Analysis and experimental verification of losses in a concentrated wound interior permanent magnet machine.
Concentrated non-overlapping windings (CW) have been steadily gaining popularity for a wide range of applications including washing machines, wind generators, ship propulsion and electric vehicle drives . This is due to a compact design by reduction in end winding length and simplified manufacturing process. The recent work on application of CW in surface permanent magnet synchronous machine
(PMSM) showed its ability to achieve low cogging torque, sinusoidal back electromotive force (EMF) waveforms and very wide constant power speed range (CPSR) [2,3].
In comparison to surface-type PMSM, interior-type PMSM has robust rotor, additional reluctance torque and rotor saliency which is an added advantage for the sensor-less drive applications.
Authors have studied application of CW in V-shaped interior PM machine for wide CPSR. A full study of various combinations of stator slots and rotor poles was investigated for the CW IPM machine, and the 18-slot, 14-pole combination was chosen due to its intrinsic nature of producing low cogging torque, sinusoidal back electromotive force (EMF) waveforms, larger winding factor and relatively higher saliency ratio. The full design consideration and performance characteristics of this prototype machine were published elsewhere . The aim of this paper is to investigate various losses of the CW-IPM machine and its effect on the field weakening performance.
The magnetomotive force (MMF) waveforms of the concentrated winding stator are rich in harmonic and sub-harmonic contents, consequently leading to an increase in core and magnet losses . However, the presence of these harmonics also causes high slot leakage inductance in the winding; because of which the characteristic current of the PMSM can be made closer to its rated current for achieving wider CPSR . Thus, the application of CW in the PMSM offers wide CPSR and is gaining popularity. The desirable compromise between the CPSR and additional losses in the machine will be worthwhile future study.
The PM machine designed with CW for wide CPSR is most affected by the increase in harmonic related losses due to its nature of operation, of up to several times of the base frequency. Hence, losses and loss minimization techniques for permanent magnet machines with CW have been studied in a number of papers in recent years. Key recent studies include: study of core losses with phase and slot/pole combination variation [6,7], minimization by variation of rotor core/rotor magnet geometries [8,9], study of magnet losses  and minimization of magnet losses by the use of segmented magnets , effects of slot/pole variation , effects of winding layers [13,21].
There are a few papers which studied losses in CW IPM machine [14-16]. These papers present finite element (FE) studies of optimization techniques with specific characteristics. Han et al. in  presented a technique to minimize eddy current losses in the stator teeth of IPM rotors under field-weakening conditions. Yamazaki et al.  presented a method to reduce magnet eddy current losses at high rotational speeds.
In this paper, authors have used well-established loss minimization techniques for conventional distributed winding (DW) machine to minimize the losses in a CW-IPM machine designed for wide field weakening operation. The aim is to quantify all key losses present in a CW-IPM machine and subsequently verify them experimentally with a constructed prototype. Design concepts will be justified in terms of how losses are minimized. The applied techniques to minimize losses include the application of segmented magnets, variation of magnet type, variation in lamination thickness, as well as different winding methodologies.
2. LOSSES IN A CONCENTRATED WINDING PM MACHINE
Compared to DW, the air-gap MMF waveform of the CW contains additional space harmonics and sub-harmonics which do not rotate in sync with the rotor. These additional harmonic components contribute to frequency related losses which occur primarily in the core and magnets of the machine.
Figures 1(a) and 1(b) show magnetic flux distribution of a CW and DW machine of same rotor pole number respectively.
Assuming highly permeable core, no saturation and zero permanent magnet field, the relation between the stator current and
I = [B.sub.s][A.sub.rot][R.sub.air]/N (1)
the air-gap flux produced by this current can be found as where [B.sub.s] is the flux density produced by the stator current, [A.sub.rot] the airgap of surface area, [R.sub.air] the air-gap reluctance, and N the number of turns per stator coil.
