regime.Double-layer designs are an efficient alternative to toroidal windings, but are constrained in certain operating regimes.All the designs have high efficiency over a wide operating regime because of variable-pole operation and a copper rotor.

V. EXPERIMENTAL SETUP AND RESULTS
Fig. 14 shows the experimental setup.A toroidally wound 36-slot IM with external access to all its slots, shown in Fig. 15, is driven by an 18-leg converter.Table VII provides the specifications of the experimental machine and drive system.The detailed design and pole-changing operation of the 18-leg drive is provided in [8].The dynamometer is controlled through LabVIEW to load the motor.A Zedboard FPGA is used to command inverter pulsewidth modulation and record current and speed measurements.The current and voltage values are logged to MATLAB Simulink in real-time to compute the motor electrical input power.The output power is computed by multiplying the commanded torque in LabVIEW by the motor speed.These measurements are used to calculate the experimental losses in the motor which include electrical copper and core losses and mechanical losses due to the nonideal coupling of the motor and dynamometer.The inverter achieves electronic pole changing by modulating phase shift as in Table I, and Fig. 16 shows the stator currents in the 18 toroidal coils at two, four, and six poles.Switching harmonics are low in the currents which have a pure sinsoidal shape because reconfiguring to lower poles lowers the fundamental frequency (55 Hz) and using a high number of inverter legs enables high switching frequency (50 kHz) [8].This unique advantage of variable-pole designs could be used to minimize additional motor losses and torque ripple caused by PWM switching.
Each pair of adjacent slots (slots 1 and 2, 3, and 4 etc.) are connected in series to form the 18-terminal winding configuration shown in Fig. 17.The winding can be reconfigured to emulate a single-layer winding by externally connecting slots which are 180 • apart (e.g., slots 1 and 19), as shown in Fig. 18, although the leakage inductance and resistance will differ from a conventional single-layer winding.This approach can be used to investigate benefits gained from a toroidal winding's extra flexibility.Fig. 19 shows the torque-speed characteristics for the six-, four-, and two-pole operations.Beyond points 1 and 2, the four-and two-pole configurations have higher torque capability than six-pole, respectively.Because a toroidal winding has the flexibility to reconfigure to the four-pole operation, it has higher torque capability in the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The torque available with a toroidal winding is higher than for an ideal single-layer winding at maximum speed because of lower leakage.Here, the experimental torques are the same for both the arrangements since the single-layer winding is emulated using the same toroidal winding.Figs.21 and 22 show comparison of experimental loss versus torque at 900 and 1300 rpm, respectively.Reconfiguration to the four-pole operation reduces losses at intermediate torque levels at 900 rpm between points C and D. At 1300 rpm, a four-pole configuration reduces loss significantly for any torque above 1 N • m.Thus, the extra flexibility of toroidal windings to reconfigure to four-pole reduces losses intermediate torque and speed range compared with conventional single-layer design.
Fig. 23 shows the experimental motor current and speed when two phases are out, which leads to voltage imbalances.Experimental torque versus speed characteristics for the six-, four-, and two-pole configurations.Variable-pole operation improves the high-speed torque capability by shifting to the four-and two-pole operations at points 1 and 2, respectively [8].The motor maintains its average 900 rpm speed at the cost of an increase in phase current amplitude and current imbalances.Thus, the high number of inverter legs used with the toroidal design improves the fault tolerance.In addition, this 18-leg converter has lower thermal stress and higher efficiency compared with a three-leg converter with the same rating [8].
While the IM was rewound (the original motor is WEG model # 00536OT3E182T) and not designed to have the best possible aspect ratio for a toroidal winding, it is used to validate the analytical models used in Section III.Analytical torque, calculated using (10), matches with the experimental result within 10%, as shown in Table VIII.Moreover, the detailed loss model of Section III-B, which estimates copper and core losses for all winding designs, is within 12% of the  The motor speed is maintained at 900 rpm even with two phases out at the cost of higher current per phase compared with Fig. 16 and phase imbalances.

TABLE VIII FRAMEWORK VALIDATION USING EXPERIMENTAL MOTOR
measured value.The dependence of the magnetizing inductance on pole count is verified through no-load testing.These key results, summarized in Table VIII, validate the proposed design framework used to assess the impact of aspect ratio on efficiency and volume and compare the four variable-pole winding design alternatives.

VI. CONCLUSION
This article investigated four winding design approaches for a variable-pole IM based on toroidal and distributed single-and double-layer windings.An analytical framework, combined with FEA simulations, was used to compare the efficiency, power density, and torque-speed envelop of these windings.A toroidal design is most flexible for pole changing but it is critical to design it with a low aspect ratio to maximize efficiency and power density.A single-layer distributed winding suffers from long coil pitch in a variable-pole application because it is designed at the lowest pole count.This leads to high leakage and losses.Double-layer designs are an efficient solution but can only match the efficiency of a low aspect ratio toroidal design at either low or high speed but not both.An experimental 36-slot toroidally wound IM driven by an 18-leg converter was used to validate the design framework.The toroidal setup was also configured externally to emulate a single-layer winding.Efficiency and torque-speed envelop improvements are achieved with a toroidal configuration compared with single-layer windings because of extra pole-changing flexibility.The 18-leg toroidal design also showed fault tolerance capability by maintaining its speed under voltage imbalances caused by having two faulty phases at the cost of higher current amplitude and imbalance.This article shows that a toroidally wound IM designed with a low aspect ratio has high power density, efficiency, and fault tolerance over the wide operating torque-speed regime needed in an EV application.

Fig. 4 .
Fig. 4. FEA simulation of flux lines and density for the six-, four-, and two-pole operations using steady-state current excitation under no-load condition with rated magnetizing current.The peak fundamental airgap flux density B g is marked.The results are summarized in Table IV.(a) Two-pole (B g = 0.36 T).(b) Four-pole (B g = 0.66 T).(c) Six-pole (B g = 0.89 T).

Fig. 6 .
Fig.6.Aspect ratio impact (a) slot and core areas A slot and A core and (b) machine volume.All the machines sized to deliver T rated at ω b using the same J s and B g and core flux densities, with the winding factor set to k w = 0.96 for all the designs.

Fig. 7 .
Fig. 7. Aspect ratio impact on electrical efficiency for the four winding types: (1) toroidal, (2) single-layer, (3) double-layer designed at p min , and (4) double-layer designed at p max at (a) base and (b) maximum speeds.Toroidal windings are the most efficient in the low aspect ratio Zone 1.

Fig. 8 .
Fig. 8.Torque-speed envelope of variable-pole IMs for the winding configurations of Fig.2.ω b and ω max are the base and maximum speed, respectively.All the machines are designed to meet the torque requirement of TableIIIat ω b .Pole count is selected to maximize the torque-speed envelop while operating within the current, voltage, and flux ratings.

Fig. 11 .
Fig. 11.(a) Copper and (b) core loss distribution for the toroidal winding layout.Operating points C and E are example of the six-to four-pole transition points while D and F are the four-to two-pole transitions.Switching to lower pole enlarges lower loss contour maps and particularly results in low core losses at high speeds.

Fig. 12 .
Fig. 12. Loss breakdown at rated torque and base speed.(a) Toroidal design and (b) and (c) distributed single-and double-layer designs are using a six-pole configuration while (d) is configured for the four-pole operation.

Fig. 13 .
Fig. 13.Loss breakdown at a speed and torque of 0.8 and 0.2 p.u., respectively.This represents high-speed low-torque operation, and all the motors are using a two-pole configuration.(a) Toroidal design 1, (b) single-layer design 2, (c) double-layer design 3, and (d) double-layer design 4.

Fig. 14 .
Fig. 14.Experimental setup and test rig.An 18-leg converter is used to drive the variable-pole toroidally wound IM.This 18-leg converter includes individual phase current sensors, speed encoder, and analog-to-digital converters which are interfaced with an FPGA.The FPGA controls the converter PWM switching and logs the measurements in real-time to MATLAB Simulink to record losses and speed.The dynamometer is used to command load torque through LabVIEW.

Fig. 17 .
Fig. 17.Winding and drive configuration for toroidally wound IM with 36 slots.Each pair of adjacent torodial coils, physically spaced by 10 • , is grouped in series to form a winding.

Fig. 18 .
Fig. 18.Winding and drive configuration to emulate a single-layer winding.Coils which are 180 • apart are connected in series to form a two-pole/nine-phase winding.

Fig. 19 .
Fig. 19.Experimental torque versus speed characteristics for the six-, four-, and two-pole configurations.Variable-pole operation improves the high-speed torque capability by shifting to the four-and two-pole operations at points 1 and 2, respectively[8].

Fig. 20 .
Fig. 20.Experimental torque versus speed characteristic for toroidal and emulated single-layer winding.Toroidal windings have extra capability in the intermediate speed range due to the four-pole operation.

Fig. 21 .
Fig. 21.Experimental power loss versus torque for toroidal and emulated single-layer windings at 900 rpm.Toroidal windings have lower loss in the intermediate torque range due to the four-pole operation.

Fig. 22 .
Fig. 22. Experimental power loss versus torque for toroidal and emulated single-layer windings at 1300 rpm.Toroidal windings have lower loss near peak torque because a four-pole configuration is used rather than a six-pole configuration.

Fig. 23 .
Fig. 23.Experimental (a) currents and (b) speed when two phases are out (open-circuit) under the following conditions: f = 15 Hz and T e = 0.9 N • m.The motor speed is maintained at 900 rpm even with two phases out at the cost of higher current per phase compared with Fig.16and phase imbalances.

TABLE I ELECTRONIC
POLE-CHANGING FOR ALL FOUR WINDINGS USING PPM.θ p IS THE MODULATED PHASE SHIFT BETWEEN TWO SUCCESSIVE WINDINGS IN FIG. 3 (E.G., C1 AND C2)

TABLE II COMPARISON
OF FUNDAMENTAL WINDING FACTOR AND THD OF STATOR MMF FOR ALL FOUR WINDING TYPES OF FIGS. 2 AND 3 WITH Q s = 36.THE THD AND DIFFERENTIAL LEAKAGE COEFFICIENT ARE COMPUTED ANALYTICALLY USING THE MODEL IN SECTION II reconfigured to six-pole by varying θ p , as shown in TableI.

TABLE III MOTOR
DESIGN SPECIFICATIONS

TABLE IV PEAK
AIRGAP FLUX DENSITY AS A FUNCTION OF POLE COUNT FOR ALL WINDINGS.WINDING (1) FEA SIMULATIONS ARE ILLUSTRATED IN FIG. 4 where B cs is the yoke flux density.Selection of this thickness limits the achievable peak airgap flux density at other operating pole counts p given by

TABLE VI MACHINE
EQUIVALENT CIRCUIT PARAMETERS FOR THE DESIGNS OF TABLE V, BASED ON FEA