It is well known that widths of the slot openings contribute to the variation of air gap permeance and cause rotor losses . However, the effect of slot opening is far less in a CW machine compared to effect of MMF space harmonics, specially the slot harmonics. The air-gap flux density waveform produced by the stator current in the DW IPM machine of Figure 1(a) with magnet removed is shown in Figure 2. Figures 3(a) and (b) show the air-gap flux density produced by the stator current for the prototype CW machine of Figure 1(b) with magnet removed.
The close inspection of the flux density waveforms of Figures 2 and 3(a) and (b) reveal that permeance variation due to the slot opening is much small compared to the DW machine. The rotor loss due to these permeance harmonics is therefore, small in a CW machine compared to DW machine. The major part of the rotor loss in CW machine thus is due to the MMF space harmonics.
The harmonic whose order is equal to rotor pole pairs is known as the main or fundamental harmonic which rotates synchronously with the rotor. The harmonics whose orders are lower than the fundamental rotates slower than the rotor and harmonics whose orders are higher than the fundamental rotates faster than the rotor. Among all these harmonics, the ones which have same winding factor as the main or fundamental harmonic, called slot harmonics contribute most toward the rotor losses .
The order of slot harmonic can be found as
[n.sub.sh] = kQ [+ or -] p (2)
where k = 0, 1, 2, ... Q is slot number and p is pole pairs.
In the prototype 18-slot/14-pole FSCW IPM machine, pole pairs p is 7 and possible slot harmonics are 11, 25, 29 etc.. The machine contains sub harmonics, but not any of them are slot harmonics. Comparing the spectrum of single and double layer CW given in Figures 3(a) and (b) respectively, it can be noticed that slot harmonic 11, 25, 32, ... are present in both single layer and double layer CW. However, compared to a single layer, double layer has far less over all harmonics. Therefore, a double layer winding was chosen for this study. The asynchronously rotating harmonics cause increased rotor losses. Hence, it is interesting to study rotor losses caused by the slot harmonics.
Total losses in the stator and rotor core are the hysteresis and eddy current loss, which can be expressed generally by (3).
[P.sub.core] = [K.sub.e][f.sup.2][B.sup.2.sub.max] + [K.sub.h] [B.sub.h]f[B.sup.[eta]st.sub.max] (3)
[K.sub.e] = Eddy current loss constant,
[K.sub.h] = Hysteresis loss constant,
[B.sub.max] = Maximum flux density,
[[eta].sub.st] = Material dependent Steinmetz loss constant (1.6 to 2.0).
Although excess loss can be computed in the FE model using simple statistical data based formula proposed by Berotitti , its applicability with PM machine is still under scrutiny. A benchmark study on surface permanent-magnet brushless motor in  found a good correlation between experimental and computational data without considering excess losses. Another recent study  showed that individual contribution of excess and eddy-current losses cannot be separated. Because of these reasons the excess loss was not considered in this study and hence not included in (3).
While hysteresis loss density depends largely on frequency, material and flux density, the eddy current loss density is proportional to the frequency squared, making it much more susceptible to slot harmonic components, which could be several times higher than the operating frequency. In the field-weakening region, the situation is further exaggerated. For example, during operation at 10 times of the base frequency 50 Hz, a harmonic component at n = 29, would corresponds to 14500 Hz.
In order to visualize the proportion of loss densities better, it is common to keep hysteresis term constant and (3) can be simplified  as
[P.sub.core]/f[B.sup.2.sub.max] = [K.sub.e]f + [K.sub.h] (4)
Steinmetz constant was taken as 2 here.
The hysteresis loss is material dependent, and little can be done to minimize it through design variation. Hence, the emphasis will be placed on eddy current loss in which the loss minimization can be achieved through a number of techniques including well-known technique of selecting lamination thickness. Using Faraday's and Maxwell's equations, the relation between the air-gap harmonics and eddy current loss can be derived (shown in the appendix).
For integral-slot DW, a sinusoidal air-gap flux density shown in the Figure 2 can be assumed, eddy current loss is given as:
[P.sub.eddy] = [[tau].sup.2][sigma]/12 [(dB/dt).sup.2] = [[[tau].sup.2][sigma]/6 (1 + cos 2[omega]t)] [f.sup.2][B.sup.2.sub.max] (5)
where the terms in the square brackets are usually termed as the eddy current loss constant.
In CW, the function would not only depend on the fundamental but other significant harmonic components, specially the slot harmonics. Eddy current loss for CW can thus be generally expressed as (6), where Bn is the magnitude of the nth harmonic component of the waveform shown in Figures 3(a) and (b).
[P.sub.eddy] = [[tau].sup.2].[sigma]/12 [(d/dt [B.sub.n] [N.summation over (n = 1)] 1/n sin(n[omega]t).sup.2] (6)
The inclusion of additional harmonic components is unavoidable with CW; however, compared to single-layer, the double-layer CW has less harmonic terms as shown in Figure 3(b). It was confirmed in  that a higher layer number increases efficiency by eliminating eddy current losses of some harmonic terms. Therefore, double-layer CW was preferable and selected for this work. However, it should be noted here that double layer winding does not eliminate the slot harmonics as shown in Figure 3(b).
3. STUDY AND QUANTIFICATION OF LOSSES IN THE
The electrical losses of a PM AC machine include, i.e., eddy current and hysteresis losses in the stator and rotor cores, eddy current and hysteresis loss in the permanent magnet and copper loss of the stator winding. The mechanical losses include mostly bearing/friction losses and windage losses.
3.1. Core Losses
As shown in (3), core losses consist of hysteresis and eddy current losses. One method of separating these two losses is derived in . According to this derivation, in typical steel laminations, hysteresis loss at 60 Hz make up approximately 67% of the total core loss while the rest of the losses comprise of eddy current and other types of losses.
The core material used in the prototype CW IPM machine is 35RM300. The loss density curve provided by the material manufacturer is shown in Figure 4 and using the relation derived in , the estimated loss densities of the used laminated material are found to be 1.08 W/kg for eddy current loss and 2.17W/kg for hysteresis loss at 60 Hz and 1.5 T.
In order to determine the core losses due to harmonic components for various operating frequencies, the eddy current and hysteresis loss constants (K_e and Kh) must first be found for the selected laminated steel.
A narrow annular-core specimen consisting of thin laminations was modeled to find the loss constants K_e and K_h of 35RM300 from a FE model which are 0.29 and 151 respectively. These loss constants were used to obtain the core loss at various excitation frequencies in the FE model of the CW IPM machine. The FE package used in this paper is Flux 2D/3D from Magsoft/Cedrate.
The calculated hysteresis and eddy current loss constants, and some other key features for the three laminated steel grades examined are shown in Table 1. The calculated losses from the FE model at 50 and 500 Hz for all three grades are shown in Figure 6.
It should be noted here that, the inverter used in the experimental set-up uses 10 kHz carrier frequency. Figure 5 below compares calculated core loss for 50 Hz and 500 Hz in the FE model with sinusoidal current and current with PWM harmonics. The calculated core loss of PWM inverter-fed machine is about 1.2 times higher. Since this increase of loss due to the PWM harmonics in the current is relatively insignificant, the input currents were considered as pure sinusoid for subsequent FE calculations.
It can be observed in Figure 6 that both stator and rotor core losses in the constant torque region (50Hz) is low (< 2.5% of output power). However, in the higher field-weakening region (500 Hz), the core loss becomes significant (> 13% of the output power). This would result in almost a 10% difference in efficiency.
The results emphasize the importance of using thin laminations with low losses when designing machines for field-weakening applications. Thicker laminations like the 65JN800 are more suitable for machines operating at lower frequencies or with constant torque where torque density is of higher priority. Thus, the chosen steel grade for the prototype design is 35RM300. The breakdown of losses at various frequencies obtained from the FE model is shown in Figure 7.
As expected, core loss increases with frequency. The percentage of stator to rotor core loss is several times higher in the low frequency or constant torque region. In the field-weakening or high frequency region, rotor core losses also become substantial; contributing to a large part of the total core loss in the machine. As explained in Section 2, rotor core losses, especially the eddy current loss is contributed mostly by the air-gap slot harmonics. Reduction of these harmonics would make a significant difference to the efficiency. Thus, one of the future research challenges of CW-PM machine is the development of techniques to reduce these harmonics.
3.2. Magnet Losses
It is well-known that the time varying magnetic fields may create substantial losses in the magnets, (especially in SPM machines). A great deal of research interest is focused on the study and minimization of magnet losses in CW permanent magnet machines. Commonly used strategies to reduce magnet losses are by the use of bonded instead of sintered magnets, at the expense of lower magnet strength, or the use of sintered-segmented magnets [23-27].
It was explained in  that, in a polarized magnet, losses are much smaller than those of the non-polarized one. While there has been a significant amount of study on eddy current losses in magnets of PM synchronous machines, an in-depth study on hysteresis loss is not available. The phenomenon of hysteresis in a polarized and nonpolarized NdFeB magnet was studied in . It appears that hysteresis can happen in a polarized magnet if minor loops form due to load and temperature variation. According to , hysteresis losses in a polarized magnet can be significant specially, when slot harmonics in the machine is high. The FSCW IPM machine falls in the category of machines with high slot harmonics. In order to ensure that hysteresis loss of the magnet is not particularly of concern in the prototype FSCW IPM machine, a study of this loss was also conducted. The NdFeB used in the prototype is N24EH from Raremag [R] with remanance of 1.04 T.
In [10,24,29] hysteresis losses in synchronous machines were studied based on a combination of measurements and FE results. In this paper hysteresis loss of the CW-IPM machine was estimated using experimental data provided in [10, 24, 29]. The magnet losses were measured from 30 to 150 Hz and 0.01 to 0.1 T using a closedtype measuring equipment. The measured losses were separated to eddy current loss and hysteresis loss by two-frequency method. The measured losses were plotted against flux density. Since the losses were measured only up to 0.1 T, the extrapolated polynomial trendlines were fitted into measured data of [10,24] to estimate the hysteresis loss of the magnet in the prototype CW-IPM machine which is shown in Figure 8. For this work, this estimation would suffice as it will be shown later that magnet losses in the CW-IPM machine make up a very small percentage (0.5%) of the total losses.
The typical operating point of the permanent magnets in the prototype CWIPM machine is 0.6 T. Loss density values obtained from the extrapolation at this flux density are 10.1 W/kg for hysteresis and 4.6 W/kg for eddy current loss, (at 50 Hz) as show in Figure 8.
For the neodymium magnets, conductivity is readily available from the data sheets. Thus, the eddy current loss constant can be calculated from the following formula
[K.sub.e] = [sigma] [[tau].sup.2][[pi].sup.2]/6 (7)
With each magnet piece being 79 mm long, Ke for sintered and bonded neodymium magnets are calculated to be 6416 and 73 respectively. These values were used in a 3D finite element model, (shown in Figure 9), to calculate magnet eddy current loss. Sintered magnets were chosen over bonded magnets due to its higher remnant flux densities and operating temperatures. The breakdown of losses at various frequencies for the sintered magnets, obtained from the FE model, is shown in Figure 10.
The CW surface permanent magnet (SPM) machines have permanent magnets that are directly exposed to air gap flux harmonics. Thus, higher magnet losses are expected in such machine . Bonded NdFeB has been used in such machines to reduce magnet losses. In CW-IPM machine, magnets are buried in the rotor iron, hence they are less exposed to the MMF harmonics. Consequently, magnet loss in this type of machine is much less compared to a CW-SPM machine. Therefore, there is no justification of using bonded magnet in this type machine for the sole purpose of reducing magnet losses.
There are different techniques to reduce magnet loss in the CWSPM machine which uses sintered NdFeB. One of such techniques is segmentation of the magnet piece in the axial direction. Epoxy magnet coating serves as the insulation between each layer. The effects of segmenting sintered neodymium magnets have been thoroughly studied --key work in this area includes [23,25,31-33]. In  work done by Yamazaki et al., magnet losses in different rotor types due to carrier and slot harmonics where compared. With the increased number of segments, a gradual decrease of the magnet eddy current losses can be observed in a SPM machine whereas in an IPM machine, the decrease is not gradual.
In this work, the effect of segmenting V-shaped IPM is also investigated. Figure 11(a) shows the circulating eddy currents in the non-segmented pieces of the V-shaped pole magnet, (b) shows the same in the segmented pieces. These results were obtained from the 3D FE model of the CW-IPM machine.
The total magnet losses obtained at 50 and 500 Hz for the CWIPM machine was shown in Figure 12.
It can be observed from the Figure 12 that the magnet loss initially reduces with increased number of segments but then peaks with 9 segments; thus, complying with Yamazaki's findings in [11,33]. With 12 segments, the loss has reduced by about 50%. However, since the total magnet loss is insignificant making up for a mere 0.5% of the total loss, it is arguable whether magnet segmentation is necessary in a CW-IPM machine.
3.3. Stator Winding Copper Losses
Stator winding loss--also known as [I.sup.2]R, copper or joule loss, is generated when the armature windings are excited by an external source. Of the total loss in PM machines, the largest portion is usually due to [I.sup.2]R loss . If the chosen copper conductors are sufficiently thin, the skin effect is negligible and hence, [I.sup.2]R can reasonably assume to be frequency independent.
[I.sup.2]R loss is described in the following formula:
[I.sup.2]R = 2[N.sub.Coil][I.sup.2][rho] [l.sub.eff]/[A.sub.w] (8)
[N.sub.Coil] = Number of turns per coil,
[rho] = Conductor resistivity (1.68 x [10.sup.-8] for copper),
[A.sub.w] = Cross-sectional area of wire.
The slot area in the stator can be maximized by optimizing tooth and yoke area so that the flux densities in these areas are kept just under the saturating limit of the core. With a fixed slot area, the only way to increase conductor size and lower I2R loss is by increasing the slot-fill factor ([S.sub.ff]) given by the following equation:
[S.sub.ff] = [N.sub.coil][A.sub.w]/[A.sub.s] (9)
Typical slot-fill factors achievable by commercial winders are in the range of 35% to 44%. Approximately 60% can be achieved by highly skilled winders [35,36]. Unlike DW, which overlap one or more stator teeth, CW are wound around individual stator teeth. The coil around individual stator teeth can take advantage of more advanced winding methods, such as the joint lapped core methods [35, 37] and use of modular stator tooth pieces . These methods claimed to achieve up to 75% and 78% slot-fill factor respectively.
Concentrated windings can be wound in one of two methods: the horizontal slot-fill method, as shown in Figure 13(a), or the vertical slot-fill method, as shown in 13(b). The prototype machine is wound using the former method to keep the winding process simple and cheaper.
The prototype machine has 115 turns per coil, and 6 coils per phase. The slot-fill factor achieved with American wire gauge (AWG) 22 was 41%. The measured length of 1 turn is 276 mm as shown in Figure 13(a). Due to the high number of turns used, winding resistance per phase amounted to 10[OHM]. The rated current of the machine is 2.2 A/ph. Thus, total copper loss under full load operating condition is about 145 W (18% of the total output power). As it can be seen from the measured loss break-down given in Table 3, it is the most significant loss of the prototype machine.
4. MECHANICAL LOSSES
Mechanical losses consist of mainly bearing and windage losses [18, 34, 38]. Bearing loss is dependent on factors such as the bearing type, bearing diameter, rotor speed, load and lubricant used. Windage loss occurs when friction is created with the rotating parts of the machine and the surrounding air.
Bearing losses can be calculated with the following formula:
[P.sub.bearing] = 0.5[[omega].sub.m][k.sub.b]F[D.sub.b] (10)
[[omega].sub.m] = Mechanical speed of the rotor,
[k.sub.b] = Bearing loss constant,
F = Force acting on the bearing,
[D.sub.b] = Bearing inner diameter.
The Figure 14 shows the drawing of the IPM rotor highlighting the mechanical parts responsible for losses. The mass is calculated based on the known volume and density of the various materials used. Bearing friction loss occurs in both bearings. From the estimated weight of the rotor, the downward force acting on the bearings can be calculated from
F = mg (11)
m = Mass of the rotor, g = Gravity (9.81 m/[s.sup.2]).
Unlike frictional loss, windage loss increases non-linearly with speed. The rotor can be modeled as a rotating cylinder in an enclosure and power loss can be modeled as the resisting drag torque on the cylinder. This can be expressed as follows :
[P.sub.windage] = 0.03125[[omega].sup.3.sub.m][pi][k.sub.ct][k.sub.r][[rho].sub.air][D.sup.4.sub.r][l.sub.r] (12)
[k.sub.ct] = Torque coefficient (which has to be separately determined),
[k.sub.r] = Roughness coefficient (between 1-1.4),
pair = Density of air (1.184 kg/m3),
[D.sub.r] = rotor diameter,
[l.sub.r] = rotor length.
To determine the torque coefficient, the Couette Reynolds number needs to be determined first. The Reynolds number [N.sub.Re] is given as:
[N.sub.Re] = [[rho.sub.]air][[omega].sub.m][D.sub.r][l.sub.ag]/2[[mu].sub.vis(air)] (13)
[l.sub.ag] = Airgap length,
[[mu].sub.vis(air)] = Dynamic viscosity of air (18.6[mu]Pa).
For [N.sub.Re] between 64 and 500, the torque coefficient is given as,
[k.sub.ct] = 2 [(2[l.sub.ag]/[D.sub.r]).sup.0.3]/[([N.sub.Re]).sup.0.6] (14)
And for NRe between 500 and 50000, the torque coefficient is given by:
[k.sub.ct] = 1.03 [(2[l.sub.ag]/[D.sub.r]).sup.0.3]/[([N.sub.Re]).sup.0.5] (15)
Using (10) and (12), windage and friction losses of the prototype machine are calculated for various speeds are shown in Figure 15.
5. EXPERIMENTAL VERIFICATION OF TOTAL LOSS
Figure 16 shows the experimental set-up used to measure the performance of the constructed prototype machine. Table 2 shows some key parameters of the machine.
Table 3 shows the segregation of the measured losses: copper, core, magnet, bearing and windage loss. No load losses at various speeds were measured with and without the magnet inserted in the rotor. Thus, core loss and magnet losses were segregated. By driving the prototype machine without the magnet excitation by another machine with known losses, total mechanical losses were measured. Windage and friction losses were segregated from the total mechanical loss after calculating the windage loss using Equation (12). Copper loss was calculated using measured resistance and current.
It can be seen from this Table 3 that the largest percentage of losses arise from copper loss, which makes up 84.8% of the total loss at maximum speed, followed by the core loss which makes up 14.6%. Compared to these two losses, the other losses are extremely small.
Figure 17 compares output, input powers and efficiency obtained from the FE model with the measured values from the experimental setup. The field-weakening performance indicating the constant power speed range (CPSR) is also shown in the same figure.
6. EFFICIENCY OPTIMIZATION STUDY
The results in the previous section show that the majority of losses in the prototype machine arise from the copper loss. It should be noted here that the design of the prototype machine was optimized with a size constraint. This 800-W CW-IPM machine was designed to fit into the frame size of a commonly used 4-pole, 550 W induction machine. Because of this size constraint, there was not enough room to increase slot area to create space for larger conductor size to reduce copper losses.
An efficiency optimization study of the prototype machine was carried out by removing the size constraint.
Figure 18 shows two possible methods in which the slot size can be increased by: i) keeping the stator outer diameter and stack length same as the constructed prototype, but reduce the stator inner diameter allowing a reduced volume for the rotor to make space for a larger stator width; (ii) decreasing the stack length to half while increasing the stator outer diameter proportionally. The total machine volumes in the both designs are kept same as the constructed prototype machine for a fair comparison. For convenience sake, these two designs will be called IPM-Eq (for the design with equal dimensions, but reduced rotor size) and the IPM-Short (for the design with reduced stack length).
Key parameters for the two designs are shown in Table 4. To ensure designs are practical, the slot-fill factor is set at 45%.
Figures 19(a) and 19(b) give the performance characteristics for CW IPM-Eq and CW IPM-Short respectively obtained from the FE models.
It can be seen in Figures 19(a) and (b) efficiencies of the IPM-Eq is over 91% and IPM-Short is over 93% in the whole operating speed range. Both models produce between 900 W to 1 kW of power over a 6 : 1 CPSR. Between the two models, the IPM-Short resulted in higher efficiency despite higher copper loss. This was due to its capability of producing higher power density (with peak power slightly over 1 kW) as compared to the IPM-Eq.
This paper investigated losses in the CW-IPM machine designed for wide field-weakening applications. This study has revealed a few intriguing facts about losses in a CW-IPM machine:
(i) In CW-IPM machine losses of the magnet is not a significant concern as it is in a CW-SPM machine. Magnet loss minimization techniques may not be as important.
(ii) Various techniques to reduce rotor and stator core loss are very important. The rotor loss is mainly caused by the asynchronously rotating slot harmonics. One of the future design challenges for the CW-IPM machine is to develop techniques to reduce these slot harmonics.
(iii) Copper loss minimization is also very important for high efficiency. Careful consideration of the slot-area during the design optimization process can lead to minimization of copper loss significantly.
Thus, for a CW-IPM machine, rotor and stator core loss and copper loss are the main concern. Well-established techniques such as use of thin lamination sheet are still the best core loss minimization technique for such machine. The presence of asynchronously rotating slot harmonics which cause additional rotor losses depends on slot number and pole pairs. Careful selection of slot and pole number can eliminate some of these harmonics. For example when slot number is equal or higher than the pole number, sub-slot harmonics will be eliminated.
Copper loss minimization can be linked to maximization of slot area for a given dimension. Use of modular stator design can further reduce end-winding length of a FSCW which can also reduce copper loss by reducing winding effective length for a given dimension.
Authors hope that this detailed study of the loss analysis will help future designers of the CW IPM machines to make appropriate design decisions.
Equating the electric field ([bar.E]) in a closed path c along the surface to the induced voltage ([v.sub.ind]) and flux linkage ([lambda]):
[[??].sub.c] [bar.E] x dl = [v.sub.ind] = d/dt [[integral].sub.s] [bar.B] x ds = d[lambda] /dt (A1)
The current density J and the electric field is related by the conductivity [sigma],
J = [sigma]E (A2)
If a fluctuating magnetic flux density (B) acts on a thin piece of material with conductivity ([sigma]), thickness ([tau]) and width (w). Eddy current ([P.sub.eddy]) induced in this conductor can be expressed as follows:
[P.sub.eddy] = 1/[tau]w [integral] [J.sup.2]/ [sigma] dv (A3)
Assuming that flux density is uniform across the surface, flux linkage will be:
[lambda] = B[tau]w (A4)
The induced voltage can be expressed as:
[V.sub.ind] = d[lambda]/dt = [tau]w dB/dt (A5)
If [tau] is reduced to infinitely thin sections (x), the electric field along the closed path in can be described by:
E = [v.sub.ind]/2w = x dB/dt (A6)
From (A2) and (A6), the induced current density at the surface of the material is given by:
J = [sigma]E = [sigma]x dB/dt (A7)
The Eddy current loss shown in (A3) in terms of the induced current density can be described as follows:
[P.sub.eddy] = 1/[tau]w [[integral].sup.[tau]/2.sub.[tau]/2 1/[sigma] [([sigma]x dB/dt).sup.2] wdx (A8)
[P.sub.eddy] = [[tau].sup.2][sigma]/12 [(dB/dt).sup.2] (A9)
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Rukmi Dutta *, Lester Chong, and Fazlur M. Rahman
University of New South Wales, Australia
* Corresponding author: Rukmi Dutta (email@example.com).
Received 7 November 2012, Accepted 25 January 2013, Scheduled 28 January 2013
Table 1. Key features of three core material types. 35RM300 50JN350 65JN800 Lamination thickness 0.35 mm 0.50mm 0.65 mm Sat. mag. (B50) 1.68T 1.68T 1.72T Stacking factor 95% 96% 97% Total core loss (@60 Hz/1.5 T) 3.25 W/kg 4.45 W/kg 10.15 W/kg [K.sub.h] 151 263 495 [K.sub.e] 0.29 0.39 0.89 Table 2. Key specifications of the 800 W CW-IPM machine. Stator outer diameter 130 mm Rotor outer diameter 80 mm Air-gap length 1.2 mm Stack length (stator) 80 mm Stack Length (rotor) 79 mm Number of poles 14 poles Number of slots 18 slots/double-layer Rated voltage 320 [V.sub.rms]/phase Rated current 2.2 [A.sub.rms]/phase Magnet remnant flux density 1.04T Core material Non-oriented FeSi Saturation mag. of laminations 1.68T@5000A/m Predicted core loss at 50Hz/1.5T 2.60 W/Kg Slot-fill factor 41% Copper loss 10[OHM]/ph Table 3. Loss breakdown of the 800 W CW-IPM machine. Freq. Copper Core Magnet Friction Windage Loss Loss Loss Loss Loss 50 142.5 6.04 0.052 0.044 0.001 100 142.5 6.3 0.120 0.087 0.007 200 142.5 11.17 0.280 0.175 0.037 300 142.5 17.58 0.465 0.262 0.101 400 142.5 25.01 0.673 0.35 0.208 500 142.5 33.41 0.900 0.437 0.363 Table 4. Key specifications of the two optimized CW-IPM machine designs. IPM-Eq IPM-Short Total machine volume 1.06[e.sup.-3] 1.06[e.sup.-3] [mm.sup.3] [mm.sup.3] Stator outer diameter 130 mm 183.85 mm Rotor outer diameter 36 mm 45.7 Slot opening width 1.2 mm 1.2 mm Stack length 80 mm 40 mm Rated current 2.2[A.sub.rms]/ph 2.2[A.sub.rms]/ph Conductor size AWG 20 AWG 21 No. of turns per coil 163 turns 127 turns Stator resistance 4.5[OMEGA]/ph 5.5[OMEGA]/ph Mag. remanent flux 1.13T 1.13T Slot-fill factor 45% 45% Figure 6. Core loss comparison at 50 and 500 Hz with different steel grades. 35RM3000 50JN350 65JN800 Rotor core loss @50Hz 1.4 2.4 4.5 Stator core loss @50Hz 4.7 8 15.3 Total core loss @50Hz 6 10.3 19.7 Rtoro core loss @500Hz 14.3 24.2 46.6 Stator core loss @500Hz 19.1 29.5 60.9 Total core loss @500Hz 33.4 53.7 107.5 Note: Table made from bar graph.
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|Author:||Dutta, Rukmi; Chong, Lester; Rahman, Fazlur M.|
|Publication:||Progress In Electromagnetics Research B|
|Date:||Mar 1, 2013|
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